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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1087-1104 
    ISSN: 0029-5981
    Keywords: elastodynamic energy fracture parameters ; heterogeneous media ; generalized domain integral method ; large elastic deformation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The elastodynamic energy fracture parameters for a stationary crack in 2-D heterogeneous media are evaluated with a presented generalized Domain Integral Method (DIM). The method, incorporated with the finite element solutions, is demonstrated to be patch-independent in a generalized sense. In the context of dynamic response, the near-tip region is always involved in the calculation. The method is used for determination of the associated Energy Release Rate (ERR) for the cases when the crack tip is away from the material interface, with the formulation valid for both small and large elastic deformations. Numerical results for such problems appear to be very insensitive to the crack-tip finite element models. As to the instances when the tip terminates normally at the material interface, the ERR is not feasible for use as a fracture criterion. The generalized DIM is then applied for calculation of the alternative elastodynamic energy parameter JR0/Rλ0. The exponential order λ, with regard to the strength of stress singularity, is also properly evaluated in the calculation. No particular singular finite element is required throughout the study. © 1998 John Wiley & Sons, Ltd.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1133-1151 
    ISSN: 0029-5981
    Keywords: flow control ; numerical solution of Navier-Stokes equation ; Karhunen-Loève Galerkin procedure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of solving the Navier-Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen-Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier-Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier-Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier-Stokes equation. © 1998 John Wiley & Sons, Ltd.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1105-1131 
    ISSN: 0029-5981
    Keywords: infinite elements ; unbounded domains ; acoustics ; finite element methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel approach to the development of infinite element formulations for exterior problems of time-harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domain-based computation of exterior problems. Special cases include non-reflecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative discontinuities across infinite element boundaries, typical of standard infinite element approximations. Continuity between finite elements and infinite elements is enforced weakly, precluding compatibility requirements. Various infinite element approximations for two-dimensional configurations with circular interfaces are presented. Implementation requirements are relatively simple. Numerical results demonstrate the good performance of this scheme. © 1998 John Wiley & Sons, Ltd.
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  • 4
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1153-1166 
    ISSN: 0029-5981
    Keywords: unsteady ; dual-time ; incompressible ; two-dimensional ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for computing unsteady incompressible viscous flows on moving or deforming meshes is described. It uses a well-established time-marching finite-volume flow solver, developed for steady compressible flows past rigid bodies. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. Such methods can be extended to steady incompressible flows using an artificial compressibility scheme. A time-accurate scheme for unsteady incompressible flows is achieved by using an implicit real-time discretization and a dual-time approach, which uses a technique similar to the artificial compressibility scheme. Results are presented for test cases on both fixed and deforming meshes. Experimental, numerical and theoretical data have been included for comparison where available and reasonable agreement has been achieved. © 1998 John Wiley & Sons, Ltd.
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  • 5
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1215-1233 
    ISSN: 0029-5981
    Keywords: meshless ; projections ; approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique for incorporating discontinuities in derivatives into meshless methods is presented. The technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives. The special shape functions have compact support which results in banded matrix equations. The technique is described in element-free Galerkin context, but is easily applicable to other meshless methods and projections. Numerical results for problems in one and two dimensions are reported. © 1998 John Wiley & Sons, Ltd.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1195-1213 
    ISSN: 0029-5981
    Keywords: geometrically non-linear ; refined hybrid element method ; degenerated shell element ; non-conforming modes ; orthogonal approach ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a variational principle with relaxed inter-element continuity requirements, a refined hybrid quadrilateral degenerated shell element GNRH6, which is a non-conforming model with six internal displacements, is proposed for the geometrically non-linear analysis. The orthogonal approach and non-conforming modes are incorporated into the geometrically non-linear formulation. Numerical results show that the orthogonal approach can improve computational efficiency while the non-conforming modes can eliminate the shear/membrane locking phenomenon and improve the accuracy. © 1998 John Wiley & Sons, Ltd.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1171-1194 
    ISSN: 0029-5981
    Keywords: fully utilized design ; force method ; optimization techniques ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the Fully Utilized Design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the Modified Fully Utilized Design (MFUD) method, has been tested successfully on a number of problems that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favourably with the optimum results that can be generated by using non-linear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favour traditional design methods rather than methods based on advanced calculus and non-linear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are examined along with a number of illustrative examples. © 1998 This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.
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  • 8
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1235-1254 
    ISSN: 0029-5981
    Keywords: unbounded domain ; wave equation ; steady ; transient ; finite element ; infinite element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a family of axisymmetric, spheroidal ‘wave envelope’ elements for modelling exterior wave problems. They are of variable radial order and can be used to represent steady and transient wave fields. The formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries. These offer the prospect of reduced dimensionality - in comparison to conventional, spherically formulated elements - when used to represent wave fields in the vicinity of slender or flat objects. Conjugated weighting functions are used to give frequency-independent acoustic ‘mass’, ‘stiffness’ and ‘damping’ matrices. This facilitates a simple extension of the method to transient problems. The effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation, by a rigid sphere excited from rest, and by a circular plate vibrating in a plane baffle. © 1998 John Wiley & Sons, Ltd.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1277-1296 
    ISSN: 0029-5981
    Keywords: structural dynamics ; damping ; discrete elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Algorithmic aspects of energy dissipation mechanisms of dynamic structural systems in conjunction with central difference time integration method are investigated and damping proportional to M(M-1K)m (where K is the stiffness matrix, M is the mass matrix and m is a damping parameter) is proposed. Detailed algorithms for M(M-1K)m proportional damping for the central difference time integration method are presented together with stability criteria and numerical test problems. © 1998 John Wiley & Sons, Ltd.
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  • 10
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1297-1319 
    ISSN: 0029-5981
    Keywords: earthing grid ; horizontally stratified multilayer earth ; integral equation formulation ; finite element technique ; average potential method ; exponential approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new numerical procedure for analysing earthing grids buried in horizontally stratified multilayer earth. The procedure is very efficient and general. The total number of layers and the total number of metallically disconnected earthing grids are completely arbitrary. A single earthing grid can be positioned in several layers. The procedure is based on an integral equation formulation. Earthing grid conductors are subdivided into segments and the average potential method is used. Efficiency and generality of the computation procedure are based on the successful application of numerical approximations of two kernel functions of the integral expression for the potential distribution within a single layer which is caused by a point current source. Each kernel function of the observed layer is approximated using a linear combination of 15 exponential functions. Extension from the point source to a segment of the earthing grid conductor is done by integrating the potential contribution due to a line of point current sources along the segment axis. This computational procedure gives highly accurate results in a short execution time. © 1998 John Wiley & Sons, Ltd.
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  • 11
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1417-1434 
    ISSN: 0029-5981
    Keywords: topology optimization ; finite elements ; slope constraints ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density-energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing pointwise bounds on the density slopes. A finite element discretization procedure is described, and a proof of convergence of finite element solutions to exact solutions is given, as well as numerical examples obtained by a continuation/SLP (sequential linear programming) method. The convergence proof implies that checkerboard patterns and other numerical anomalies will not be present, or at least, that they can be made arbitrarily weak. © 1998 John Wiley & Sons, Ltd.
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  • 12
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1435-1462 
    ISSN: 0029-5981
    Keywords: Reissner's plate theory ; Winkler foundation ; boundary element method ; fundamental solutions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the application of the boundary element method to thick plates resting on a Winkler foundation is presented. The Reissner plate bending theory is used to model the plate behaviour. The Winkler foundation model is represented by continuous springs which are directly incorporated into the governing differential equation. The fundamental solutions are constructed using operator decoupling technique. These fundamental solutions represent three different cases depending on the problem constants. The explicit forms of the boundary and internal point kernels are given in all cases. Quadratic isoparametric boundary elements are used to model the plate boundary. Several examples are presented to demonstrate the accuracy of the present formulation. © 1998 John Wiley & Sons, Ltd.
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  • 13
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1463-1484 
    ISSN: 0029-5981
    Keywords: optimization ; shape design ; heuristics ; evolutionary optimization ; splines ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of finding the optimal shape of a continuous structure is addressed using, alternatively, heuristic, evolutionary and mixed evolutionary and heuristic optimization strategies. Boundaries are represented by B-splines. Two heuristics for minimizing the weight of a structure subject to limits on von Mises stresses and geometrical constraints are implemented: ‘generalized biological growth’ and ‘penalized biological growth’. Penalized biological growth adds to generalized biological growth a control for shape changes. This control is based on the overall state of constraints satisfaction in the structure. The two heuristics are very efficient at improving the designs, but they do not yield globally optimal shapes. Therefore, they are interfaced with an evolutionary optimizer. Different strategies for mixing evolutionary search and biological growth are compared. Results are obtained for fan disk shape problems. They show that mixing evolutionary search with biological growth improves the efficiency of the optimization. The method offers to the designer new paths for a better component determination. © 1998 John Wiley & Sons, Ltd.
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  • 14
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1485-1505 
    ISSN: 0029-5981
    Keywords: viscous flow ; boundary element ; indirect formulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present work, we propose an indirect boundary-only integral equation approach for the numerical solution of the Navier-Stokes system of equations in a three-dimensional flow cavity. The formulation is based on an indirect integral representational formula for the permanent Stokes equations, and the use of a particular solution of a nonhomogeneous Stokes system of equations in order to obtain in an iterative way the corresponding complete solution of the problem. Previous boundary-only integral equation approaches to the present problem, using direct boundary elements formulations, result in a series of matrix multiplications that make these approaches computationally costly. Due to the use of an indirect formulation, the present approach is free from those matrix multiplications. © 1998 John Wiley & Sons, Ltd.
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  • 15
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1507-1525 
    ISSN: 0029-5981
    Keywords: refined triangular discrete Kirchhoff plate element ; C1-continuity requirement ; natural frequency of vibration ; critical load of buckling ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A refined triangular discrete Kirchhoff thin plate bending element RDKT which can be used to improve the original triangular discrete Kirchhoff thin plate bending element DKT is presented. In order to improve the accuracy of the analysis a simple explicit expression of a refined constant strain matrix with an adjustable constant can be introduced into its formulation. The new element displacement function can be used to formulate a mass matrix called combined mass matrix for calculation of the natural frequency and in the same way a combined geometric stiffness matrix can be obtained for buckling analysis. Numerical examples are presented to show that the present methods indeed, can improve the accuracy of thin plate bending, vibration and buckling analysis. © 1998 John Wiley & Sons, Ltd.
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1527-1541 
    ISSN: 0029-5981
    Keywords: boundary element method ; acoustic scattering ; design optimisation ; fluid-structure interaction ; boundary integral equation ; inverse problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented. Also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems. The formulation developed utilizes the boundary integral equation of the Helmholtz equation for the external problem and the Cauchy-Navier equation for the internal elastic problem. The sensitivities are obtained by the implicit differentiation technique. Examples are presented to demonstrate the accuracy of the proposed formulations. © 1998 John Wiley & Sons, Ltd.
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  • 17
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 1-14 
    ISSN: 0029-5981
    Keywords: accuracy of numerical solution ; time-step ; finite element ; finite difference ; time-stepping schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This study presents an experimental approach to estimate time steps that integrate the two-dimensional field equation over a square element within 5 per cent accuracy from the exact solution. The time-step estimates were determined for three finite element, and three finite difference schemes. Comparisons between finite element and finite difference methods and the various time-stepping schemes were conducted. The dynamic time-step estimates are functions of grid size and the smallest eigenvalue of the system of ODEs, λ1. The results indicate that the finite element and finite difference methods generate similar time-step estimates and are at similar accuracy levels. The central difference scheme is superior to the other two schemes as far as the flexibility in allowing larger time step while maintaining the accuracy. The backward difference and the forward difference schemes were very close in their level of accuracy. © 1998 John Wiley & Sons, Ltd.
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  • 18
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 15-48 
    ISSN: 0029-5981
    Keywords: shape optimization ; sensitivity analysis ; non-linear arch ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A shape optimization method for geometrically non-linear structural mechanics based on a sensitivity gradient is proposed. This gradient is computed by means of an adjoint state equation and the structure is analysed with a total Lagrangian formulation. This classical method is well understood for regular cases, but standard equations have to be modified for limit points and simple bifurcation points. These modifications introduce numerical problems which occur at limit points. Numerical systems are very stiff and the quadratic convergence of Newton-Raphson algorithm vanishes, then higher-order derivatives have to be computed with respect to state variables. A geometrically non-linear curved arch is implemented with a finite element method via a formal calculus approach. Thickness and/or shape for differentiable costs under linear and non-linear constraints are optimized. Numerical results are given for linear and non-linear examples and are compared with analytic solutions. © 1998 John Wiley & Sons, Ltd.
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  • 19
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 49-69 
    ISSN: 0029-5981
    Keywords: linear finite element analysis ; geometrically non-linear finite element analysis ; element technology ; shell elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present contribution we propose a so-called solid-shell concept which incorporates only displacement degrees of freedom. Thus, some major disadvantages of the usually used degenerated shell concept are overcome. These disadvantages are related to boundary conditions - the handling of soft and hard support, the need for special co-ordinate systems at boundaries, the connection with continuum elements - and, in geometrically non-linear analyses, to a complicated update of the rotation vector.First, the kinematics of the so-called solid-shell concept in analogy to the degenerated shell concept are introduced. Then several modifications of the solid-shell concept are proposed to obtain locking-free solid-shell elements, leading also to formulations which allow the use of general three-dimensional material laws and which are also able to represent the normal stresses and strains in thickness direction. Numerical analyses of geometrically linear and non-linear problems are finally performed using solely assumed natural shear strain elements with a linear approximation in in-plane direction.Although some considerations are needed to get comparable boundary conditions in the examples analysed, the solid-shell elements prove to work as good as the degenerated shell elements. The numerical examples show that neither thickness nor shear locking are present even for distorted element shapes. © 1998 John Wiley & Sons, Ltd.
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  • 20
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 71-91 
    ISSN: 0029-5981
    Keywords: design sensitivity ; semi-analytic ; rigid body motions ; shells ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the recent past inaccuracy problems have been reported that arise when computing shape design sensitivities by the semi-analytical method. Since both the analytical and the global finite-difference method do not show these severe inaccuracies, it has been concluded that these errors are due to the numerical differentiation of the finite-element stiffness matrices, which is inherent in the semi-analytical method. Moreover, it has also been observed that these inaccuracies become especially dominant when relatively large rigid body motions can be identified for individual elements. So far, improvements to the semi-analytical method are focusing on the numerical differentiation of the finite-element stiffness matrices. It is shown in the present paper that the contribution to the design sensitivities corresponding to the rigid body motions can be evaluated by exact differentiation of the rigid body modes. This approach requires only minor programming effort and the additional computing time is very small. As shown by numerical examples, the proposed method eliminates the problem of abnormal errors occurring in the semi-analytical method. © 1998 John Wiley & Sons, Ltd.
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  • 21
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 93-103 
    ISSN: 0029-5981
    Keywords: structural dynamics ; time integration ; weighted residuals ; implicit procedure ; unconditional stability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An unconditionally stable single-step implicit algorithm for the integration of the equations of motion arising in structural dynamics is presented. Within a time step, the displacement for a single degree of freedom system is approximated by a function which is cubic in time. The four coefficients of the cubic are chosen to satisfy the two initial conditions and two weighted integral equations. By considering general weight functions, six additional coefficients arise. In a series of steps, these coefficients are selected to (i) maximize algebraic accuracy by matching terms of Taylor's expansions of exact and approximate solutions, (ii) ensure unconditional stability and (iii) optimize numerical conditioning of the equations in a limiting case. Equations required to implement the procedure are presented. The method as presented has no algorithmic damping of higher modes, although it is indicated how this may be achieved. The error in period elongation obtained using the proposed method is shown to be far less than using alternative procedures. © 1998 John Wiley & Sons, Ltd.
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 127-143 
    ISSN: 0029-5981
    Keywords: unsymmetric sparse matrices ; frontal solver ; direct methods ; finite elements ; BLAS ; computational kernels ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the implementation of a frontal code for the solution of large sparse unsymmetric linear systems on a high-performance computer where data must be in the cache before arithmetic operations can be performed on it. In particular, we show how we can modify the frontal solution algorithm to enhance the proportion of arithmetic operations performed using Level 3 BLAS thus enabling better reuse of data in the cache. We illustrate the effects of this on Silicon Graphics Power Challenge machines using problems which arise in real engineering and industrial applications. © 1998 John Wiley & Sons, Ltd.
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 105-126 
    ISSN: 0029-5981
    Keywords: neural networks ; training ; constitutive models ; non-linear ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method, termed autoprogressive training, for training neural networks to learn complex stress-strain behaviour of materials using global load-deflection response measured in a structural test is described. The richness of the constitutive information that is generally implicitly contained in the results of structural tests may in many cases make it possible to train a neural network material model from only a small number of such tests, thus overcoming one of the perceived limitations of a neural network approach to modelling of material behaviour; namely, that a voluminous amount of material test data is required. The method uses the partially-trained neural network in a central way in an iterative non-linear finite element analysis of the test specimen in order to extract approximate, but gradually improving, stress-strain information with which to train the neural network.An example is presented in which a simple neural network constitutive model of a T300/976 graphite/epoxy unidirectional lamina is trained, using the load-deflection response recorded during a destructive compressive test of a [(±45)6]S laminated structural plate containing an open hole. The results of a subsequent forward analysis are also presented, in which the trained material model is used to simulate the response of a compressively loaded [(±30)6]S structural laminate containing an open hole. Avenues for further improvement of the neural network model are also suggested.The proposed autoprogressive algorithm appears to have wide application in the general area of Non-Destructive Evaluation (NDE) and damage detection. Most NDE experiments can be viewed as structural tests and the proposed methodology can be used to determine certain damage indices, similar to the way in which constitutive models are determined. © 1998 John Wiley & Sons, Ltd.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 145-173 
    ISSN: 0029-5981
    Keywords: contact ; friction ; complementarity ; Newton's method ; interior point method ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 175-189 
    ISSN: 0029-5981
    Keywords: incompressible flow ; rotor-stator configurations ; multigrid methods ; parallel computing ; moving grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A parallel multigrid finite volume solver for the prediction of unsteady flows in rotor-stator configurations using a moving-grid technique is presented. The numerical solution procedure is based on a second-order finite volume discretization with collocated block-structured grids, an implicit time discretization, a pressure-correction procedure of SIMPLE type, a non-linear multigrid method and a grid partitioning technique for parallelization. For the handling of the rotation and the relative movement of stationary and moving parts of the configuration a splitting technique is employed, which, based on the block structuring, divides the computational domain in a stationary and a rotating part. According to this splitting, the time-dependent flow equations are solved in a stationary and rotating frame of reference, and a special coupling procedure is used for the interfacial blocks. The method is investigated with respect to its accuracy, where special emphasis is given to the influence of different interpolation techniques of pressure-related terms within the non-staggered pressure-correction scheme. As a practical application, the flow in a stirrer configuration with baffles is studied, for which also results concerning the numerical and parallel efficiency of the proposed method are given. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 195-217 
    ISSN: 0029-5981
    Keywords: boundary element method ; stiffened panels ; repair patches ; fracture mechanics ; damage tolerance ; stress intensity factors ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a formulation based on the Dual Boundary Element Method and on the Dual Reciprocity Method for the analysis of thin cracked metal sheets to which thin metal patches and stiffeners are adhesively bonded.The stiffened cracked sheet is modelled with the Dual Boundary Element Method. Adhesive shear stresses are modelled as action-reaction body forces exchanged by the sheet and patches. The Dual Reciprocity Method is used to avoid the discretization of the patches attachment domain into internal cells.Several examples are presented to demonstrate the efficiency and robustness of the method developed. The examples include sheets with embedded or edge cracks, stiffened or not, to which single or double patches are adhesively bonded. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 219-236 
    ISSN: 0029-5981
    Keywords: secant and tangent stiffness matrices ; structural analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non-linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application. © 1998 John Wiley & Sons, Ltd.
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  • 28
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 237-256 
    ISSN: 0029-5981
    Keywords: elastoplastic analysis ; boundary element method ; fracture mechanics ; dual boundary element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a general boundary element formulation for the three-dimensional elastoplastic analysis of cracked bodies is presented. The non-linear formulation is based on the Dual Boundary Element Method. The continuity requirements of the field variables are fulfilled by a discretization strategy that incorporates continuous, semi-discontinuous and discontinuous boundary elements as well as continuous and semi-discontinuous domain cells. Suitable integration procedures are used for the accurate integration of the Cauchy surface and volume integrals. The explicit version of the initial strain formulation is used to satisfy the non-linearity. Several examples are presented to demonstrate the application of the proposed method. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 257-288 
    ISSN: 0029-5981
    Keywords: parallel computing ; finite elements ; substructures ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The FETI algorithms are a family of numerically scalable substructuring methods with Lagrange multipliers that have been designed for solving iteratively large-scale systems of equations arising from the finite element discretization of structural engineering, solid mechanics, and structural dynamics problems. In this paper, we present a unified framework that simplifies the interpretation of several of the previously presented FETI concepts. This framework has enabled the improvement of the robustness and performance of the transient FETI method, and the design of a new family of coarse operators for iterative substructuring algorithms with Lagrange multipliers. We report on both of these new developments, discuss their impact on the iterative solution of large-scale finite element systems of equations by the FETI method, and illustrate them with a few static and dynamic structural analyses on an IBM SP2 parallel processor. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 289-311 
    ISSN: 0029-5981
    Keywords: viscoplasticity ; finite strain ; localization ; consistent linearization ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work extends a previously developed methodology for computational plasticity at finite strains that is based on the exponential map and logarithmic stretches to the context of isotropic elasto-viscoplastic solids. A particular form of the strain-energy function, given in terms of its principal values is employed. It is noticeable that within the proposed framework, the small strain integration algorithms, and the corresponding consistent tangent operators, automatically extend to the finite strain regime. Central to the effort of this formulation is the derivation of the closed form of a tangent modulus obtained by linearization of incremental non-linear problem. This ensures asymptotically quadratic rates of convergence of the Newton-Raphson procedure in the implicit finite element solution. To illustrate the performance of the presented formulation, several numerical examples, involving failure by strain localization and finite deformations, are given. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 313-340 
    ISSN: 0029-5981
    Keywords: element-free Galerkin method ; diffuse element method ; coupled EFGM(DEM)-FEM technique ; discontinuity ; three-phase deforming media ; partially saturated solid ; seepage surface ; free surface ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the proposed element-free Galerkin method for deforming multiphase porous media, displacement of the porous-solid skeleton is modelled by standard finite elements while wetting and non-wetting fluid pore pressures are included as element-free nodes. The matrix formulation is derived from the variational formulation of the multiphase governing equations. The case of a domain with a material or field discontinuity is handled by using Lagrange multipliers. One- and two-dimensional applications are presented for which the results, compared with those obtained by either the closed-form solution standard finite-element approach or experimental tests, show the efficiency of the proposed technique. The necessity of taking air pore pressure into account for partially saturated soils is discussed: free surface capturing is analysed and the problem of its intersection with outer boundaries (so-called seepage surface) is studied. © 1998 John Wiley & Sons, Ltd.
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  • 32
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 341-360 
    ISSN: 0029-5981
    Keywords: infinite domain ; finite element ; Dirichlet-to-Neumann (DtN) ; non-linear elliptic problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of non-linear elliptic problems in infinite domains is considered, with non-linearities extending to infinity. Examples include steady-state heat radiation from an infinite plate, and the deflection of an infinite membrane on a non-linear elastic foundation. Also, this class of problems may serve as a starting point for treating non-linear wave problems. The Dirichlet-to-Neumann (DtN) Finite Element Method, which was originally developed for linear problems in infinite domains, is extended here to solve these non-linear problems. Several DtN schemes are proposed, with a trade-off between accuracy and computational effort. Numerical experiments which demonstrate the performance of these schemes are presented. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 941-953 
    ISSN: 0029-5981
    Keywords: muscle model ; numerical stress calculation ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a numerical algorithm for the determination of muscle response by the finite element method. Hill's three-element model is used as a basis for our analysis. The model consists of one linear elastic element, coupled in parallel with one non-linear elastic element, and one non-linear contractile element connected in series. An activation function is defined for the model in order to describe a time-dependent character of the contractile element with respect to stimulation.Complex mechanical response of muscle, accounting for non-linear force-displacement relation and change of geometrical shape, is possible by the finite element method. In an incremental-iterative scheme of calculation of equilibrium configurations of a muscle, the key step is determination of stresses corresponding to a strain increment. We present here the stress calculation for Hill's model which is reduced to the solution of one non-linear equation with respect to the stretch increment of the serial elastic element. The muscle fibers can be arbitrarily oriented in space and we give a corresponding computational procedure of calculation of nodal forces and stiffness of finite elements.The proposed computational scheme is built in our FE package PAK, so that real muscles of complex three-dimensional shapes can be modelled. In numerical examples we illustrate the main characteristic of the developed numerical model and the possibilities of solution of real problems in muscle functioning. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 909-924 
    ISSN: 0029-5981
    Keywords: solid shell formulation ; four-node element ; assumed strain fields ; bubble function displacement ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A set of four-node shell element models based on the assumed strain formulation is considered here. The formulation allows for changes in the shell thickness. As a result, the kinematics of deformation are described by purely vectorial variables, without using rotational angles. The present study investigates the use of bubble function displacements and the assumed strain field. Careful selection of the assumed strain terms generates an element whose order of numerical integration does not increase even when the bubble function displacements are added. Results for the four-node element without any bubble function terms show sensitivity to element distortion. Use of the bubble functions with a carefully chosen assumed strain field greatly improves element performance. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 925-940 
    ISSN: 0029-5981
    Keywords: curved beam element ; hybrid-mixed formulation ; nodeless degrees of freedom ; field-consistency ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of this work is to show the successful use of nodeless degrees of freedom in developing a highly accurate, locking free hybrid-mixed C0 curved beam element. In the performance evaluation process of the present field-consistent higher-order element, the effect of field consistency and the role of higher-order interpolation on both displacement-type and hybrid-mixed-type elements are carefully examined. Several benchmark tests confirm the superior behaviour of the present element. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 979-996 
    ISSN: 0029-5981
    Keywords: boundary element method ; mesh refinement ; numerical error ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a mesh refinement technique for boundary element method in which the number of elements, the size of elements and the element end location are determined iteratively in order to obtain a user specified accuracy. The method uses L1 norm as a measure of error in the density function and a grading function that ensures that error over each element is the same. The use of grading function along with L1 norm makes the mesh refinement technique applicable to Direct and Indirect boundary element method formulation for a variety of boundary element method applications. Numerical problems in elastostatics, fracture mechanics, and bending of plate solved using Direct and Indirect method in which the density functions are approximated by Linear Lagrange, Quadratic Lagrange or Cubic Hermite polynomials validate the effectiveness of the proposed mesh refinement technique. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1085-1108 
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; structural optimization ; truss structures ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to structural sensitivity analysis based on the so-called virtual distortion method is presented. The proposed methodology enables the calculation of derivatives for elastic as well as elasto-plastic structures on the basis of knowledge of current strains, permanent plastic deformations and influence matrix, describing interactions between a chosen member and the entire structure. The analytical basis as well as numerical verification of the concept is demonstrated. Advantages of the proposed approach, in the sense of numerical cost, are summarized in conclusions. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1053-1068 
    ISSN: 0029-5981
    Keywords: finite element method ; variational inequalities ; contact problems ; heuristic algorithms ; nondifferential optimization methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article is devoted to the development of a new heuristic algorithm for the solution of the general variational inequality arising in frictional contact problems. The existing algorithms devised for the treatment of the variational inequality representing frictional contact rely on the decomposition of the physical problem into two sub-problems which are then solved iteratively. In addition, the penalty function method and/or the regularization techniques are typically used in the solution of these reduced sub-problems. These techniques introduce user-defined parameters which could influence the convergence and accuracy of the solution. The new method presented in this article overcomes these difficulties by providing a solution for the general variational inequality without decomposition into sub-problems. This is accomplished using a new heuristic algorithm which utilizes mathematical programming techniques, and thus avoids the use of penalty or regularization methods. The versatility and reliability of the developed algorithm were demonstrated through implementation to the case of frictional contact of an elastic hollow cylinder with a rigid foundation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1127-1141 
    ISSN: 0029-5981
    Keywords: contact ; double sided ; shells ; variational inequalities ; large deformation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new formulation is presented for the analysis of contact in degenerate shell elements. This formulation accounts for the transverse stress and strain through the shell thickness and can accommodate double-sided shell contact. The kinematic contact conditions are expressed accurately in terms of the physical shell contacting surfaces, and the problem is formulated in terms of Variational Inequalities (VI). Large deformations and rotations are accounted for by invoking the appropriate stress and strain measures. The solution of the variational inequality is obtained using Lagrange multipliers. This guarantees that the kinematic contact constraints are accurately satisfied and that the solution is free from user-defined parameters. Two examples involving three beams in contact and ring compression are simulated to establish the validity of the developed formulations and the solution technique. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1173-1191 
    ISSN: 0029-5981
    Keywords: warping ; bimoment ; Vlasov's thin-walled beam ; block stiffness matrix ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element for the analysis of thin-walled open beams with an arbitrary cross section is presented. Combining Timoshenko beam theory and Vlasov thin-walled beam theory, the derived element includes both flexural shear deformations and warping deformations caused by the bimoment. By adopting an orthogonal Cartesian co-ordinate system, one can obviate the ad hoc introduction of St. Venant stiffness. The derived block stiffness matrix is comparable but more general than the one given by earlier researchers. The versatility and accuracy of the new element are demonstrated by comparing the numerical results with the classical solutions or other numerical results available in the literature. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1193-1222 
    ISSN: 0029-5981
    Keywords: non-linear dynamics ; 3-D beams ; dissipative algorithms ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of dynamic procedures for three-dimensional (3-D) beams requires extensive use of the algebra pertaining to the non-linear character of the rotation group in space. The corresponding extraction procedure to obtain the rotations that span a time step has certain limitations, which can have a detrimental effect on the overall stability of a time-integration scheme. The paper describes two algorithms for the dynamics of 3-D beams, which differ in their manifestation of the above limitation. The first has already been described in the literature and involves the interpolation of iterative rotations, while an alternative formulation, which eliminates the above effect by design, requires interpolation of incremental rotations. Theoretical arguments are backed by numerical results. Similarities between the conventional and new formulation are pointed out and are shown to be big enough to enable easy transformation of the conventional formulation into the new one. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1223-1252 
    ISSN: 0029-5981
    Keywords: stress recovery ; superconvergent patch recovery technique ; recovery by equilibrium in patches ; equilibrium and boundary constraints ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of three different stress recovery procedures, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and a combined method known as the LP procedure is reviewed. Different order of polynomials and various patch formation strategies have been employed in the numerical studies for the construction of smoothed stress fields. Two 2-D elastostatic problems of different characteristics are used to assess the behaviour of the stress recovery procedures. The numerical results obtained indicate that when the order of polynomial used in the recovery procedure is equal to that of the finite element analysis, the behaviours of all three recovery procedures are very similar and all of them are adequate to provide a reliable recovered stress field for error estimation. In case that the order of polynomial of the recovered stress is increased, the LP procedure seems to give a more stable recovery matrix and a more reliable recovered stress field than the REP procedure. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1295-1307 
    ISSN: 0029-5981
    Keywords: energy conservation ; mesh refinement ; error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By generalizing the conservation of energy statement in classical mechanics, a useful and relatively simple approach has been developed for checking the conservation requirements in finite element analysis. By way of illustration several examples are provided from fields of stress analysis, heat transfer and fluid flow. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1383-1400 
    ISSN: 0029-5981
    Keywords: multilevel ; preconditioner ; p finite elements ; PCG ; elastostatics ; plates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study, a multilevel, recursively defined preconditioner, for use with the Preconditioned Conjugate Gradient (PCG) algorithm in connection with the finite element analysis of elastostatics is developed. The preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p-version of the finite element method. Results from parametric studies evaluating the effects of skewed elements, orthotropic material properties, and extreme span ratios, for p=2 and 3 are given. The results indicate that the preconditioner may be used to produce an efficient solver. The efficiency of the iterative procedure is illustrated using thin elastic solids. Results indicate that the preconditioner developed herein can be used to produce an efficient iterative solver for two- and three-dimensional problems in structural mechanics. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1421-1435 
    ISSN: 0029-5981
    Keywords: method of fundamental solutions ; particular solution ; diffusion equations ; quasi-Monte-Carlo method ; Laplace transform ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Laplace transform is applied to remove the time-dependent variable in the diffusion equation. For non-harmonic initial conditions this gives rise to a non-homogeneous modified Helmholtz equation which we solve by the method of fundamental solutions. To do this a particular solution must be obtained which we find through a method suggested by Atkinson. To avoid costly Gaussian quadratures, we approximate the particular solution using quasi-Monte-Carlo integration which has the advantage of ignoring the singularity in the integrand. The approximate transformed solution is then inverted numerically using Stehfest's algorithm. Two numerical examples are given to illustrate the simplicity and effectiveness of our approach to solving diffusion equations in 2-D and 3-D. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1453-1478 
    ISSN: 0029-5981
    Keywords: topology optimization ; stress constraints ; continua ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model that extends the power penalized stiffness model (also called SIMP for Solid Isotropic Microstructure with Penalization for inter-mediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called ‘singularity’ phenomenon of stress constraints in topology design, an ∊-constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1505-1521 
    ISSN: 0029-5981
    Keywords: boundary integral equations ; Fredholm integral equations ; circulant preconditioners ; preconditioned conjugate gradient method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we consider solving potential equations by the boundary integral equation approach. The equations so derived are Fredholm integral equations of the first kind and are known to be ill-conditioned. Their discretized matrices are dense and have condition numbers growing like O(n) where n is the matrix size. We propose to solve the equations by the preconditioned conjugate gradient method with circulant integral operators as preconditioners. These are convolution operators with periodic kernels and hence can be inverted efficiently by using fast Fourier transforms. We prove that the preconditioned systems are well conditioned, and hence the convergence rate of the method is linear. Numerical results for two types of regions are given to illustrate the fast convergence. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 127-135 
    ISSN: 0029-5981
    Keywords: renumbering ; profile ; wavefront ; matrix ; FEM ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient renumbering method for high-order finite element models is presented. The method can be used to reduce the profile and wavefront of a coefficient matrix arising in high-order finite element computation. The method indirectly performs node renumbering and involves three main steps. In the first step, nodes at corners of the elements are numbered using an existing renumbering algorithm. In the second step, elements are numbered in an ascending order of their least new corner node numbers. Finally, based on the new element numbers, both corner and non-corner nodes are renumbered using an algorithm that simulates the node elimination procedure in a frontal solution method. The method is compared to the algorithms that directly perform node renumbering. The numerical results indicate that the three-step algorithm presented here is an order of magnitude faster and the resulting renumbering produces excellent profile and wavefront characteristics of the coefficient matrix. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 137-166 
    ISSN: 0029-5981
    Keywords: meshless methods ; reproducing kernel particle methods ; large deformation ; non-linear elasticity ; underwater bubble dynamics ; reference configuration ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The explicit Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the finite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An efficient treatment of essential boundary conditions is also proposed for explicit time integration. The Lagrangian method based on the reference configuration is employed for the RKPM simulation of large deformation problems. Several examples of non-linear elastic materials are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the explicit Lagrangian RKPM formulation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 167-192 
    ISSN: 0029-5981
    Keywords: fluid-structure interaction ; porous medium ; symmetric finite element equations ; weighted residual formulation ; noise and vibration transmission ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A weak solution of the coupled, acoustic-elastic, wave propagation problem for a flexible porous material is proposed for a 3-D continuum. Symmetry in the matrix equations; with respect to both volume, i.e. ‘porous frame’-‘pore fluid’, and surface, i.e. ‘porous frame/pore fluid’-‘non-porous media’, fluid-structure interaction; is ensured with only five unknowns per node; fluid pore pressure, fluid-displacement potential and three Cartesian components of the porous frame displacement field. Taking Biot's general theory as starting point, the discretized form of the equations is derived from a weighted residual statement, using a standard Galerkin approximation and iso-parametric interpolation of the dependent variables. The coupling integrals appearing along the boundary of the porous medium are derived for a number of different surface conditions.The primary application of the proposed symmetric 3-D finite element formulation is modelling of noise transmission in typical transportation vehicles, such as aircraft, cars, etc., where porous materials are used for both temperature and noise insulation purposes. As an example of an application of the implemented finite elements, the noise transmission through a double panel with porous filling and different boundary conditions at the two panel boundaries are analysed. © 1998 John Wiley & Sons, Ltd.
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  • 51
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 211-231 
    ISSN: 0029-5981
    Keywords: mechanical reliability ; lifetime assessment ; eutectic tin-lead(-silver) solder ; strain-rate dependent constitutive (evolution) equations ; creep damage ; large strains ; logarithmic (or Hencky) strain-space description ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The continuum mechanical and constitutive description of eutectic tin-lead(-silver) solder is discussed with respect to the expected mean lifetime of solder joints of electronic devices under thermal cycling conditions, especially, the creep damage evolution in the joints. Since the mechanical loads are introduced into the model by thermal loads and due to the thermal expansion mismatch of different components, the solder joints are modelled by fine meshes of non-linear triangular finite elements, whereas the remaining surrounding structure is modelled by linear beams, linear quadrilaterals and specific compatibility elements. The strain-rate and temperature-dependent creep evolution and stress-strain relations of tin-lead(-silver) are presented in tensorial form. A hypothesis of the creep damage evolution is also offered. Simulation results on the creep damage evolution in solder joints of quad flat packs (QFP) with gull wing leads are discussed and compared with thermal cycling experiments. © 1998 John Wiley & Sons, Ltd.
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  • 52
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 443-472 
    ISSN: 0029-5981
    Keywords: finite element method ; error estimation ; stress recovery ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we investigate an approach for a posteriori error estimation based on recovery of an improved stress field. The qualitative properties of the recovered stress field necessary to obtain a conservative error estimator, i.e. an upper bound on the true error, are given. A specific procedure for recovery of an improved stress field is then developed. The procedure can be classified as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. Herein the interior equilibrium is satisfied a priori within each nodal patch. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative estimate. The performance of the developed error estimator is illustrated by investigating two plane strain problems with known closed-form solutions. © 1998 John Wiley & Sons, Ltd.
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  • 53
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 409-442 
    ISSN: 0029-5981
    Keywords: non-linear shell dynamics ; energy-momentum method ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Continuum and numerical formulations for non-linear dynamics of thin shells are presented in this work. An elastodynamic shell model is developed from the three-dimensional continuum by employing standard assumptions of the first-order shear-deformation theories. Motion of the shell-director is described by a singularity-free formulation based on the rotation vector. Temporal discretization is performed by an implicit, one-step, second-order accurate, time-integration scheme. In this work, an energy and momentum conserving algorithm, which exactly preserves the fundamental constants of the shell motion and guaranties unconditional algorithmic stability, is used. It may be regarded as a modification of the standard mid-point rule. Spatial discretization is based on the four-noded isoparametric element. Particular attention is devoted to the consistent linearization of the weak form of the initial boundary value problem discretized in time and space, in order to achieve a quadratic rate of asymptotic convergence typical for the Newton-Raphson based solution procedures. An unconditionally stable time finite element formulation suitable for the long-term dynamic computations of flexible shell-like structures, which may be undergoing large displacements, large rotations and large motions is therefore obtained. A set of numerical examples is presented to illustrate the present approach and the performance of the isoparametric four-noded shell finite element in conjunction with the implicit energy and momentum conserving time-integration algorithm. © 1998 John Wiley & Sons, Ltd.
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  • 54
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 473-498 
    ISSN: 0029-5981
    Keywords: finite element ; penalty ; barrier ; cross-constraints ; constrained minimisation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a further method is presented to solve problems involving contact mechanics. The basic idea is related to a special modification of the unconstrained functional to include inequality constraints. The modification is constructed in such a way that minimal point of the unconstrained potential can be exactly shifted to the constraint limit. Moreover, the functional remains smooth and the admissible range of the solution is not restricted. The solution search process with iterative techniques takes advantage from these features. In fact, due to a better control of gap status changes, a more stable solution path with respect to other methods is usually obtained.The characteristics of the method are evidenced and compared to other classical techniques, like penalty and barrier methods. The finite element discretization of the proposed method is included and some numerical applications are shown. © 1998 John Wiley & Sons, Ltd.
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  • 55
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 499-515 
    ISSN: 0029-5981
    Keywords: error estimation ; constitutive error formulation ; complementary solutions ; numerical methods ; finite element methods ; virtual work principle ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Most engineering problems are solved by means of numerical methods that are able to provide only approximate solutions, for which it would be extremely useful to have efficient error estimators.Upper and lower bounds for quantities of integral character, like the stored magnetic energy or the ohmic power dissipated in the domain of interest, had been clearly established along with the procedures to obtain them numerically.However, upper and lower bounds for local quantities would be of paramount interest in several fields of applications like Non-Destructive Testing or Nuclear Magnetic Resonance.We present here a procedure for the determination of upper and lower bounds of local field quantities, namely the average value of a field component in an arbitrarily small region. It is based on the introduction of an auxiliary field, and is the natural extension of the method establishing the bounds of global quantities.Our technique can be used for any linear system in stationary conditions for which a virtual work principle can be applied. Its efficiency is demonstrated with the analysis of some stationary 2D and 3D electromagnetic problems. © 1998 John Wiley & Sons, Ltd.
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  • 56
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 821-838 
    ISSN: 0029-5981
    Keywords: inverse problem ; incompressible ; shape design ; seal design ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a formulation for incorporating quasi-incompressibility in inverse design problems for finite elastostatics where deformed configurations and Cauchy tractions are known. In the recent paper of Govindjee and Mihalic [1996, Comput. Methods Appl. Mech. Engng., 136, 47-57.] a method for solving this class of inverse problems was presented for compressible materials; here we extend this work to the important case of nearly incompressible materials. A displacement-pressure mixed formulation is combined with a penalty method to enforce the quasi-incompressible constraint without locking. Numerical examples are presented and compared to known solutions; further examples present practical applications of this research to active problems in elastomeric component design. © 1998 John Wiley & Sons, Ltd.
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 955-974 
    ISSN: 0029-5981
    Keywords: Von Neumann ; stability ; consolidation ; Galerkin finite element ; soil consolidation ; porous media ; biphasic tissue mechanics ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Von Neumann stability analysis is performed for a Galerkin finite element formulation of Biot's consolidation equations on two-dimensional bilinear elements. Two dimensionless groups - the Time Factor and Void Factor - are identified and these quantities, along with the time-integration weighting, are used to explore the stability implications for variations in physical property and discretization parameters. The results show that the presence and persistence of stable spurious oscillations in the pore pressure are influenced by the ratio of time-step size to the square of the space-step for fixed time-integration weightings and physical property selections. In general, increasing the time-step or decreasing the mesh spacing has a smoothing effect on the discrete solution, however, special cases exist that violate this generality which can be readily identified through the Von Neumann approach. The analysis also reveals that explicitly dominated schemes are not stable for saturated media and only become possible through a decoupling of the equilibrium and continuity equations. In the case of unsaturated media, a break down in the Von Neumann results has been shown to occur due to the influence of boundary conditions on stability. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1167-1167 
    ISSN: 0029-5981
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: No abstract
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  • 59
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 997-1016 
    ISSN: 0029-5981
    Keywords: domain decomposition ; multipoint constraints ; numerical scalability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the iterative solution by a class of substructuring methods of the large-scale systems of equations arising from the finite element discretization of structural models with an arbitrary set of linear multipoint constraints. We present a methodology for generalizing to such problems numerically scalable substructure based iterative solvers, without interfering with their formulations and their well-established local and global preconditioners. We apply this methodology to the FETI method, and show that the resulting algorithm is numerically scalable with respect to both the substructure and problem sizes. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1029-1052 
    ISSN: 0029-5981
    Keywords: soil-pore fluid interaction ; staggered solution ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new class of unconditionally stable staggered implicit-implicit time-stepping algorithms for coupled soil-pore fluid dynamic problems is presented. The proposed schemes are stabilized with a pressure correction method and the staggered procedure introduced earlier by the second author is a simplified case of the new algorithms. The stabilized procedure is efficient in numerical time domain analysis of soil-pore fluid interaction occurring in earthquake and consolidation problems. Several examples of linear and non-linear problems demonstrate the stability and accuracy of the proposed numerical solution algorithms. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1069-1083 
    ISSN: 0029-5981
    Keywords: parallel algorithm ; frontal solution ; coupled heat and mass transfer ; deforming porous media ; phase change ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology