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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 81-97 
    ISSN: 0029-5981
    Keywords: porous media ; mixture theories ; fluid-saturated binary model ; incompressible constituents ; non-linear elasticity ; dynamic loading ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the theory of porous media (mixture theories extended by the concept of volume fractions), a model describing the dynamical behaviour of a saturated binary porous medium is presented including both geometrical and material non-linearities. Transformed toward a weak formulation, the model equations are solved by use of the finite element method. Applications of the model range from one-dimensional linear problems to two-dimensional problems including the full dynamics and non-linearities.
    Additional Material: 9 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
    Additional Material: 6 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 99-114 
    ISSN: 0029-5981
    Keywords: helical spring ; free vibration ; frequency ; transfer matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A set of 12 partial differential equations pertaining to helical springs is solved for free vibrations by the transfer matrix method. The dynamic transfer matrix including the axial and the shear deformations and the rotational inertia effects for any number of coils is numerically determined up to any desired precision in an efficient way. It is proved that the coefficients of the characteristic determinant of the dynamic differential matrix, [D], with odd-numbered subscripts are equal to zero which is based on the peculiarity that the traces of the same matrix with odd powers are all equal to zero. This important property of [D] has been the essence of the developed solution algorithm. The validity of the computer program coded in Fortran-77 has been verified by means of comparisons with the results given in literature. Next, the effects of the helix angle, the boundary conditions, the number of coils, and the ratio of (cylinder diameter/wire diameter) on the free vibration frequencies are investigated.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 185-187 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 115-139 
    ISSN: 0029-5981
    Keywords: boundary element methods ; subdomain technique ; viscous fluid flow ; iterative methods ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of Navier-Stokes equations of time-dependent incompressible viscous fluid flow in planar geometry by the Boundary Domain Integral Method (BDIM) is discussed. The introduction of a subdomain technique to fluid flow problems is considered and improved in order to maintain the stability of BDIM. To avoid problems with flow kinematics computation in the sudomain mesh, a segmentation technique is proposed which combines the original BDIM with its subdomain variant and preserves its numerical stability. In order to reduce the computational cost of BDIM, which greatly depends on the solution of systems of linear equations, iterative methods are used. Conjugate gradient methods, conjugate gradients squared and an improved version of the biconjugate gradient method BiCGSTAB, together with the generalized minimal residual method, are used as iterative solvers. Different types of preconditioning, from simple Jacobi to incomplete LU factorization, are carried out and the performance of chosen iterative methods and preconditioners are reported. Test examples include backward facing step flow and flow through tubular heat exchangers. Test computation results show that BDIM is an accurate approximation technique which, together with the subdomain technique and powerful iterative solvers, can exhibit some significant savings in storage and CPU time requirements.
    Additional Material: 13 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 219-233 
    ISSN: 0029-5981
    Keywords: evaporation ; condensation ; phase change ; internal energy formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work is to develop a control volume finite-difference method to model the bulk evaporation and condensation processes involved in liquid-vapour phase changes. An internal energy formulation, for these phase change processes that occur under the constraint of constant volume, is proposed. All calculations are carried out on a fixed grid using the cylindrical co-ordinate system. The well-established enthalpy formulation and the proposed internal energy formulation are compared. Both formulations yield identical results with similar computational efficiencies, while the internal energy formulation has a more concise and compact form. Two iterative methods for the update of the vapour-phase fraction, the E-based and T-based methods, are investigated. Numerical experiments reveal that for the evaporation problems, the E-based method is superior to the T-based method in terms of computational efficiency. The internal energy formulation and the E-based method are used to compute the bulk evaporation and condensation processes under different conditions. The evolution of the phase change processes is investigated.
    Additional Material: 6 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 261-279 
    ISSN: 0029-5981
    Keywords: numerical methods ; viscoplasticity ; integration techniques ; viscoplastic models ; explicit integration algorithms ; inelasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several explicit integration algorithms with self-adaptive time integration strategies are developed and investigated for efficiency and accuracy. These algorithms involve the Runge-Kutta second order, the lower Runge-Kutta method of orders one and two, and the exponential integration method. The algorithms are applied to viscoplastic models put forth by Freed and Verrilli and Bodner and Partom for thermal/mechanical loadings (including tensile, relaxation, and cyclic loadings).The large amount of computations performed showed that, for comparable accuracy, the efficiency of an integration algorithm depends significantly on the type of application (loading). However, in general, for the aforementioned loadings and viscoplastic models, the exponential integration algorithm with the proposed self-adaptive time integration strategy worked more (or comparably) efficiently and accurately than the other integration algorithms. Using this strategy for integrating viscoplastic models may lead to considerable saving in computer time (better efficiency) without adversely affecting the accuracy of the results. This conclusion should encourage the utilization of viscoplastic models in the stress analysis and design of structural components.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 309-320 
    ISSN: 0029-5981
    Keywords: hyperelastic ; elastic-viscoplastic ; finite deformation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of this paper is to present a numerical algorithm for calculating hyperelastic constitutive equations characterizing the thermomechanical response of elastically isotropic elastic-viscoplastic materials. The algorithm is developed within the context of an alternative formulation of plasticity in which elastic distortional deformation is determined directly by integrating an evolution equation which includes the current velocity gradient and quantities that depend only on the present state of the material. Consequently, the formulation is independent of the particular choice of a measure of plastic deformation, the reference configuration, and the total deformation gradient from the reference configuration. These features allow the constitutive equations to be easily implemented into computer codes which currently use a hypoelastic formulation for calculating plasticity.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 321-354 
    ISSN: 0029-5981
    Keywords: dynamics ; flexible ; geometric nonlinearity ; reciprocity ; boundary element ; multibody systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the implementation of the Boundary Element Method in the dynamics of flexible multibody systems. Kane's equations are used to formulate the governing boundary initial value problem for an arbitrary three-dimensional elastic body subjected to large overall base motion. Using continuum mechanics principles, direct boundary element incremental formulations are derived. The Galerkin approach was employed to generate the weighted residual statement which serves as a transitory point between continuum mechanics and boundary integral equations. By adapting the updated Langrangian formulation for large displacements analysis and using the Maxwell-Betti reciprocal theorem, integral representations for geometric stiffening were also derived. The non-linear terms were found to be functions of the time-variant stresses associated with the inertial forces at the reference configuration. The domain integrals arising from body forces (such as gravitational loads, inertia loads and thermal loads, etc.) are presented as DRM integrals (Dual-Reciprocity Method). Using the substructuring technique the elastic body is divided into several regions leading to a system of equations whose matrices are sparse (block-banded). The linearized equations of motion were discretized along the boundary of the body, and an algorithm for the integration involving the Houbolt method was used to establish an algebraic system of pseudo-static equilibrium equations. A Newton-Raphson-type iteration scheme was used to solve these discretized balance equations. To take advantage of the sparsity of the matrices, special routines were used to decompose and solve the resulting linear system of equations.An illustrative example is presented to demonstrate the validity of the method as well as how the effects of geometric stiffening effects are captured. The example consists of spin-up manoeuvre of a tapered beam attached to a moving base. The beam was modelled as two-dimensional plane strain problem divided into a number of substructures. Numerical simulation results show how the phenomenon of dynamic stiffening is captured by the present approach.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 361-382 
    ISSN: 0029-5981
    Keywords: optimization ; genetic ; algorithms ; trusses ; real-world ; multicriteria ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Genetic algorithms, a search technique which combines Darwinian ‘survival-of-the-fittest’ with randomized well structured information, is applied to the problems of real-world truss optimization. In this work a population of binary strings or ‘chromosomes’, which represent the coded truss design variables, a ‘fitness’ as a ranking measure of the adaptability to the environment, selection criteria and mechanical natural operators such as crossover and mutation are used to improve the population, so that over the generations the genetic algorithm gets better and better and at the end of the convergence, a ‘rebirth’ of the population is used to improve the usual process.An overview of the genetic algorithm will be described, continuing the rebirth effect; then, the chromosome representation of trusses is exposed. Afterwards, the objective scalar function is defined taking into account that it seems reasonable in real world to optimize trusses in minimum weight trying, at the same time, to use the minimum number of cross-section types obtained from the market. It also seems reasonable to have the possibility to change the shape of the conceptual design, moving some joints. To simulate nearly real conditions, several load cases, constraints in the elastic joint displacements, ultimate tensile and elastic and plastic buckling in the bars have been taken into account. A hyperstatic 10 bars truss is subjected to a deep analysis in different situations in order to evaluate with other authors when possible as truss optimization with two criteria and buckling effect has not been found in specialized literature. A 160-bar transmission tower is also optimized.
    Additional Material: 14 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 489-497 
    ISSN: 0029-5981
    Keywords: FETM-method ; vector processing ; ultimate dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A category of methods developed in the branch of structural dynamics known as a FETM methods are suggested for vector processing approach for problems in ultimate dynamics. Mathematical and physical backgrounds of the approach developed are explained. The applications are performed on the adoption of up-to-date vectorized approaches for wave propagation and ultimate transient dynamics problems in the branch of slender shell bridge structures.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 527-544 
    ISSN: 0029-5981
    Keywords: boundary strip ; elastostatics ; potential problems ; BEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper develops the idea of the boundary strip method, and presents its fundamentals, merits, applications and also some closed-form or non-element solutions based on it. The present approach combines the Boundary Integral Equation Method (BIEM) and the finite strip method, taking the advantages of both. The finite strip method is installed into the BIEM by expanding the unknown parameters of problems in terms of trigonometric series. This combination creates a new powerful numerical method with three advantages over other numerical methods, namely, a shorter computation time, a better accuracy and a reduction of one and a half dimensions in mesh generation. Applications in two-dimensional potential and field problems demonstrate the efficiency and the accuracy of the proposed method. Finally, closed-form presentations for Laplace equation and elastostatics are given, along circular segments.
    Additional Material: 10 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 549-567 
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; viscous compressible flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of generating general tetrahedral meshes suitable for use in viscous flow simulations is proposed. The approach which is followed consists of the initial generation of a number of unstructured layers of highly stretched elements, in the vicinity of solid walls, followed by the discretisation of the remainder of the domain, by a standard advancing front procedure. The numerical performance of the proposed methodology is demonstrated by the generation of meshes suitable for viscous flow analysis over a number of three-dimensional aerodynamic configurations of current practical interest.
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  • 16
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 585-604 
    ISSN: 0029-5981
    Keywords: large displacements ; finite volumes ; mixed formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses the problem of the numerical solution of beam statics undergoing large displacements. A kinematic analysis outlines the beam geometrical model through the definition of its Lagrangian co-ordinate and strain parameters. A definition of the stress parameters, a constitutive law and an expression for the strain energy of the beam are then provided under the hypothesis of small strain. The equations governing the beam equilibrium are introduced and their weak form is derived. These equations are then proved to be equivalent to the primal and mixed form of Principle of Virtual Work. The numerical approximation is introduced by applying the bidiscontinuous finite elements method on the linearized weak form. The weak-weak formulation is attained by using the lowest interpolation order both for test and trial functions on two staggered decompositions of the space domain. Some numerical examples prove the capability of present formulation in handling actual problems.
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  • 17
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 605-618 
    ISSN: 0029-5981
    Keywords: inverse heat conduction problem ; heat capacity determination ; non-linear problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An inverse analysis utilizing the conjugate gradient method and the minimization of adjoint equation is used successfully to estimate the temperature dependent heat capacity per unit volume in a homogeneous medium.No prior information is available on the functional form of the unknown heat capacity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that an excellent estimation on the heat capacity per unit volume can be obtained by using just boundary measurements (i.e. internal measurements are unnecessary) and the CPU time used in VAX-9420 computer is less than one second.The advantages of applying this algorithm in inverse analysis can greatly simplify the experimental set-up, diminish the sensitivity to the measurement errors and reduce the CPU time in inverse calculation, while the reliable predictions can still be achieved.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 635-661 
    ISSN: 0029-5981
    Keywords: fracture ; damage ; microcracking ; finite element analysis ; nonlocal models ; concrete structures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A recently proposed new nonlocal concept based on microcrack interactions is discussed, its implementation in a smeared cracking finite element code for concrete is presented, numerical studies are reported, and comparisons with experimental results are made. The nonlocality is not merely a mathematical device to prevent excessive spurious localization into a zone of zero volume but is a necessary physical consequence of microcrack interactions. Since the constitutive law itself is strictly local, the new nonlocal concept can be combined with any type of constitutive law for strain-softening nonlocal damage, which is here chosen to be the microplane model. A simple method is formulated to approximately identify the material parameters in the model from the basic characteristics of concrete such as the tensile strength, fracture energy and maximum aggregate size. The results of finite element analysis are shown to be mesh insensitive, and good convergence is obtained. Cracking damage is found to localize into a volume whose size and shape depend on the macroscopic concrete properties as well as the current stress-strain state. Although the damage is considered to be tensile on the microlevel, due solely to mode I microcracks, the new nonlocal model can describe well not only mode I fracture tests but also complex shear-dominated and mixed-mode types of failure such a diagonal shear, and can do so for the same values of material parameters (which was not the case for previous nonlocal models). Most importantly, the new nonlocal model can correctly capture the size effect of quasibrittle fracture, in approximate agreement with Bažant's size effect law.
    Additional Material: 20 Ill.
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  • 19
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 663-686 
    ISSN: 0029-5981
    Keywords: beams ; bending ; Chebyshev approximations ; quantifier elimination ; Sturm sequences ; tensionless elastic foundation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The well-known Sturm's theorem (based on Sturm's sequences) for the determination of the number of distinct real zeros of polynomials in a finite or infinite real interval has been already used in elementary quantifier elimination problems including applied mechanics and elasticity problems. Here it is further suggested that this theorem can also be used for quantifier elimination, but in more complicated problems where the functions involved are not simply polynomials, but they may contain arbitrary transcendental functions. In this case, it is suggested that the related transcendental equations/inequalities can be numerically approximated by polynomial equations/inequalities with the help of Chebyshev series expansions in numerical analysis. The classical problem of a straight isotropic elastic beam on a tensionless elastic foundation, where the deflection function (incorporating both the exponential function and trigonometric functions) should be continuously positive (this giving rise to a quantifier elimination problem along the length of the beam) is used as an appropriate vehicle for the illustration of the present mixed (symbolic-numerical) approach. Two such elementary beam problems are considered in some detail (with the help of the Maple V computer algebra system) and the related simple quantifier-free formulae are established and seen to coincide with those already available in the literature for the same beam problems. More complicated problems, probably necessitating the use of more advanced computer algebra techniques (together with Sturm's theorem), such as the Collins well-known and powerful cylindrical algebraic decomposition method for quantifier elimination, can also easily be employed in the present approximate (because of the use of Chebyshev series expansions) symbolic-numerical computational environment.
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  • 20
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 717-718 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 21
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 829-846 
    ISSN: 0029-5981
    Keywords: structural optimization ; approximation method ; convex approximation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for solving structural optimization problems using a local function approximation algorithm is proposed. This new algorithm, called the Generalized Convex Approximation (GCA), uses the design sensitivity information from the current and previous design points to generate a sequence of convex, separable subproblems. The paper contains the derivation of the parameters associated with the approximation and the formulation of the approximated problem. Numerical results from standard test problems solved using this method are presented. It is observed that this algorithm generates local approximations which lead to faster convergence for structural optimization problems.
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  • 22
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 847-865 
    ISSN: 0029-5981
    Keywords: interlaminar shear stress ; layer reduction technique ; composite laminate ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Interlaminar stress plays an important role in the delamination failure of laminated composites. A recently presented theory, the Interlaminar Shear Stress Continuity Theory (ISSCT), can directly and accurately predict interlaminar shear stresses in laminated composites by the constitutive equations. The present study further generalizes the derivation to a complete form from which many displacement-based laminate theories can be derived. Most of all, both the single-layer and multiple-layer approaches are incorporated into the analysis in the thickness direction. The laminate is discretized into several sublaminates and, then, a layerwise theory is applied in the analysis of this reduced laminate. This reduction in the number of layers used in the analysis makes the calculation of interlaminar shear stresses on the interested interface in a thick laminate more efficient. In addition, numerical solutions in closed-form and finite element form for laminates under cylindrical bending and bidirectional bending are examined. It is found that in the thickness direction the cubic order of the interpolation function and the discretization with four to six sublaminates can reduce the computational efforts dramatically and retain the accuracy of the predicted stresses within ±8 per cent.
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  • 23
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1-32 
    ISSN: 0029-5981
    Keywords: finite volumes ; finite elements ; compressible flows ; unstructured grids ; hybrid grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A framework for the construction of node-centred schemes to solve the compressible Euler and Navier-Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.
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  • 24
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 141-163 
    ISSN: 0029-5981
    Keywords: induction heating ; coupled problem ; three-dimensional analysis ; eddy current temperature analysis ; thin conducting sheet model ; eddy current boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a special finite element formulation for the computer simulation of an inductive heating device for thin moving metal strips. The calculation includes both the electromagnetic field and the temperature distribution resulting from the losses of the induced currents. The electromagnetic field is described by an electric vector potential and a magnetic scalar potential, the induced eddy currents are represented by a special boundary condition for the magnetic scalar potential along the surface of the current-carrying strip. This avoids the necessity to discretize the thin secondary region. The thermal model includes the movement of the strip as well as convection and radiation as its surfaces. The field equations are discretized using the Galerkin variant of the Method of Weighted Residuals. The mutually coupled electromagnetic and temperature fields are then calculated using an iterative, staggered solution scheme. Comparisons between calculated and measured temperature profiles show the validity of the presented approach.
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 165-184 
    ISSN: 0029-5981
    Keywords: curved unilateral contact ; augmented Lagrangian ; frictional contact element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a mixed formulation approach, a frictional contact element is proposed for the numerical solution of contact problems including strongly curved rigid obstacles. The implementation of the frictional contact element is analogous to that of a finite element. This feature facilitates its implementation in implicit finite element programmes, since the structure of the code need not be modified.For efficient modelling of the forming tool geometries by Computer Aided Geometric Design techniques and in order to achieve a high performance of the contact search, the numerical schemes of the frictional contact element operate directly on parametric polynomial surface patches. Thus, no discretization of curved contact surfaces is performed.Numerical simulations of deep drawing processes demonstrate the performance of the method in the case of large sliding increments upon curved tools and in the case of elasto-plasticity.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 51-65 
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forging ; preform design ; optimal design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 355-356 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: No Abstract
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  • 28
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 189-217 
    ISSN: 0029-5981
    Keywords: a posteriori error ; finite element ; plasticity ; adaptativity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method is developed to control the parameters of a finite element computation for time-dependent material models. This method allows the user to obtain a prescribed accuracy with a computational cost as low as possible. To evaluate discretization errors, we use a global error measure in constitutive relation based on Drucker's inequality. This error includes, over the studied time interval, the error of the finite element model and the error of the algorithm being used. In order to master the size of the elements of the mesh and the length of the time increments, an error estimator, which permits estimating the errors due to the time discretization, is proposed. These tools are used to elaborate two procedures of adaptivity. Various examples for monotonous or non-monotonous loadings, for 2-D or axisymmetric problems, show the reliability of these procedures.
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 235-259 
    ISSN: 0029-5981
    Keywords: dynamic relaxation ; parallel processing ; non-linear mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for non-linear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly non-linear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly non-linear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the non-linear static response of two- and three-dimensional hyperelastic systems involving contact. Impressive relative speed-ups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.
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  • 30
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1295-1312 
    ISSN: 0029-5981
    Keywords: finite elements ; mixed models ; hybrid models ; plates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed-hybrid formulation for stress finite elements is presented. The stresses and the displacements in the domain of the element and the displacements on the boundary are simultaneously and independently approximated using orthogonal functions. The stress approximation functions are used as weighting functions in the weighted residual enforcement of the local compatibility and constitutive equations. Similarly, the displacement approximation functions in the domain and on the boundary are used as weighting functions in the weighting residual enforcement of the local equilibrium equation and of the static boundary conditions, respectively. Legendre polynomials and Fourier series are used to illustrate the performance of the finite element formulation when applied to elastostatic problems.
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  • 31
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1313-1340 
    ISSN: 0029-5981
    Keywords: iterative methods for linear systems ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The preconditioned conjugate gradient algorithm is a well-known and powerful method used to solve large sparse symmetric positive definite linear systems. Such systems are generated by the finite element discretization in structural analysis but users of finite elements in this context generally still rely on direct methods. It is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods.
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  • 32
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1357-1382 
    ISSN: 0029-5981
    Keywords: numerical reduced minimization ; non-uniform isoparametric mapping ; unmatched coefficient ; spurious constraint ; optimal minimization ; locking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the effects of various numerical integrations on the behaviour of C0-continuous beam elements under non-uniform isoparametric mapping are investigated by using numerical reduced minimization theory. The theory shows that stress recovery can be achieved by sampling stresses at the optimal integration points once a reduced integration is employed. It rationalizes the continued acceptance of the conventional reduced integration of constrained strain energy as one of remedies for locking due to spurious constraint.
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  • 33
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1383-1403 
    ISSN: 0029-5981
    Keywords: crashworthiness ; homogenization ; topology design ; automotive structure optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density.Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored.The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.
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  • 34
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1419-1431 
    ISSN: 0029-5981
    Keywords: integral equations ; scattering ; boundary elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a boundary integral equation (boundary element) method for the solution of a variety of transient acoustic problems. The spatial and temporal discretization employs quadratic isoparametric elements with high-order Gauss quadrature, and the ensuing equations are implicit. The implicit formulation both eliminates the instabilities reported in explicit treatments, and permits a freedom of choice of timestep which can reduce costs dramatically. The accuracy of the approach is demonstrated by comparison with the analytical solution for a sphere. Results for more demanding sphere-cone-sphere geometries extending to seven wavelengths long are presented, and compared to those obtained from a related frequency domain approach.
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  • 35
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1433-1435 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 36
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1437-1454 
    ISSN: 0029-5981
    Keywords: large elastic deformations ; enhanced strain method ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical simulation of processes undergoing finite deformations requires robust elements. For a broad range of applications these elements should have a good performance in bending dominated situations as well as in the case of incompressibility. The element should be insensitive against mesh distortions which frequently occurs during finite deformations. Furthermore, due to efficiency reasons a good coarse mesh accuracy in required in non-linear analysis. The QS6 element, developed in this paper, tries to fulfil the above-mentioned requirements. The performance is depicted by means of numerical examples.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1475-1489 
    ISSN: 0029-5981
    Keywords: meshing ; three-dimensional ; surfaces ; quadrilateral ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three-dimensional trimmed surfaces. Methods of calculating angles, projecting elements, and detecting collisions between paving boundaries, for general surfaces are presented. Extensions of the smoothing algorithms for three dimensions are set forth. Advances in the use of scalar sizing functions are presented. These functions can be used to better approximate internal mesh density from boundary densities and surface characteristics.
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  • 38
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1517-1534 
    ISSN: 0029-5981
    Keywords: spectral elements ; viscoelasticity ; time-splitting method ; drag factor ; Uzawa algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady flow of a viscoelastic fluid past a sphere in a cylindrical tube is considered. A spectral element method is used to solve the system of coupled non-linear partial differential equations governing the flow. The spectral element method combines the flexibility of the traditional finite element method with the accuracy of spectral methods. A time-splitting algorithm is used to determine the solution to the steady problem. Results are presented for the Oldroyd B model. These show excellent agreement with the literature. The results converge with mesh refinement. A limiting Deborah number of approximately 0⋅6 is found, irrespective of the spatial resolution.
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  • 39
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    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 40
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1436-1436 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 41
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1455-1473 
    ISSN: 0029-5981
    Keywords: transient loads ; advective-diffusive equations ; Petrov-Galerkin ; Galerkin Leask-Square ; boundary layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov-Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective-diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least-Square method.
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  • 42
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1491-1516 
    ISSN: 0029-5981
    Keywords: impact ; composite laminates ; finite element ; matrix cracking ; delamination ; contact technique ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The modelling of the behaviour of laminates during low velocity impact requires, first, an analysis of the efficiency of the numerical tool used. A logical development in relation to the numerical structure of the code and the experimental observations is proposed. Four aspects of the code implementation are discussed. The first one is the representation of the impact loading by a macro-contact model using the Lagrange multiplier technique. The second is the development of this technique on the meso-scale to represent the assembly of plies of the laminate. The third step is the modelling of the evolution of the non homogeneous cracked state in the composite with an averaging technique, based on the Laws-Dvorak-Hejazi model, developed on the finite element scale. The fourth step is the modelling of the delamination between plies as a lack of contact set off by a mixed criterion matrix-cracking/interfacial forces. Numerical results on a glass-epoxy [02/906/02] laminate impacted at 27 J are in a good agreement with experimental observations.
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  • 43
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1535-1553 
    ISSN: 0029-5981
    Keywords: electric machinery ; electromagnetic losses ; Preisach model ; finite element-finite difference method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a numerical method for the evaluation of the magnetic iron losses in steel laminations used in rotating electric machinery. The magnetic hysteresis and the eddy current effects are directly and simultaneously taken into account. Hereby commonly used analytic expressions for the distribution function in the widely adapted Preisach hysteresis model are found to be not quite accurate. The magnetic circuit is decomposed into magnetic and air gap network elements, connected by fundamental loops. The magnetic network elements show a finite element structure. The kinematics of the electric machine is deliberately taken into account by an interpolation technique. Although the model retains the essential features of a cumbersome 3-D problem, a relatively simple algorithm may be developed. For the resulting algebraic system, we propose a suitable decoupling technique, which is efficient from the computational point of view. Numerical experiments show that the results obtained by our numerical approach are in good agreement with the known behaviour of the magnetic material.
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  • 44
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1585-1606 
    ISSN: 0029-5981
    Keywords: adaptive mesh refinement ; solid transition element ; non-conforming modes ; superconvergent patch recovery ; error estimation ; neighbouring element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automated three-dimensional adaptive h-refinement strategy using the solid transition elements with variable midside nodes at edges and faces of the element is presented. The basic behaviour of these transition elements were improved by addition of associated non-conforming modes. By introducing these transition elements, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in the conventional adaptive h-refinement are easily overcome. A superconvergent patch recovery technique is also extended to three-dimensional problem. Numerical examples show the effectiveness of the proposed adaptive mesh refinement scheme using transition elements.
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  • 45
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1619-1620 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 46
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1659-1680 
    ISSN: 0029-5981
    Keywords: elasticity ; stress singularity ; finite elements ; optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A semianalytical singular element is proposed to model the stress fields in plane and axisymmetric elastic bodies in the vicinity of singular points. The element generation is performed taking into account the structure of analytical solution in the vicinity of such points. This renders the element well suited for any type of singular points. Introduction of specially generated shape functions in the approximating expressions for displacements enables one to ensure the displacement compatibility with the standard elements. A detailed consideration is given to the convergence of the finite-element procedure. The extensive possibilities of the proposed singular element are exemplified by solving particular elastic problems. The applicability of the elaborated singular element is discussed with respect to optimization of geometry and material properties in the vicinity of singular points. Two optimization problems are presented to illustrate a search for the body geometry providing the optimal stress distribution.
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  • 47
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1635-1657 
    ISSN: 0029-5981
    Keywords: finite element method ; radiation boundary conditions ; absorbing boundary conditions ; discontinuous Galerkin method ; structural acoustics ; wave equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A time-discontinuous Galerkin space-time finite element method is formulated for the exterior structural acoustics problem in two space dimensions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time variational equation, i.e. they are enforced weakly in both space and time. Following Bayliss and Turkel, time-dependent radiation boundary conditions for the two-dimensional wave equation are developed from an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a non-dimensional wavenumber. In this paper, we undertake a brief development of the time-dependent radiation boundary conditions, establishing their relationship to the exact impedance (Dirichlet-to-Neumann map) for the acoustic fluid, and characterize their accuracy when implemented in our space-time finite element formulation for transient structural acoustics. Stability estimates are reported together with an analysis of the positive form of the matrix problem emanating from the space-time variational equations for the coupled fluid-structure system. Several numerical simulations of transient radiation and scattering in two space dimensions are presented to demonstrate the effectiveness of the space-time method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1721-1736 
    ISSN: 0029-5981
    Keywords: material stability ; loss of ellipticity ; discontinuous bifurcation ; numerical solution ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Material instability occurs when ellipticity is lost for symmetric constitutive equations. Prior to loss of ellipticity it is possible that the second-order work of Hill or Drucker becomes negative. There are implications in the literature that numerical solutions cease to be meaningful when a material strain softens and the second-order work is not positive. The instant that the second-order work is zero or negative simultaneously with the additional restriction that the strain increments satisfy compatibility is equivalent to the loss of the ellipticity criterion for symmetric constitutive relations. The loss of ellipticity criterion is the appropriate one for identifying when numerical solutions cease to show convergence and may also be a suitable criterion for identifying the instant at which material failure is initiated. An analytical development is provided for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane. Numerical solutions are given for several sample problems. For all cases, the numerical solutions based on the finite element method conform to the theoretical expectations that unique numerical solutions exist prior to the point at which ellipticity is lost.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1681-1705 
    ISSN: 0029-5981
    Keywords: hypersingular boundary integral equations ; boundary element method ; fracture mechanics ; dynamic stress intensity factor ; wave propagation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topic of hypersingular boundary integral equations is a rapidly developing one due to the advantages which this kind of formulation offers compared to the standard boundary integral one. In this paper the hypersingular formulation is developed for time-domain antiplane elastodynamic problems. Firstly, the gradient representation is found from the displacement one, removing the strong singularities (Dirac's delta functions) which arise due to the differentiation process. The gradient representation is carried to the boundary through a limiting process and the resulting equation is shown to be consistent with the static formulation. Next, the numerical treatment of the traction boundary integral equation and its application to crack problems are presented. For the boundary discretization, conforming quadratic elements are tested, which are introduced in this paper for the first time, and it is shown that the results are very good in spite of the lesser number of unknowns of this approach in comparison to the non-conforming element alternative. A procedure is devised to numerically perform the hypersingular integrals that is both accurate and versatile. Several crack problems are solved to show the possibilities of the method. To this end both straight and curved elements are employed as well as regular and distorted quarter point elements.
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  • 50
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1791-1792 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1797-1820 
    ISSN: 0029-5981
    Keywords: Multilayered plates ; HSDT modelling ; C0 continuity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Concerning composites plate theories and FEM (Finite Element Method) applications this paper presents some multilayered plate elements which meet computational requirements and include both the zig-zag distribution along the thickness co-ordinate of the in-plane displacements and the interlaminar continuity (equilibrium) for the transverse shear stresses. This is viewed as the extension to multilayered structures of well-known C0 Reissner-Mindlin finite plate elements. Two different fields along the plate thickness co-ordinate are assumed for the transverse shear stresses and for the displacements, respectively. In order to eliminate stress unknowns, reference is made to a Reissner mixed variational theorem. Sample tests have shown that the proposed elements, named RMZC, numerically work as the standard Reissner-Mindlin ones. Furthermore, comparisons with other results related to available higher-order shear deformation theories and to three-dimensional solutions have demonstrated the good performance of the RMZC elements.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1839-1857 
    ISSN: 0029-5981
    Keywords: combined methods ; finite difference method ; Ritz-Galerkin method ; coupling strategy ; penalty method ; hybrid method ; elliptic equation ; singularity problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents six combinations of the Ritz-Galerkin method and the finite difference method for solving elliptic boundary value problems. Not only optimal convergence rates of solutions but also superconvergence rates of solution derivatives can be achieved. The non-conforming combination and other five new combinations are given in algorithms, error analysis, convergence rates, outlines of proofs, numerical experiments and their comparisons.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1879-1888 
    ISSN: 0029-5981
    Keywords: FEM ; dynamics ; lumping ; acoustics ; accuracy ; convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for deriving hexahedral finite elements with lumped mass matrices for 3-D-problems is presented. These elements meet the theoretical conditions for high order convergence, and two numerical examples based on the 3-D scalar wave equation show that this is also the case in practice and that their accuracy is comparable to elements with consistent mass matrices.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1889-1901 
    ISSN: 0029-5981
    Keywords: coupled finite element boundary element analysis ; iterative solution ; plate-foundation interaction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper, a scheme is developed for the coupled FE/BE analysis of a plate-foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEM/BEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter selection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 56
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1933-1953 
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    Keywords: structures ; optimization ; large scale ; structural design ; sequential quadratic programming ; self-scaling ; numerical algorithms ; algorithm evaluation ; test problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic idea of an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems - small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.
    Additional Material: 4 Ill.
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  • 57
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1981-1983 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 58
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2005-2029 
    ISSN: 0029-5981
    Keywords: residual estimates ; singular and hypersingular residuals ; error estimates ; boundary element method ; singular integrals ; hypersingular integrals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new approach for a posteriori ‘pointwise’ error estimation in the boundary element method. The estimator relies upon evaluation of the residual of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. Extensive computational experiments have been performed for the two-dimensional Laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also predicted.
    Additional Material: 13 Ill.
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  • 59
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 60
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2477-2505 
    ISSN: 0029-5981
    Keywords: higher-order continua ; plasticity ; localization ; mixed elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Improved algorithms are proposed for a gradient plasticity theory in which the Laplacian of an invariant plastic strain measure enters the yield function. Particular attention is given to the type of finite elements that can be used within the format of gradient-dependent plasticity. Assuming a weak satisfaction of the yield function, mixed finite elements are developed, in which the invariant plastic strain measure and the displacements are discretized. Two families of finite elements are developed: one in which the invariant plastic strain measure is interpolated using C1-continuous polynomials, and one in which penalty-enhanced C0-continuous interpolants are used. The performance of both families of finite elements is assessed numerically in one-dimensional and two-dimensional boundary value problems. The regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated, both for mesh refinement and for the directional bias of the grid lines.
    Additional Material: 21 Ill.
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  • 61
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2509-2529 
    ISSN: 0029-5981
    Keywords: refined nonconforming element method ; hybrid element method ; quadrilateral axisymmetric element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general approach for constituting non-conforming displacement function has been developed for axisymmetric finite element analysis and a pure non-conforming quadrilateral axisymmetric element, from a non-conforming displacement function and without any reduced integration technique, is given.Based on a proposed functional for formulating axisymmetric element and the orthogonal approach, a quadrilateral axisymmetric refined hybrid element has been presented which can be used to achieve superior performances such as higher accuracy and free from locking.
    Additional Material: 7 Ill.
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  • 62
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2555-2573 
    ISSN: 0029-5981
    Keywords: 3-D boundary element method ; elastoplastic analysis ; hypersingular formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 3-D hypersingular Boundary Integral Equation (BIE) of elastoplasticity is derived. Using this formulation the displacement rate gradients and the complete stress tensor on the boundary can be evaluated directly as opposed to the classical approach, where the shape functions derivatives are to be calculated. The regularization of strongly singular and hypersingular boundary integrals, as well as strongly singular domain integrals for a source point positioned on the boundary is carried out in a general manner. Arbitrary types of elements and arbitrary positions of the source point with respect to continuity requirements can be used. Numerical 3-D elastoplastic examples (notch and crack problems) illustrate the advantages of the proposed method.
    Additional Material: 16 Ill.
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  • 63
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2635-2646 
    ISSN: 0029-5981
    Keywords: non-linear elasticity ; finite element method ; Newton method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.
    Additional Material: 6 Ill.
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  • 64
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2593-2618 
    ISSN: 0029-5981
    Keywords: space-time coupled ; p-version ; least squares ; time-marching ; accuracy and stability