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  • 1
    ISSN: 0029-5981
    Keywords: derivative boundary integral equations ; Hermite interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper reports on some problems that can arise with the use of regularized derivative boundary integral equations. It concentrates on developing a formulation for the simple Laplace equation using a cubic Hermite interpolation and shows how certain combinations of derivative and conventional boundary integral equations can result in a solution scheme severely lacking in stability. With some simple two- and three-dimensional geometries, the derivative equations on their own do not provide enough information to solve a Dirichlet problem. Even combinations of the conventional and derivative equations fail for some simple geometries. We conclude that the only consistently successful combination is that of the conventional equation with the tangential derivative equation, which showed cubic convergence of results with mesh refinement. Numerical results are presented for this scheme in both two and three dimensions.
    Additional Material: 5 Ill.
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  • 2
    ISSN: 0029-5981
    Keywords: post buckling ; interaction ; composite materials ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a finite element formulation for the buckling mode interaction analysis of structures modelled as plate assemblies. The main assumptions are linear elasticity, a linear fundamental path, the existence of distinct critical states that are coincident or near coincident, and a coupled path arising from a linear combination of modal displacements due to interaction. The formulation adopted is known as the W-formulation, in which the energy is written in terms of a sliding set of incremental co-ordinates measured with respect to the fundamental path. The energy is then expressed with respect to a reduced modal co-ordinate basis and the coupled solution arising from interaction is computed. An example of a fibre-reinforced composite I-beam subjected to axial compression illustrates the procedure. The results are compared to a simplified model developed by the authors. Also, an imperfection sensitivity analysis is performed.
    Additional Material: 9 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    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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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    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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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: spatial stability ; finite element ; thin-walled ; space frame ; warping ; semitargential ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A clearly consistent finite element formulation for spatial stability analysis of thin-walled space frames is presented by applying linearized virtual work principle and introducing Vlasov's assumption. The improved displacement field for unsymmetric thin-walled cross-sections is introduced based on inclusion of second-order terms of finite rotations, and the potential energy corresponding to the semitangential moments is consistently derived. In the present formulation, displacement parameters of axial and bending deformations are defined at the centroid axis and parameters of lateral and torsional deformations at the shear centre axis, and all bending-torsional coupling effects due to unsymmetric cross-sections are taken into account. For finite element analysis, cubic Hermitian polynomials for the flexural beam with four types of end conditions are utilized as shape functions of Hermitian space frame element. Also, load correction stiffness matrices for off-axis point loadings are derived based on the second-order rotation terms. Finite element solutions for the spatial buckling analysis of thin-walled space frames are compared with available solutions and other researcher's results.
    Additional Material: 13 Ill.
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 8
    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.
    Additional Material: 18 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: stress elements ; Trefftz method ; fracture ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formulation based on the approximation of the stress field is used to compute directly the stress intensity factors in crack problems. The boundary displacements are independently approximated. In each finite element, the assumed stresses may model multipoint singularities of variable order. The differential equilibrium equations are locally satisfied as solutions of the governing differential system are used to build the stress approximation basis. The approximation on the boundary displacements is constrained to satisfy locally the kinematic boundary conditions. The remaining fundamental conditions, namely the differential compatibility equations, the constitutive relations and the static boundary conditions are enforced through weighted residual statements. The approximation criteria are so chosen as to ensure that the finite element model is described by a sparse, adaptive and symmetric governing system described by structural matrices with boundary integral expressions. Numerical applications are presented to show that accurate solutions can be obtained using structural discretizations based on coarse meshes of few but highly rich elements, each of which may have different geometries and alternative approximation laws.
    Additional Material: 9 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: gradient plasticity ; strain localization ; mixed strain element method ; large strain ; consistent algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense.The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis; the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived.Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.
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  • 11
    ISSN: 0029-5981
    Keywords: contact ; impact ; structural dynamics ; explicit methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New explicit dynamic computational developments in conjunction with finite element formulations for impact problems are described in this paper. The proposed methodology is based on employing a variational inequality for dynamic problems involving Coulomb friction with the so-called forward incremental displacement-central difference method specially formulated in this paper for this class of problems. To enforce the constraints on the contact boundary, a linear complementary equation is established by means of a minimization problem subjected to constraints, which is equivalent to discretization of the variational inequality of the dynamic problem. In conjunction with these developments, a new conjugate gradient based explicit solution strategy is described for effectively solving the linear complementary equations. With the motivation for providing effective computational procedures suitable for vectorization and parallel computations, the proposed developments not only provide a fundamentally sound and robust theoretical basis but also serve to be ideally suited for impact problems involving frictional contact on high speed computing environments.
    Additional Material: 11 Ill.
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  • 12
    ISSN: 0029-5981
    Keywords: global/local analysis ; 3-D finite elements ; global/local interface identification ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: One of the key components in computational mechanics procedures using global/local methods is the specification of the global/local interface. Global/local interfaces are usually specified by visually examining some measure of response such as colour-coded contour plots of stresses or strain energy. However, when both global and local domains are modelled in three dimensions, such a specification is not as obvious, and it lacks objectivity and uniqueness. An Objective Search Method (OSM) is presented to specify the global/local interface in three dimensions in a precise, repeatable and automated manner. The OSM performs the search incrementally in all directions in three dimensions radiating from a location of interest until certain generalized guidelines are satisfied and the global/local interface is identified. The OSM is suited to problems where localized phenomena exist but where their domains are not known a priori. The generalized guidelines for the OSM require the identification of nodes lying on the external surfaces of the model. As an important component of the OSM, a unique method to identify surface nodes has been developed and is also presented. Finally, the uniqueness, sensitivity and versatility of the OSM is illustrated using two example problems and the computational effort involved with the OSM is discussed in the context of a third example problem.
    Additional Material: 17 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    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.
    Additional Material: 5 Ill.
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  • 14
    ISSN: 0029-5981
    Keywords: ground temperature ; golf links ; pesticide pollution ; finite element method ; optimal control ; bang-bang control ; practical use ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation and physical experiment related to control of the ground temperature by bang-bang control theory are discussed in this paper. Comparing the computed results with the results obtained by the experiments and measurements, it is shown that the bang-bang control theory is adaptable for practical use. The basic equation of the ground temperature is discretized by the finite element method in space and the Crank-Nicolson method in time. To obtain the optimal control temperature, the performance function is minimized by the Sakawa-Shindo method.
    Additional Material: 27 Ill.
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  • 15
    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.
    Additional Material: 13 Ill.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    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.
    Additional Material: 10 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: automatic ; load stepping ; load incrementation ; algorithm ; error control ; elastoplastic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm for controlling the error in non-linear finite element analysis which is caused by the use of finite load steps. In contrast to most recent schemes, the proposed technique is non-iterative and treats the governing load-deflection relations as a system of ordinary differential equations. This permits the governing equations to be integrated adaptively where the step size is controlled by monitoring the local truncation error. The latter is measured by computing the difference between two estimates of the displacement increments for each load step, with the initial estimate being found from the first-order Euler scheme and the improved estimate being found from the second-order modified Euler scheme. If the local truncation error exceeds a specified tolerance, then the load step is abandoned and the integration is repeated with a smaller load step whose size is found by local extrapolation. Local extrapolation is also used to predict the size of the next load step following a successful update. In order to control not only the local load path error, but also the global load path error, the proposed scheme incorporates a correction for the unbalanced forces. Overall, the cost of the automatic error control is modest since it requires only one additional equation solution for each successful load step. Because the solution scheme is non-iterative and founded on successful techniques for integrating systems of ordinary differential equations, it is particularly robust. To illustrate the ability of the scheme to constrain the load path error to lie near a desired tolerance, detailed results are presented for a variety of elastoplastic boundary value problems.
    Additional Material: 14 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: boundary elements ; domain integrals ; heat conduction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In employing the Boundary Element Method (BEM) to solve linear transient heat conduction problems, domain integrals need to be calculated. These integrals are generated by initial or pseudo-initial conditions and can be calculated directly by discretizing the domain. The need for domain meshing undermines the elegance of the boundary element approach and so a number of techniques have been developed in an attempt to overcome this. The most recent of these being the Multiple and Dual Reciprocity methods.This paper is concerned with a new approach which involves the direct approximation of fundamental solutions using linear combinations of sources positioned at different points in time. The weighting associated with each source is determined by minimization of the maximum absolute error using a single point exchange algorithm. In this way it is possible to determine the domain integrals to a high degree of accuracy with minimal computational effort. Error bounds for the approximation are naturally provided by the error reduction procedure giving an indication of the number of sources required for accurate domain integrals.The procedure is developed in detail for two and three-dimensional parabolic integral equations. Accuracy and stability are examined and the results of numerical tests are presented.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 22
    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.
    Additional Material: 9 Ill.
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  • 23
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: No Abstract
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    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.
    Additional Material: 14 Ill.
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  • 25
    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.
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  • 26
    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.
    Additional Material: 15 Ill.
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  • 27
    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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  • 28
    ISSN: 0029-5981
    Keywords: hybrid-Trefftz finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An equilibrium hybrid-Trefftz formulation based on the direct approximation of the stress and boundary displacement fields is presented. The general solution of the governing differential equations is used to approximate the stress field and the boundary displacements are represented by polynomial functions. When singular solutions are implemented to model local high stress gradients due to concentrated loads or to the presence of wedges or cracks, rational functions are used to approximate the boundary displacements in the neighbourhood of such singular stress points. The equilibrium conditions and the kinematic boundary conditions are locally satisfied. The remaining fundamental relations - the compatibility conditions, the static boundary conditions and the constitutive relations - are enforced in a weighted residual form so designed as to preserve the duality and constitutive reciprocity. The resulting governing system is symmetric and all intervening structural operators have boundary integral expressions. Numerical applications are presented to illustrate the performance of the formulation.
    Additional Material: 21 Ill.
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  • 29
    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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  • 30
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    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.
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  • 31
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 32
    ISSN: 0029-5981
    Keywords: structural dynamics ; finite elements ; algorithms ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An overview of new and recent advances towards a VIrtual-Pulse (VIP) time-integral methodology for general linear/non-linear dynamic systems is presented. Attention is focused on providing a brief overview and an indepth evaluation of the developments, methodology, computational issues and implementation aspects for practical problems. Different from the way we have been looking at the developments encompassing existing direct time-integration type methods and mode superposition techniques, the proposed methodology capitalizes on the computational attributes of both and thereby offers new perspectives and several attractive favourable features in terms of stability and accuracy, storage, and computational costs for a wide variety of inertial dynamic problems. Recently, the authors have shown the theoretical developments via the VIP methodology for transient structural problems and for transient thermal problems. The purpose of the present paper is to summarize the theoretical developments, improve upon the computational/implementation aspects for general linear/non-linear dynamic structural problems, and demonstrate the pros and cons via numerous illustrative test cases. The theoretical analysis and results of several test cases show that the VIP methodology has improved accuracy/stability characteristics and computational advantages in comparison to the commonly advocated explicit and implicit methods such as the Newmark family. Overall, an analysis of the theoretical developments, algorithmic study, and the implementation and evaluation of the formulations strongly suggest the proposition that the VIP methodology is a viable alternative for general structural dynamic applications encountered in practical engineering problems.
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  • 33
    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.
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  • 34
    ISSN: 0029-5981
    Keywords: shape design ; optimization ; boundary integral equation ; design sensitivity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A design optimization procedure is developed using the boundary integral equation (BIE) method for linear elastostatic two-dimensional domains. Optimal shape design problems are treated where design variables are geometric parameters such as the positions and sizing dimensions of entire features on a component or structure. A fully analytical approach is adopted for the design sensitivity analysis where the BIE is implicitly differentiated. The ability to evaluate response sensitivity derivatives with respect to design variables such as feature positions is achieved through the definition of appropriate design velocity fields for these variables. How the advantages of the BIE method are amplified when extended to sensitivity analysis for this category of shape design problems is also highlighted. A mathematical programming approach with the penalty function method is used for solving the overall optimization problem. The procedure is applied to three example problems to demonstrate the optimum positioning of holes and optimization of radial dimensions of circular arcs on structures.
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  • 35
    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.
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  • 36
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; optimization ; smoothing ; finite elements ; finite volume methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.
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  • 37
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    Chichester [u.a.] : Wiley-Blackwell
    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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  • 38
    ISSN: 0029-5981
    Keywords: boundary element method ; traction equation ; continuous elements ; three-dimensional fracture ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary element method is presented for single-domain analysis of cracked three-dimensional isotropic elastostatic solids. A numerical treatment for the hypersingular Boundary Integro-Differential Equation (BIDE) for displacement derivatives is described, in which continuous boundary elements may be used. Hadamard principal values of the hypersingular integrals arising in the formulation are evaluated using polar co-ordinates defined on the tangent planes at the source point, and the free term coefficients are calculated directly using a numerical technique. The forms of the Boundary Integral Equation (BIE) and the BIDE are considered for a source point on the coincident surfaces of a crack, and a scheme is given for defining the Traction Boundary Integral Equation TBIE so that it optimally incorporates the traction information deficient in its complementary partner, the BIE. Numerical results for some example mixed-mode crack problems are presented.
    Additional Material: 5 Ill.
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  • 39
    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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  • 40
    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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  • 41
    ISSN: 0029-5981
    Keywords: constrained optimization ; feasible descent ; mathematical programming ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Feasible Descent Cone (FDC) method for constrained optimization, previously restricted to linear objectives, is here generalized to include non-linear objective functions as well. In the basic and exact algorithm a sequence of descent steps is taken through the interior of the feasible region along the central lines of mathematically defined descent cones, constructed at successive boundary points. Here the basic algorithm is modified to allow for a minimum to occur within the interior, along a central descent ray in the case of non-linear objectives. A special interior procedure, with desirable mathematical properties, is adopted should the latter occur. To ensure economic implementation, the new generalized and exact algorithm, referred to as SSOPT2, is successively applied to a sequence of approximate quadratic subproblems. The overall generalized procedure that includes the successive application of SSOPT2 to the approximate subproblems, is referred to as the successive approximation version 2 algorithm (SAM2). The practical performance of SAM2 is assessed through its application to a number of small but otherwise representative test problems.
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  • 42
    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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  • 43
    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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  • 44
    ISSN: 0029-5981
    Keywords: RTM ; control volume ; free surface ; porous medium ; sparse matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient numerical scheme is presented for simulating isothermal flow in resin transfer molding. The problem involves transient, free surface flow of an incompressible fluid into a non-deforming porous medium. A new variant of the Control Volume Finite Element (CVFE) algorithm is explained in detail. It is shown how the pressure solutions at each time step can be obtained by adding a single row and column to the Cholesky factorization of the stiffness matrix derived from a finite element formulation for the pressure field. This approach reduces the computation of a new pressure solution at each time step to essentially just two sparse matrix back-substitutions. The resulting performance improvement facilitates interactive simulation and the solution of inverse problems which require many simulations of the filling problem. The computational complexity of the calculation is bounded by O(n2⋅5), where n is the number of nodes in the finite element mesh. A 100-fold speedup over a conventional CVFE implementation was obtained for a 2213-node problem.
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  • 45
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 46
    ISSN: 0029-5981
    Keywords: biomechanics ; damage ; finite element method ; plasticity ; standard generalized material ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Motivated by mechanical analysis of cancellous bone, a 3D constitutive law describing the simultaneous flow of rate-independent plasticity and damage is developed in the framework of thermodynamics of irreversible processes with internal variables. Following the hypothesis of standard generalized materials, a free energy and a dissipation potential are postulated and the associated flow rules derived with the tools of convex analysis. On the computational side, the classical implicit projection (or catching up) algorithm used in plasticity is extended to account for the additional flow of damage. Due to the existence of a dissipation potential, linearization of the incremental algorithm provides a symmetric tangent operator. Numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the quadratic convergence of the algorithm.
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  • 47
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: global ; optimization ; algorithms ; nonlinear ; engineering ; design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: After a brief overview of the methods from the literature, two new algorithms (zooming and domain elimination) for global optimization of general NLP problems are introduced. Operations analysis and stopping criteria for the methods are discussed. Numerical evaluation of the methods is carried out using a set of mathematical programming test problems. Performance of the methods is compared with the Controlled Random Search (CRS) and the Simulated Annealing (SA) methods. The methods are superior to SA for the test problems, as they are more robust, efficient and accurate. The CRS is more efficient than the new methods; however, it is applicable to unconstrained problems only. Therefore, it is concluded that the new methods are useful for engineering optimization applications.
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  • 48
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: force method ; finite elements ; structural analysis ; orthogonalization ; redundants ; natural factor formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: If the force method is fully optimized by introducing two appropriate co-ordinate transformations on the internal generalized force unknowns, the self-stress states (or redundant force systems) are determined so as to be an orthonormal set which is also orthogonal to the particular solution. The magnitudes of the redundant forces then become zero for any loading. This eliminates all operations with the redundants. In other words, the particular solution which is found is the solution to the problem. The result is a large decrease in the amount of computation necessary in the force method by eliminating the need to form up and solve the matrices associated with the compatibility equations.Although a different approach, this optimized form of the force method is shown to result in the same numerical procedures as those for the natural factor formulation of the displacement method.The same transformations developed to orthogonalize completely the self-stress states may also be applied directly to the compatibility and equilibrium equations as an alternative procedure. This approach to the solution of the structural equations is designated as the force transformation method.
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  • 49
    ISSN: 0029-5981
    Keywords: mesh generation ; hexahedral ; whisker weaving ; duality ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper introduces a new algorithm called whisker weaving for constructing unstructured, all-hexahedral finite element meshes. Whisker weaving is based on the Spatial Twist Continuum (STC), a global interpretation of the geometric dual of an all-hexahedral mesh. Whisker weaving begins with a closed, all-quadrilateral surface mesh bounding a solid geometry, then constructs hexahedral element connectivity advancing into the solid. The result of the whisker weaving algorithm is a complete representation of hex mesh connectivity only: Actual mesh node locations are determined afterwards.The basic step of whisker weaving is to form a hexahedral element by crossing or intersecting dual entities. This operation, combined with seaming or joining operations in dual space, is sufficient to mesh simple block problems. When meshing more complex geometries, certain other dual entities appear such as blind chords, merged sheets, and self-intersecting chords. Occasionally specific types of invalid connectivity arise. These are detected by a general method based on repeated STC edges. This leads into a strategy for resolving some cases of invalidities immediately.The whisker weaving implementation has so far been successful at generating meshes for simple block-type geometries and for some non-block geometries. Mesh sizes are currently limited to a few hundred elements. While the size and complexity of meshes generated by whisker weaving are currently limited, the algorithm shows promise for extension to much more general problems.
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  • 50
    ISSN: 0029-5981
    Keywords: finite plasticity ; single crystals ; multisurface plasticity ; active set search ; exponential map ; stress update algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp: sl(3) → SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of single-crystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.
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  • 51
    ISSN: 0029-5981
    Keywords: continuum damage mechanics ; localization ; gradient dependence ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
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  • 52
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: computational mechanics ; error estimation ; invariants ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper we examine the notion of invariant quantities in problems encountered in computational mechanics. These invariant quantities are then used to verify results obtained by numerical techniques. Examples in rigid-body dynamics, elastostatics and unsteady-state heat flow are presented. In Part II, we use the invariant quantities to compute consistent local errors in a finite-element analysis.
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  • 53
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 54
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 55
    ISSN: 0029-5981
    Keywords: finites elements ; open boundaries ; fluid flow ; natural boundary conditions ; Sommerfeld raiation condition ; Navier-Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld-type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier-Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.
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  • 56
    ISSN: 0029-5981
    Keywords: flexible multibody dynamics ; finite elements ; beam element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element beam formulation for modelling flexible multibody systems undergoing large rigid-body motion and large deflections is developed. In this formulation, the motion of the ‘nodes’ is referred to a global inertial reference frame. Only Cartesian position co-ordinates are used as degrees of freedom. The beam element is divided into two subelements. The first element is a truss element which gives the axial response. The second element is a torsional spring-like bending element which gives the transverse bending response. D'Alembert principle is directly used to derive the system's equations of motion by invoking the equilibrium, at the nodes, of inertia forces, structural (internal) forces and externally applied forces. Structural forces on a node are calculated from the state of deformation of the elements surrounding that node. Each element has a convected frame which translates and rotates with it. This frame is used to determine the flexible deformations of the element and to extract those deformations from the total element motion. The equations of motion are solved along with constraint equations using a direct iterative integration scheme. Two numerical examples which were presented in earlier literature are solved to demonstrate the features and accuracy of the new method.
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  • 57
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: finite elements ; pneumatics ; air springs ; containers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many engineering structures completely surround and enclose gas filled volumes. The enclosed gas adds additional stiffness to the surrounding structure. This paper shows how to account for this effect by means of an augmented virtual work principle. The additional term augmenting the virtual work equilibrium statement for the structure is the virtual boundary work done by the pressure of the enclosed gas. The augmented equations are discretized using standard finite element methods, and the additional terms are discussed. The resulting ‘pneumatic’ finite element is shown to be analogous to regular structural finite elements. To assess the accuracy and efficiency and also to illustrate the applicability of the present formulation, a series of four examples was selected. In two of the examples, the behaviour of the end cap of a partially filled plastic food product container is studied. The numerical results using the pneumatic element compare well with an alternative Rayleigh-Ritz solution of the end cap behaviour. The other two examples represent the behaviour of a double bellows air spring shock absorber under static isothermal and dynamic adiabatic conditions. For the static isothermal case, an experimental study was performed with results in good agreement with the pneumatic element solutions. For the dynamic adiabatic loading case, the dynamic stiffness of the air spring was predicted using the pneumatic element. The numerical results agree with experimental data published in an air spring application guide. The examples illustrate that the pneumatic element formulation can be applied to the large deflection analysis of structures that enclose gas filled volumes.
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  • 58
    ISSN: 0029-5981
    Keywords: renumbering ; profile ; wavefront ; matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An effective hybrid renumbering method for reducing the profile and wavefront of a sparse matrix is presented. The method is an innovative combination of the classical graph theory approach and the wavefront minimization technique. A rooted level structure is generated first and the level of each node is determined. Then, for each element, the element level is defined as the minimal level of the nodes the element is connected to. Using element levels as weighting factors, the node and element numbering are then reassigned by minimizing wavefront on an element-by-element basis. The method can be used to generate node or element numbering for efficient implementation of finite element analyses using active column solvers or frontal solvers. It can also be applied to sparse matrices with a symmetric pattern of zeros. Because of the use of element levels, the entire structure of the matrix to be renumbered is taken into account during the local element-based wavefront minimization process. Therefore, the algorithm presented here combines the effectiveness of wavefront minimization schemes in local renumbering with the reliability of classical graph theory methods for global renumbering.
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  • 59
    ISSN: 0029-5981
    Keywords: particle tracking ; Lagrangian-Eulerian finite element methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a multi-dimensional particle tracking technique for applying the Lagrangian-Eulerian finite element method to solve transport equations in transient-state simulations. In the Lagrangian- Eulerian approach, the advection term is handled in the Lagrangian step so that the associated numerical errors can be considerably reduced. It is important to have an adequate particle tracking technique for computing advection accurately in the Lagrangian step. The particle tracking technique presented here is designed to trace fictitious particles in the real-world flow field where the flow velocity is either measured or computed at a limited number of locations. The technique, named ‘in-element’ particle tracking, traces fictitious particles on an element-by-element basis. Given a velocity field, a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed. For the tracking within an element, the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements. A fictitious particle, thus, is traced one subelement by one subelement within the element. The desired number of subelements can be determined based on the complexity of the flow field being considered. The more complicated the flow field is, the more subelements are needed to achieve accurate particle tracking results. A single-velocity approach can be used to efficiently perform particle tracking in a smooth flow field, while an average-velocity approach can be employed to increase the tracking accuracy for more complex flow fields.
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  • 60
    ISSN: 0029-5981
    Keywords: post-buckling ; frictional contact ; complementarity ; arc-length method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A linear complementarity problem formulation combined with an arc-length method is presented for post-buckling analysis of geometrically non-linear structures with frictional contact constraints. The arc-length method with updated normal plane constraint is used to trace the equilibrium paths of the structures after limit points. Under the proportional loading assumption, the unknown load scale parameter used in the arc-length method is expressed in terms of contact forces, and eliminated to formulate as a linear complementarity problem. The unknown contact variables such as contact status and contact forces can be directly solved in this formulation without any ad hoc technique. Complicated non-linear buckling behaviours, such as snap-buckling, can be efficiently solved by the developed method, as shown by several buckling and post-buckling problems with frictional contact constraints.
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  • 61
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: multigrid ; shell ; unstructured mesh ; finite element ; solver ; acceleration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An accelerated multigrid method, which exploits shell element formulation to speed up the iterative process, is developed for inherently poor conditioned thin domain problems on unstructured grids. Its building blocks are: (i) intergrid transfer operators based on the shell element shape functions, (ii) heavy smoothing procedures in the form of Modified Incomplete Cholesky factorization, and (iii) various two- and three-parameter acceleration schemes. Both the flat shell triangular element and the assumed strain degenerated solid shell element are considered. Numerical results show a remarkable robustness for a wide spectrum of span/thickness ratios encountered in practical applications.
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  • 62
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; shape optimization ; extrusion ; drawing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper develops a numerical technique for determining the shape sensitivity parameters in steady metal- forming processes such as drawing and rolling. The adjoint method is applied to the discrete non-linear system of equations in the finite element model in order to determine the discrete matrix of sensitivity parameters. In this work, two specific cases are considered. The first case involves determining the sensitivity of the process power requirement to the process geometry and the second case involves determining the sensitivity of the internal state variable distribution in the final product to the process geometry. The process geometry is assumed to be characterized by a finite number of shape parameters. The internal state variable distribution in this case represents the resistance to plastic flow and is considered to be related to the quality of the final product. Numerical examples for a simple drawing process are presented to demonstrate the efficiency of the algorithm.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 63
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    Signatur Availability
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  • 64
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    Signatur Availability
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  • 65
    ISSN: 0029-5981
    Keywords: optimization ; algorithms ; structural ; design ; comparative ; evaluation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement