bluuebunny/crossref_metadata_2025 huggingface dataset:
Preconditioned conjugate gradient methods for three‐dimensional linear elasticity
Authors: Dickinson J. K. , Forsyth P. A.
Published: August 2005

Finite element modelling of three‐dimensional elasticity problems give rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two‐level hierarchical basis are developed. Various techniques for ensuring that the incomplete factors have positive pivots are presented. Computational tests are carried out for problems generated using unstructured tetrahedral meshes. Quadratic basis functions are used. The performance of the iterative methods is compared to a standard direct sparse matrix solver. Problems with up to 70 000 degrees of freedom and small (≪1) element aspect ratio are considered.
Shape optimization in frictionless contact problems
Authors: Fancello Eduardo A. , Feijóo Raúl A.
Published: August 2005

A finite element approach for shape optimization in two‐dimensional (2‐D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary.

The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B‐spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented‐Lagrangian techniques (to solve the contact problem) and an interior‐point mathematical‐programming algorithm (for shape optimization), we obtain several results reported at the end of the article.
Introduction to wavelets in engineering
Authors: Williams John R. , Amaratunga Kevin
Published: August 2005

The aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications. The paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet‐based numerical algorithms. In particular, we provide extensive details of the derivation of Mallat's transform and Daubechies' wavelet coefficients, since these are fundamental to gaining an insight into the properties of wavelets. The potential benefits of using wavelets are highlighted by presenting results of our research in one‐ and two‐dimensional data analysis and in wavelet solutions of partial differential equations.
Generation of oriented three‐dimensional Delaunay grids suitable for the control volume integration method
Authors: Conti Paolo , Tomizawa Masaaki , Yoshii Akira
Published: August 2005

A fully automatic algorithm for three‐dimensional mesh generation is presented. The algorithm preserves the robustness and time efficiency of the finite octree technique; replacing octrees by more general 2–4–8‐ trees, it is capable of generating oriented meshes. In a post‐processing step, meshes are transformed in order to satisfy the Delaunay criterion, and so that non‐overlapping, closed control volumes can be defined for each mesh point through edge bisectors. The method is shown to be appropriate for modelling semiconductor devices, where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved, and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical.
Incremental finite element sensitivity analysis for non‐linear mechanics applications
Authors: Kleiber Michal , Hien Tran Duong , Postek Eligiusz
Published: August 2005

Finite element formulations for structural sensitivity analysis of non‐linear systems with fixed overall shape are discussed. Both the direct differentiation and adjoint variable methods are employed. The resulting sensitivity algorithms are consistent with time integration scheme adopted for solving equilibrium problem. Effectiveness and computational aspects of the procedures are discussed and compared. Numerical algorithms are shown to be readily implemented in existing finite element codes. Large‐scale examples illustrate the paper.
Adaptive control system using the fuzzy theory for transient multi‐dimensional thermohydraulics calculations
Authors: Muramatsu Toshiharu , Ninokata Hisashi
Published: August 2005

An adaptive control system to yield optimum time step sizes was developed using the fuzzy theory for transient single‐phase multi‐dimensional thermohydraulic calculations. Applications of the control system revealed a considerable amount of the computing time savings, typically by 50–75 per cent of the computing time required when the time step size was not controlled by the system. The result obtained in this work is very encouraging in the sense that the adaptive control system would be used as one of the efficient measures to save computing efforts when one wishes to perform extremely large scale computations in transient thermohydraulics.
Isoparametric Hermite elements
Authors: Petera J. , Pittman J. F. T.
Published: August 2005

Isoparametric Hermite elements are created using Bogner–Fox–Schmit rectangles on a reference domain and mapping these numerically onto the computational domain. The difficulties involved in devising explicit C1 shape functions for isoparametric elements are thus avoided, and the resulting elements have all the benefits of full C1 continuity, the simplicity of the Bogner–Fox–Schmit element and the geometrical flexibility expected from higher‐order isoparametric elements. The numerical mapping consists in the finite element solution of a linear boundary value problem, which is inexpensive and is carried out as a preprocessing operation—the required derivatives of the mapping then being supplied to the main analysis as data. Some care is required in defining the differential boundary conditions, and guidance on this is provided. Examples are given showing the success of the mapping procedure, and the use of the resulting elements in the solution of some boundary value problems. The numerical results confirm a convergence analysis provided for the new isoparametric Hermite element.
Dynamic condensation: The ‘Free Mode’ method
Authors: Dubigeon S. , Peseux B.
Published: August 2005

The dynamic condensation methods make it possible to reduce the size of large matrix systems occurring in mechanics in order to obtain an accurate description of behaviours. In the first instance, we have reviewed the methods currently available. Then, we have presented the latest improvements which have been introduced with respect to the ‘Free Mode’ method. The use of an innovative technique for the determination of residual flexibility matrices, the consideration of an additional term in the expansions and a shift in frequencies have made this method particularly accurate and worthy of interest. In the present paper, we have presented an example which, however simple, has the merit of highlighting the qualities of the proposed method by drawing comparisons with the results achieved through the application of other methods.
A study of the factorization fill‐in for a parallel implementation of the finite element method
Authors: Taylor Valerie E. , Nour‐Omid Bahram
Published: August 2005

In this paper we investigate the additional storage overhead needed for a parallel implementation of finite element applications. In particular, we compare the storage requirements for the factorization of the sparse matrices that would occur on a parallel processor vs. a uniprocessor. This variation in storage results from the factorization fill‐in. We address the question of whether the storage overhead is so large for parallel implementations that it imposes severe limitations on the problem size in contrast to the problems executed sequentially on a uniprocessor. The storage requirements for the parallel implementation are based upon a new ordering scheme, the combination mesh‐based scheme. This scheme uses a domain decomposition method which attempts to balance the processors' loads and decreases the interprocessor communication. The storage requirements for the sequential implementation is based upon the minimum degree algorithm. The difference between the two storage requirements corresponds to the storage overhead attributed to the parallel scheme.

Experiments were conducted on regular and irregular, 2‐D and 3‐D problems. The meshes were decomposed into 2–256 subdomains which can be executed on 2–256 processors, respectively. The total storage requirements or fill‐in for most of the 2‐D problems were less than a factor of two increase over the sequential execution. In contrast, large 3‐D problems had zero increase in storage or fill‐in over the sequential execution; the fill‐in was less for the parallel execution than the sequential execution. Thus, we conclude that the storage overhead attributed to the use of parallel processors will not impose severe constraints on the problem size. Further, for large 3‐D applications, the combination mesh‐based algorithm does better than minimum degree for reducing the fill‐in.
Symmetric FE–BE coupling with iterations on the interface
Authors: Dostál Zdeněk , Malík Josef
Published: August 2005

The paper presents an algorithm for the solution of problems that are discretized partly by the finite element method and partly by the boundary element method. The algorithm is based on the conjugate gradient method with preconditioning by an auxiliary conjugate projector that reduces the iterations to the interface. A numerical example is presented to illustrate the performance of the algorithm. The method may prove useful also in parallel environment.
An energetic formulation for the linear viscoelastic problem. Part I: Theoretical results and first calculations
Authors: Carini A. , Gelfi P. , Marchina E.
Published: August 2005

An extremal principle is formulated for the linear viscoelastic problem with general viscous kernel. This is an extension of the classical total potential energy principle of the linear elasticity. Then a discretized formulation in space and time is shown for frame structures, using finite element technique. Several numerical examples, for two different kinds of viscoelastic materials, testify the accuracy and reliability of the proposed method. The matrix conditioning indexes obtained are compared with those achieved by applying the least square method.
Tetrahedral mesh generation in convex primitives
Authors: Kettunen Lauri , Forsman Kimmo
Published: August 2005

This paper presents a method for generating tetrahedral meshes in three‐dimensional primitives. Given a set of closed and convex polyhedra having non‐zero volume and some mesh controlling parameters, the polyhedra are automatically split to tetrahedra satisfying the criteria of standard finite element meshes. The algorithm tries to generate elements close to regular tetrahedra by maximizing locally the minimum solid angles associated to a set of a few neighbouring tetrahedra. The input parameters define the size of the tetrahedra and they can be used to increase or decrease the discretization locally. All the new nodes, which are not needed to describe the geometry, are generated automatically.
Elasto‐plastic finite element analysis with fuzzy parameters
Authors: Valliappan S. , Pham T. D.
Published: August 2005

In this paper, an elastoplastic analysis based on fuzzy mathematics and using finite element method will be described. The Drucker–Prager yield criterion and the elasto‐plastic matrix are fuzzified for the non‐linear analyses which adopt the initial stress method for the solution. A numerical example is given to illustrate the possible variations in the displacements and the extent of plastic zones at the discrete membership functions. A reliability index of a membership grade based on the concept of non‐probabilistic entropy is also proposed.
A return mapping algorithm for a class of cyclic plasticity models
Authors: Hopperstad O. S. , Remseth S.
Published: August 2005

A return mapping algorithm for a class of cyclic plasticity models is presented. The constitutive model includes a quadratic yield criterion and multi‐component formulations of non‐linear isotropic and kinematic hardening. Thus, both initially isotropic and anisotropic materials can be described, and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained. The return mapping algorithm employs the closest point projection scheme in combination with a decomposition method, to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is derived in closed form, and is found to be unsymmetric due to the non‐linear evolution of the kinematic hardening terms. The accuracy and robustness of the algorithm are assessed through numerical examples.
Theory and numerics of ductile micropolar elastoplastic damage
Authors: Steinmann Paul
Published: August 2005

The aim of this work is to extend an isotropic elastoplastic damage concept for ductile materials within a generalized micropolar continuum framework. The underlying motivation is on the one hand to model softening behaviour by damage evolution and on the other hand to regularize the impending loss of ellipticity which results in strong mesh dependence of localization computations. To this end, the classical displacement field is supplemented by an independent rotation field to yield an enhanced continuum. For the model originally proposed by Lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity. Special emphasis is directed towards the numerical implementation of the constitutive model within the framework of finite element analysis of inelastic boundary value problems. To compare damage evolution and standard strain softening the results are contrasted to the outcome of an analysis with the micropolar version of the classical von Mises model. Thereby, the intriguing correspondence of strain softening and damage evolution is highlighted. Additionally, several planar micropolar finite element formulations are derived within mixed variational principles to enhance the poor performance of the standard bilinear displacement and rotation expansions used so far in the literature. The merits of these new element developments are demonstrated for the example of localization within a compression problem.
Cost‐effective staggered schemes for the numerical simulation of wave propagation
Authors: Kamel A. , Sguazzero P. , Kindelan M.
Published: August 2005

This paper presents a cost‐effectiveness analysis of explicit Finite Difference (FD) methods for the numerical integration of the wave equation. Formal notions of computational cost (expressed in floating point operations) and numerical dispersion error are introduced. Restricting the analysis to leapfrog timemarching, for sake of simplicity, various spatial discrete differentiators are examined. For each scheme, by minimizing the cost at a given error threshold, a cost‐effective operating poin (time sampling rate and number of gridpoints per shortest wavelength) is obtained, which is remarkably different from the stability limit. Different schemes, each operated at its cost‐effective point, are then compared. High‐order dispersion‐bounded operators, in the sense of Holberg,1 are found to be competitive with the Pseudo‐spectral (PS) method.

New optimal schemes improving over the Holberg's spatial differentiators are introduced together with accurate expansions of the convolutional weights is terms of the design error threshold. It is also shown that the composition of two distinct Holberg's operators of consecutive orders, with opposite phase properties, minimizes dispersion and yields cost‐effective schemes.

Numerical experiments illustrate the suitability of the new methods for large‐scale wave‐equation seismic modelling.
Bounding‐surface plasticity for non‐linear analysis of space structures
Authors: Al‐Bermani F. G. A. , Zhu K. , Kitipornchai S.
Published: August 2005

This paper presents a method for the non‐linear analysis of space structures subjected to static and cyclic loading. A bounding‐surface kinematic hardening plasticity model is used to simulate the hardening and hysteritic material behaviour. The model is used in conjunction with the lumped plasticity assumption coupled with the concept of a yield surface in force space. A hardening coefficient matrix which is a function of the plastic strain and the elastic stiffness matrix is introduced while the vectorial nature of the material memory parameters is maintained. This provides a smooth transition from the elastic to the plastic regime which simulates the hysteresis loops quite accurately. An updated Lagrangian formulation is used together with a predictor/corrector solution method. Several examples are presented to demonstrate the accuracy and efficiency of the method.
Extension of moment‐method solutions to vector scattering by three‐dimensional non‐linear dielectric objects in free space
Authors: Caorsi Salvatore , Massa Andrea , Pastorino Matteo
Published: August 2005

In this paper, we explore the possibility of applying the moment method to determine the electromagnetic field distributions inside three‐dimensional bounded non‐linear dielectric objects of arbitrary shapes. The moment method has usually been employed to solve linear scattering problems. We start with an integral equation formulation, and derive a non‐linear system of algebraic equations that allows us to obtain an approximate solution for the harmonic vector components of the electric field. Preliminary results of some numerical simulations are reported.
A new fundamental solution for boundary element analysis of thin plates on Winkler foundation
Authors: El‐Zafrany A. , Fadhil S. , Al‐Hosani K.
Published: August 2005

This paper introduces an efficient boundary element approach for the analysis of thin plates, with arbitrary shapes and boundary conditions, resting on an elastic Winkler foundation. Boundary integral equations with three degrees‐of‐freedom per node are derived without unknown corner terms. A fundamental solution based upon newly defined modified Kelvin functions is formulated and it leads to a simple solution to the problem of divergent integrals. Reduction of domain loading terms for cases of distributed and concentrated loading is also provided. Case studies, including plates with free‐edge conditions, are demonstrated, and the boundary element results are compared with corresponding analytical solutions. The presented formulations provide a very accurate boundary element solution for plates with different shapes and boundary conditions.
The use of bubble functions for the post‐local buckling of plate assemblies by the finite strip method
Authors: Azhari M. , Bradford M. A.
Published: August 2005

The finite strip displacement functions for post‐local buckling are augmented with so‐called bubble functions, which are extra modes associated with internal or nodeless degrees of freedom. A non‐linear finite strip method of analysis including bubble functions is described for the post‐local buckling of geometrically imperfect plate assemblies. It is shown that the use of bubble functions improves significantly the convergence of the method. The non‐linear finite strip method is then used to study channel and I‐section members in compression and bending.
A finite element algorithm to study creep cracks based on the creep hardening surface
Authors: Krishnaswamy P. , Brust F. W. , Ghadiali N. D.
Published: August 2005

This work addresses finite element (FE) modelling of creep cracks under reversed and cyclic loads in steels. A constitutive model based on the creep hardening surface developed by Murakami and Ohno has been selected for this purpose. This model is particularly accurate for describing creep under reversed and cyclic loads and requires no additional material constants. An FE algorithm for this model has been derived and implemented into a research code FVP. The algorithm is verified by comparing the numerical predictions with closed form solutions for simple geometries and loading configurations. FE predictions are compared with experimental data for a stationary crack in a compact tension specimen. The stress and strain fields in the vicinity of a crack under a sustained load are compared with those for the intermediate unloading case. Several integral fracture parameters are investigated as to their appropriateness for describing creep cracks under reversed and cyclic loads.
A successive bounding method to find the exact eigenvalues of transcendental stiffness matrix formulations
Authors: Ye Jianqiao , Williams F. W.
Published: August 2005

An alternative algorithm for finding exact natural frequencies or buckling loads from the transcendental, e.g. dynamic, stiffness matrix method is presented in this paper and evaluated by using the plate assembly testbed program VICONOPT. The method is based on the bounding properties of the eigenvalues provided by either linear or quadratic matrix pencils on the exact solutions of the transcendental eigenvalue problem. The procedure presented has five stages, including two accuracy checking stages which prevent unnecessary calculations. Numerical tests on buckling of general anisotropic plate assemblies show that significant time savings can be achieved compared with an earlier multiple determinant parabolic interpolation method.
Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials
Authors: Ghosh Somnath , Liu Yunshan
Published: August 2005

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady‐state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.
Parallel performance and scalability for block preconditioned finite element (p) solution of viscous flow
Authors: Barragy E. , Carey G. F. , Van De Geijn R.
Published: August 2005

A two‐dimensional p‐type finite element scheme for distributed parallel computation of viscous flows is developed. The approach is based on an element‐by‐element implementation of the Biconjugate Gradient Stabilized 2 iterative method coupled with a recently developed class of block preconditioners. Critical to the overall parallel performance is the parallel solution of the imbedded bilinear preconditioner. Performance results are presented for the 2‐D driven cavity incompressible viscous flow problem solved using incremental continuation in the Reynolds number on the Intel Touchstone Delta. These results are used to validate a run‐time model. The run‐time model is then used to examine the scaling properties of the method over a range of p and h.
An efficient multilevel solution scheme for large scale non‐linear systems
Authors: Fish J. , Pandheeradi M. , Belsky V.
Published: August 2005

We present a new approach for the fast, efficient solution of large systems of non‐linear equations arising from the finite element discretization. The proposed non‐linear solver builds on the advantages of the popular methods of solution that are currently being employed, while eliminating most of their undesirable features. It combines the well‐known BFGS method with the FAS version of the multigrid method, introduced by Brandt,1 to form a fast, efficient solution method for non‐linear problems. We present numerical performance studies that are indicative of the convergence properties as well as the stability of the new method.
Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures
Authors: Potyondy David O. , Wawrzynek Paul A. , Ingraffea Anthony R.
Published: August 2005

A methodology for simulating the growth of long through cracks in the skin of pressurized aircraft fuselage structures is described. Crack trajectories are allowed to be arbitrary and are computed as part of the simulation. The interaction between the mechanical loads acting on the superstructure and the local structural response near the crack tips is accounted for by employing a hierarchical modelling strategy. The structural response for each cracked configuration is obtained using a geometrically non‐linear shell finite element analysis procedure. Four stress intensity factors, two for membrane behaviour and two for bending using Kirchhoff plate theory, are computed using an extension of the modified crack closure integral method. Crack trajectories are determined by applying the maximum tangential stress criterion. Crack growth results in localized mesh deletion, and the deletion regions are remeshed automatically using a newly developed all‐quadrilateral meshing algorithm. The effectiveness of the methodology, and its applicability to performing practical analyses of realistic structures, is demonstrated by simulating curvilinear crack growth in a fuselage panel that is representative of a typical narrow‐body aircraft. The predicted crack trajectory and fatigue life compare well with measurements of these same quantities from a full‐scale pressurized panel test.
Hypersingular quarter‐point boundary elements for crack problems
Authors: Sáez A. , Gallego R. , Dominguez J.
Published: August 2005

The present paper deals with the study and effective implementation for Stress Intensity Factor computation of a mixed boundary element approach based on the standard displacement integral equation and the hypersingular traction integral equation. Expressions for the evaluation of the hypersingular integrals along general curved quadratic line elements are presented. The integration is carried out by transformation of the hypersingular integrals into regular integrals, which are evaluated by standard quadratures, and simple singular integrals, which are integrated analytically. The generality of the method allows for the modelling of curved cracks and the use of straight line quarter‐point elements. The Stress Intensity Factors can be computed very accurately from the Crack Opening Displacement at collocation points extremely close to the crack tip. Several examples with different crack geometries are analyzed. The computed results show that the proposed approach for Stress Intensity Factors evaluation is simple, produces very accurate solutions and has little dependence on the size of the elements near the crack tip.
A robust incomplete factorization based on value and space constraints
Authors: Suarjana Made , Law Kincho H.
Published: August 2005

This paper describes an incomplete factorization method for computing a preconditioning matrix for the conjugate gradient method. The incomplete factorization satisfies the stability requirement that the incomplete factor remains positive definite throughout the factorization. When selecting a preconditioner for the conjugate gradient method, the number of non‐zero entries to be retained in the incomplete factor should be limited so that the amount of computations involving the preconditioning matrix is minimized. This paper introduces a method to generate an effective preconditioning matrix within a predefined space. Numerical results are presented to demonstrate the effectiveness of the incomplete factor as a preconditioner for the conjugate gradient method for solving large‐scale structural engineering problems.
Structural reliability optimization using an efficient safety index calculation procedure
Authors: Wang Liping , Grandhi Ramana V. , Hopkins Dale A.
Published: August 2005

The objective of this paper is to conduct reliability‐based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate examples.
A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh
Authors: Bailey C. , Cross M.
Published: August 2005

A Finite Volume (FV) procedure is described for solving the elastic solid mechanics equations in three dimensions on an unstructured mesh, for bodies undergoing thermal or mechanical loads. The FV procedure is developed in parallel with the conventional FE Galerkin procedure so that the differences in each approach may be clearly distinguished. The matrix form of the FV procedure is described, and is implemented in parallel with the FE procedure, both for two‐dimensional quadrilateral and three‐dimensional brick meshes. The FV and FE procedures are then compared against a range of benchmark problems that test the basic capability of the FV technique. It is shown to be approximately as accurate as the FE procedure on similar meshes, though its system matrix set‐up time is twice as long for a node by node set‐up procedure.
Reliable stress and fracture mechanics analysis of complex components using a h–p version of FEM
Authors: Andersson Börje , Falk Urban , Babus̆ka Ivo , Von Petersdorff Tobias
Published: August 2005

We develop effective approaches with which complex three‐dimensional components may be analysed with a high and virtually guaranteed accuracy. The main computational tool is a h‐p version of FEM practically realized with the p‐version program STRIPE having a mesh generator for automatic mesh refinement at edges and vertices. Use of advanced extraction methods and new theoretical approaches give exponential convergence rates for accuracies in all engineering data of interest. New methods for reliable calculation of local stresses and stress intensity data at edges and vertices to be used for fatigue dimensioning at fillets, damage tolerance assessment of three‐dimensional flaws, etc., are given. A complex real‐life problem is reliably analysed in order to demonstrate the practical usefulness of the procedures advocated. The technical details will be given in forthcoming papers.
h‐Hierarchical adaptive boundary element method using local reanalysis
Authors: Charafi A. , Neves A. C. , Wrobel L. C.
Published: August 2005

An adaptive boundary element scheme is developed using the concept of local reanalysis and h‐hierarchical functions for the construction of near‐optimal computational models. The use of local reanalysis in the error estimation guarantees the reliability of the modelling process while the use of quadratic and quartic h‐hieararchical elements guarantees the efficiency of the adaptive algorithm. The technique is developed for the elastic analysis of two‐dimensional models. Numerical examples show the rapid convergence of the results with a few refinement steps.
An explicit time integration technique for dynamic analyses
Authors: Pezeshk S. , Camp C. V.
Published: August 2005

A simple explicit solution technique for problems in structural dynamics, based on a Modified Trapezoidal rule Method (MTM) approximation of the governing ordinary differential equations, is developed. The resulting conditionally stable explicit method (MTM) can be easily implemented and is extremely simple to use. Particular attention is focused herein on the concept of numerical stability of the proposed method for a free‐vibrational response of a linear undamped Single‐Degree‐Of‐Freedom system (SDOF). To examine the effectiveness, strengths, and limitations of MTM, error analyses for the natural period, the displacement, the velocity and the associated phase angle for a free undamped simple mass–spring system are derived and compared with Modified Euler Method (MEM) and the well‐known Newmark Beta Method (NBM). Numerical examples for a SDOF system and a Multi‐Degree‐Of‐Freedom (MDOF) system are presented to illustrate the strengths and the limitations of the proposed method.
A unified parametric design approach to structural shape optimization
Authors: Zhang Wei‐Hong , Beckers Pierre , Fleury Claude
Published: August 2005

This paper presents a general parametric design approach for 2‐D shape optimization problems. This approach has been achieved by integrating practical design methodologies into numerical procedures. It is characterized by three features: (i) automatic selection of a minimum number of shape design variables based on the CAD geometric model; (ii) integration of sequential convex programming algorithms to solve equality constrained optimization problems; (iii) efficient sensitivity analysis by means of the improved semi‐analytical method. It is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities.

Numerical solutions are performed to demonstrate the applicability of the proposed approach. A discussion of the results is also given:
A consistent DXDR method for elastic‐plastic problems
Authors: Kadkhodayan M. , Zhang L. C.
Published: August 2005

This paper proposed a new efficient method, the consistent DXDR method, for analysing general elastic‐plastic problems. Two important factors in computational plasticity, the convergence and stability, were addressed. The method was constructed through a natural combination of two vital components: the DXDR algorithm which had been proved to be a powerful equation solver developed by the authors and a stable consistent algorithm for the integration of the constitutive equations of plasticity. Numerical examples demonstrated in detail the efficiency, accuracy, and stability attainable in solving various engineering problems.
A hybrid finite element analysis of interface cracks
Authors: Lee Jin , Gao Huajian
Published: August 2005

A versatile hybrid finite element scheme consisting of special crack‐tip elements and crack face contact elements is developed to analyse a partially closed interface crack between two dissimilar anisotropic elastic materials. The crack‐tip element incorporates higher‐order asymptotic solutions for an interfacial crack tip. These solutions are obtained from complex variable methods in Stroh formalism. For a closed interfacial crack tip, a generalized contact model in which the crack‐tip oscillation is eliminated is adopted in the calculation. The hybrid finite element modelling allows the stress singularity at an open and closed crack tip to be accurately treated. The accuracy and convergence of the developed scheme are tested with respect to the known interface crack solutions. Utilizing this numerical scheme, the stress intensity factors and contact zone are calculated for a finite interface crack between a laminated composite material.
Application of cubic Hermitian algorithms to boundary element analysis of heat conduction
Authors: Singh K. M. , Kalra M. S.
Published: August 2005

This paper presents the application of cubic Hermitian interpolation based finite element schemes for the time integration of the differential‐algebraic system arising in the dual reciprocity boundary element formulation of transient diffusion problems. Weighted residual procedure is used to obtain the desired recurrence relations. Numerical results presented for three representative problems involving different types of boundary conditions amply demonstrate the high accuracy of the cubic Hermitian schemes.
Numerical integration of non‐linear elastic multi‐body systems
Authors: Bauchau O. A. , Damilano G. , Theron N. J.
Published: August 2005

This paper is concerned with the modelling of nonlinear elastic multi‐body systems discretized using the finite element method. The formulation uses Cartesian co‐ordinates to represent the position of each elastic body with respect to a single inertial frame. The kinematic constraints among the various bodies of the system are enforced via the Lagrange multiplier technique. The resulting equations of motion are stiff, non‐linear, differential‐algebraic equations. The integration of these equations presents a real challenge as most available techniques are either numerically unstable, or present undesirable high frequency oscillations of a purely numerical origin. An approach is proposed in which the equations of motion are discretized so that they imply conservation of the total energy for the elastic components of the system, whereas the forces of constraint are discretized so that the work they perform vanishes exactly. The combination of these two features of the discretization guarantees the stability of the numerical integration process for non‐linear elastic multi‐body systems. Examples of the procedure are presented.
Non‐linear finite element formulation of kinematic limit analysis
Authors: Jiang Gong‐Liang
Published: August 2005

The objective of the research presented in this paper was to develop a general computational method for kinematic limit analysis problems that involve the determination of an optimal kinematically admissible velocity field of the studied structure under external loads. With the failure velocity field available, we can obtain a numerical estimate of the limit load exerted to the structure. The general kinematic limit analysis is characterized by the minimization of the plastic potential power dissipation functional of the mechanical system. This minimization problem was approached previously by linear and non‐linear programming schemes. In this paper, a new non‐linear solution scheme is described which is based on previous research on the regularized method. The regularized functional is a convex and non‐linear functional whose minimum represents a viscoplastic potential power dissipation, the velocity which minimizes this functional was proved to be kinematically admissible and can be obtained by the augmented Lagrangian method. This paper demonstrates that the non‐linear programming scheme is applicable to direct limit analysis. The basic idea of using this optimization method is to tranform the functional with a non‐linear term of the first‐order derivatives of the velocity to a functional in which this term is uncoupled with the strain rates, and in consequence the augmented Lagrangian (transformed functional) can be solved more easily. Some special problems related to incompressibility and discontinuity are discussed. A simple and accurate scheme is proposed to deal with the incompressibility problem and the problem of the linear Mohr–Coulomb yield surface in the principal stress space. Examples of plane stress and plane strain problems are given for von Mises and Mohr–Coulomb materials. Numerical results are provided in graphical form which serves to illustrate the kinematic admissibility. The limit loads obtained agreed well with the analytical results, which demonstrates the efficiency and accuracy of the non‐linear computational method presented.
Shape design sensitivity analysis via material derivative‐adjoint variable technique for 3‐D and 2‐D curved boundary elements
Authors: Burczyński T. , Kane J. H. , Balakrishna C.
Published: August 2005

A general approach to shape design sensitivity analysis of three‐ and two‐dimensional elastic solid objects is developed using the material derivative‐adjoint variable technique and boundary element method. The formulation of the problem is general and first‐order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional. Second‐order quadrilateral surface elements (for 3‐D problems) and quadratic boundary elements (for 2‐D problems) are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities. The accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points. Numerical results are presented to demonstrate the accuracy and efficiency of this approach.
Some observations on element performance in isochoric and dilatant plastic flow
Authors: De Borst René , Groen Arend E.
Published: August 2005

The performance of finite elements is scrutinized in isochoric and dilatant/contractant plastic flow. Standard displacement based elements, uniformly and selectively integrated elements, and elements with augmented strain rate fields are considered in plane‐strain, axisymmetric and three‐dimensional configurations with particular reference to the kinematic constraint imposed by dilatant/contractant plastic flow. It turns out that findings for isochoric deformations do not necessarily carry over to cases with plastic dilatancy or contraction. For the elements with augmented strain rate fields the danger of spurious mechanisms in ideal plasticity is brought out. A particular strategy which augments only the normal strain rates at the expense of a lesser improvement for the bending behaviour does not suffer from the possibility of spurious modes, while preserving the ability to accommodate dilatant/contractant plastic flow. Illustrative examples on plane‐strain, axisymmetry and three‐dimensional structures are included which support the above findings.
Equilibrium constrained assumed natural co‐ordinate strain plate elements
Authors: Jensen Daniel D. , Park K. C.
Published: August 2005

Equilibrium constraints are used to improve the stress accuracy of existing assumed natural‐co‐ordinate strain (ANS) plate elements. This is accomplished by introducing hierarchical degrees of freedom, which are subsequently eliminated by invoking kinematic consistency and element‐interior homogeneous equilibrium conditions. The resulting element enrichments are completely contained in the strain‐displacement matrix. In addition, the modified displacement shape functions become available for consistent mass and nodal load calculations, a feat not shared by some hybrid‐type elements. The performance of the present element (ANS‐EC) is compared with other plate bending elements. This performance comparison includes convergence studies for both displacements and stresses.
A continuum approach for second‐order shape design sensitivity of elastic solids with loaded boundaries
Authors: Chen Chin‐Jung , Choi Kyung K.
Published: August 2005

A second‐order shape design sensitivity analysis (DSA) method applicable to the shape change on the loaded boundaries is derived for three‐dimensional linear elastic solids using a continuum method with the material derivative. The continuum method is also used to derive mixed second‐order variations of stress and displacement performance measures with respect to shape design variables and distribution of non‐conservative traction loads, and also with respect to shape design variables and material properties. A shape design acceleration field is defined for the second‐order shape design sensitivity. Both direct differentiation and hybrid methods are presented in this paper. A numerical method, which can be implemented using established finite element analysis (FEA) codes, is developed. The feasibility and accuracy of the proposed second‐order shape DSA method has been demonstrated by solving a structural example‐doubly curved arch dam.
On advancing front mesh generation in three dimensions
Authors: Möller Peter , Hansbo Peter
Published: August 2005

This paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the advancing front concept in a natural way.
Boundary element method for thermoelastoplastic problems
Authors: Sladek J. , Sladek V.
Published: August 2005

In this paper, we present the boundary integral formulation for inelastic stationary thermoelasticity including thermally induced non‐homogeneity. Generally, the unique BEM formulation for crack problems is achieved by using the traction boundary integral equations which are now considered in a non‐singular form. Both the two‐ and three‐dimensional boundary value problems are analysed simultaneously. Numerical examples for 2‐D problems are presented, in order to illustrate the suitability of this boundary element approach in the inelastic thermoelasticity.
Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
Authors: Ibrahimbegović Adnan , Frey François , Kožar Ivica
Published: August 2005

Theoretical and computational aspects of vector‐like parametrization of three‐dimensional finite rotations, which uses only three rotation parameters, are examined in detail in this work. The relationship of the proposed parametrization with the intrinsic representation of finite rotations (via an orthogonal matrix) is clearly identified. Careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of Reissner's non‐linear beam theory. Pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2‐node three‐dimensional beam element. A number of numerical simulations in three‐dimensional finite rotation analysis are presented in order to illustrate the proposed approach.
Unified approach to numerical methods, part II: Finite elements, boundary methods, and their coupling
Authors: Herrera Ismael
Published: August 2005

This is the second in a series of three papers devoted to the presentation of a direct procedure of analysis of numerical methods for partial differential equations. The procedure consists of applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions. Here, the general Green's formulas for operators defined in discontinuous fields developed in the first article, are applied to formulate the method of weighted residuals for arbitrary linear operators. Finite elements, boundary methods, and general procedures for coupling finite elements and boundary methods are discussed.
Mixed finite element methods for computing groundwater velocities
Authors: Allen M. B. , Ewing R. E. , Koebbe J. V.
Published: August 2005

Central to the understanding of problems in water quality and quantity for effective management of water resources is the development of accurate numerical models to stimulate groundwater flows and contaminant transfer. We discuss several important difficulties arising in modeling of subsurface flow and present promising numerical procedures for alleviating these problems. Furthermore, we describe mixed‐finite element techniques for accurately approximating fluid velocities, and review computational results on a variety of hydrologic problems.
A compact finite element method for elastic bodies
Authors: Rose Milton E.
Published: August 2005

A nonconforming finite element method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose [1] is examined. A Condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.