bluuebunny/crossref_metadata_2025_split huggingface dataset:
A continuum‐based finite element formulation for the implicit solution of multibody, large deformation‐frictional contact problems
Authors: Laursen T. A. , Simo J. C. 
Published: August 2005

AbstractIn this paper, a formulation is presented for the finite element treatment of multibody, large deformation frictional contact problems. The term multibody is used to mean that when two bodies mechanically contact, both may be deformable. A novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first, before deriving the corresponding finite element equations This feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general. In particular, the approach yields a characterization of the frictional constraint (assuming a Coulomb law) suitable for arbitrary discretizations in either two or three dimensions. A geometric framework is constructed within which both frictionless and frictional response are naturally described, making subsequent finite element discretization a straightforward substitution of finite‐dimensional solution spaces for their continuum counterparts. To our knowledge, this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature.The development includes exact linearization of the statement of virtual work, which enables optimal convergence properties for Newton‐Raphson solution strategies, and which appears to be highly desirable (if not essential) for the general robustness of implicit finite element techniques. Since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur, the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non‐linear behaviour. This assertion is substantiated through presentation of a variety of examples in both two and three dimensions.
Two‐dimensional elastoplasticity: Approximation by mixed finite elements
Authors: Weissman Shmuel L. , Jamjian Michel 
Published: August 2005

AbstractTwo‐dimensional elastoplastic problems are used to assess the performance of a family of mixed finite elements in the non‐linear regime. In particular, four‐node bilinear quadrilateral elements that exhibit high accuracy in coarse meshes are used to simulate plane stress, plane strain, axisymmetric and (shear‐deformable) plate bending problems. The excellent performance of these elements is demonstrated with a number of discriminating examples selected from the literature. In addition, agreement is observed in the limit load predicted by the axisymmetric solid and plate bending elements.
Incremental kinematics for finite element applications
Authors: Rashid M. M. 
Published: August 2005

AbstractA kinematical algorithm is proposed in which the input is the incremental deformation gradient corresponding to an increment in motion for a time step, and the output is a constant rate‐of‐stretching tensor and a rotation tensor. The concept of algorithmic objectivity is discussed, with a stronger statement of objectivity than those advanced in previous works being set forth. The importance of strong objectivity is illustrated for applications in which moderately large rotation increments are to be expected. Accuracy of the proposed algorithm is discussed and illustrated with example calculations, and it is shown that the accuracy of the algorithm may be extended to arbitrary order. Also, the computational effort associated with the proposed algorithm is seen to compare favourably to that of other algorithms.
A new first‐order interior feasible direction method for structural optimization
Authors: Stander Nielen , Snyman J. A. 
Published: August 2005

AbstractA new interior feasible direction method for optimization problems with linear objective functions but non‐linear constraints is proposed. The method is particularly suitable for weight minimization problems in structural design where the design variables are the cross‐sectional areas of members and arbitrary stress and displacement constraints are applied. Four truss structures are analysed and in each case the minimum weight consistent with or lower than that currently available in the literature is achieved. Although still expensive in its current version, the method is comparable in cost and robustness with other methods such as the ‘trust region’ multiplier method. Apart from one tolerance value, a reconnaissance parameter needs to be specified. The fact that the same value of the parameter was used for all the examples, and that the method is relatively insensitive to the choice thereof, confirms the robustness of the method.
Modelling edge effects with the C0 plate bending elements: Part 1. Analysis of the mechanism
Authors: Briassoulis D. 
Published: August 2005

AbstractThe behaviour of the C0 plate elements in modelling edge zone effects is analysed by utilizing the classical and a recently proposed formulation. Boundary layers are shown to develop under the activation of an edge zone moment redistribution mechanism, being part of a more generalized moment redistribution mechanism triggered by the in‐plane twisting stiffness of the model.
A finite volume format for structural mechanics
Authors: Oñate E. , Cervera M. , Zienkiewicz O. C. 
Published: August 2005

AbstractA general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non‐Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
Element‐free Galerkin methods
Authors: Belytschko T. , Lu Y. Y. , Gu L. 
Published: August 2005

AbstractAn element‐free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least‐squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least‐squares interpolants and the choices of the weight function are also discussed in this paper.
Design sensitivity analysis of elastoplastic structures
Authors: Ohsaki M. , Arora J. S. 
Published: August 2005

AbstractAn iterative and incremental algorithm is presented for the Design Sensitivity Analysis (DSA) of elastoplastic structures. Geometrical non‐linearity is included in the formulation, and the structure may be subjected to a cyclic loading. The key concept is discussed using an elastoplastic truss. It is shown that the Design Sensitivity Coefficients (DSCs) are path‐dependent and discontinuous at the time at which yielding takes place in a member (yield time). In the proposed algorithm, the yield time is considered to be a function of the design variables. In this way, the discontinuity in the DSCs at the material transition points can be overcome in a simple and routine way. Incremental response analysis and DSA are carried out simultaneously using the Newton–Raphson type iterative procedure. Since the proposed algorithm is completely consistent with the analysis procedure, it can be implemented into an existing code for structural analysis. Application to distributed parameter structures with kinematic and/or isotropic hardening is discussed using the von Mises yield condition and the elastic‐predictor radial‐return method. DSA is carried out for a ten‐bar truss with a piecewise linear constitutive relation. It is shown that the DSCs found using the proposed method agree quite well with those calculated by the central difference method. Finally, an alternate method without any iteration for DSA is proposed and the results from the two methods are compared.
An approach to refining three‐dimensional tetrahedral meshes based on Delaunay transformations
Authors: Golias N. A. , Tsiboukis T. D. 
Published: August 2005

AbstractA technique for refining three‐dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non‐convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi–Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3‐D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.
Validation of a posteriori error estimators by numerical approach
Authors: Babuška I. , Strouboulis T. , Upadhyay C. S. , Gangaraj S. K. , Copps K. 
Published: August 2005

AbstractA numerical methodology which determines the quality (or robustness) of a posteriori error estimators is described. The methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems, namely, the local geometry of the grid and the structure of the solution. The methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations.
A consistent formulation for the integration of combined plasticity and creep
Authors: Duxbury Paul , Crook Tony , Lyons Paul 
Published: August 2005

AbstractWithin the context of the consistent tangent update, this paper outlines a stress update algorithm for combined creep and plasticity. The algorithm is implicit, providing unconditional stability, and utilizes local Newton iteration to solve SCALAR forms of the coupled constitutive equations for the creep and plastic strain increments. The tangent for the local iteration is obtained accurately providing quadratic convergence at the Gauss point level. Quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep. Further, combination with an automatic time‐stepping scheme provides an efficient, stable, accurate and robust computational algorithm. The algorithm has been implemented in the general purpose FE package LUSAS1.
An effective two‐dimensional frictional contact model for arbitrary curved geometry
Authors: Saleeb A. F. , Chen K. , Chang T. Y. P. 
Published: August 2005

AbstractA finite element model is developed on the basis of a variational formulation of the perturbed Lagrange type and the classical Coulomb law of friction, for the analysis of frictional contact problems in two dimensions. The model accounts for all geometric/kinematic non‐linearities associated with large sliding motions as well as arbitrary contact‐surface curvatures. Explicit forms for the contact force and tangent stiffness operators and a penalty‐type format is utilized in the implementation. An extensive number of numerical simulations are used to demonstrate the effectiveness and practical usefulness of the model.
Topology design with optimized, self‐adaptive materials
Authors: Jog C. S. , Haber R. B. , Bendsøe M. P. 
Published: August 2005

AbstractSignificant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems. We study the optimal shape design of a two‐dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material. The macroscopic version of this problem is not well‐posed if no restrictions are placed on the structure topoiogy; relaxation of the optimization problem via quasiconvexification or homogenization methods is required. The effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material.A combined analytical‐computational approach is proposed to solve the relaxed optimization problem. Both stress and displacement analysis methods are presented. Since rank‐2 layered composites are known to achieve optimal energy bounds, we restrict the design space to this class of microstructures whose effective properties can easily be determined in explicit form. We develop a series of reduced problems by sequentially interchanging extremization operators and analytically optimizing the microstructural design fields. This results in optimization problems involving the distribution of an adaptive material that continuously optimizes its microstructure in response to the current state of stress or strain. A further reduced problem, involving only the response field, can be obtained in the stress‐based approach, but the requisite interchange of extremization operators is not valid in the case of the displacement‐based model.Finite element optimization procedures based on the reduced displacement formulation are developed and numerical solutions are presented. Care must be taken in selecting the discrete function spaces for the design density and displacement response, since the reduced problem is a two‐field, mixed variational problem. An improper choice for the solution space leads to instabilities in the optimal design similar to those encountered in mixed formulations of the Stokes problem.
On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua
Authors: Perić Djordje , Yu Jianguo , Owen D. R. J. 
Published: August 2005

AbstractThe a posteriori error estimates based on the post‐processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J2‐elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post‐instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h‐refinement and almost uniform error distribution in all considered error norms.
Solution techniques for the p‐version of the adaptive finite element method
Authors: Papadrakakis Manolis , Babilis George P. 
Published: August 2005

AbstractThis paper investigates the performance of a class of methods based on the Preconditioned Conjugate Gradient (PCG) method for the solution of large and sparse systems of linear equations which arise from the p‐version of the adaptive finite element method. The hierarchical type of preconditioning used in the past is extended to the SSOR and incomplete factorization type preconditioning and applied with a global handling of the stiffness matrix. The paper also presents some new ideas on Domain Decomposition (DD) matrix‐handling techniques, whereby the explicit formulation of the resulting Schur complement is avoided by utilizing the PCG method with efficient preconditioners and by processing separately on the coarse and the fine mesh. The suitability of the methods to the p‐version of the adaptive finite element method is demonstrated through extensive numerical tests in two dimensions.
A new energy and momentum conserving algorithm for the non‐linear dynamics of shells
Authors: Simo J. C. , Tarnow N. 
Published: August 2005

AbstractA numerical time‐integration scheme for the dynamics of non‐linear elastic shells is presented that simultaneously and independent of the time‐step size inherits exactly the conservation laws of total linear, total angular momentum as well as total energy. The proposed technique generalizes to non‐linear shells recent work of the authors on non‐linear elastodynamics and is ideally suited for long‐term/large‐scale simulations. The algorithm is second‐order accurate and can be immediately extended with no modification to a fourth‐order accurate scheme. The property of exact energy conservation induces a strong notion of non‐linear numerical stability which manifests itself in actual simulations. The superior performance of the proposed scheme method relative to conventional time‐integrators is demonstrated in numerical simulations exhibiting large strains coupled with a large overall rigid motion. These numerical experiments show that symplectic schemes often regarded as unconditionally stable, such as the mid‐point rule, can exhibit a dramatic blow‐up in finite time while the present method remains perfectly stable.
Dynamic stability of non‐linear shells of revolution under consideration of the fluid–soil–structure interaction
Authors: Wunderlich W. , Schäpertöns B. , Temme C. 
Published: August 2005

AbstractThe dynamic behaviour of liquid‐filled shells of revolution is investigated considering the soil–structure interaction and the fluid–structure interaction, respectively. In the circumferential direction the loads and variables are approximated by Fourier series. The shell is modelled through shell ring elements including non‐linear behaviour, coupled with isoparametric continuum ring elements and special infinite elements for the soil and isoparametric pressure ring elements for the fluid. Transient loadings like earthquake excitation and the non‐linearities of the shell and the soil require an analysis in the time domain. To reduce the size of the problem, linear parts of the system are condensed by the substructure technique. The soil region is divided into two parts, a near field permitting non‐linearities like plastification or uplifting of the shell, and a far field for the treatment of radiation of energy.The boundary conditions for the shell footing have a strong influence on the distribution of the axial membrane forces and, hence, on the stability limit, which is mostly governed by plastic collapse and caused by the dynamically activated pressure acting on the tank wall. It is shown how the soil properties influence the dynamic stability of the shell under harmonic excitation and under realistic earthquake motion.
Numerical methods for optimal control of impressed cathodic protection systems
Authors: Hou L. Steven , Sun W. 
Published: August 2005

AbstractSome optimal control problems arising from impressed cathodic protection systems are considered. Our objective is to find the location of anodes and the current density on the anodes that yield an optimal potential distribution on the cathode. We present a simple formula for the linear model and a gradient algorithm for the non‐linear model. Boundary element methods are employed for the numerical calculation.
A new concept in two‐dimensional auto‐adaptative mesh generation
Authors: Remondini L. , Trompette P. , Leon J. C. , Noel F. 
Published: August 2005

AbstractThe new method presented here is capable of building finite element meshes and managing their adaptation simultaneously to the object load case and geometry before any calculations, i.e. an a priori mesh adaptation is conducted. The principle relies on an analogy between a finite element mesh and the equilibrium position of a network of branches. Each branch is adequately sized by setting force–length ratios, called force densities. Starting from these data, the nodal co‐ordinates are obtained through the solution of a linear system which describes the equilibrium state of the net. This method seems very attractive since the only given data are: a connectivity table, the number of boundary and interior nodes and a geometrical description of the boundaries.It is also demonstrated how to obtain the equilibrium nodal positions when boundary nodes are allowed to slide and evolution laws of force densities cope with punctual forces and geometric singularities. A comparison of results is conducted between meshes issued by the new technique and those obtained with standard FE codes.
A Lanczos‐based method for structural dynamic reanalysis problems
Authors: Carey Cheryl M. M. , Golub Gene H. , Law Kincho H. 
Published: August 2005

AbstractIn this paper, a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented. The method, which is based on the block Lanczos algorithm, is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs. Given the solution to the original system Ax = λx, procedures are developed for the modified standard eigenvalue Problem (A + ΔA)x̄ = λx̄, where

ΔA = ΣjBSjBT, where Sj = S ∈ ℛp × p, p ≪ n and B ∈ ℛn × p is constant for all the perturbations Sj.
ΔA = ΣiΣj BiSjBiT, where Bi ∈ ℛn × p may vary with the pertubations Sj.
The procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem. Numerical examples are given to demonstrate the applications of the method.
Elastoacoustic analysis of submerged fluid‐filled thin shells
Authors: Jeans R. A. , Mathews I. C. 
Published: August 2005

AbstractThe analysis of fluid‐filled thin shells is discussed in this paper. It is well known that a boundary element formulation of the exterior acoustic problem becomes ill‐conditioned at certain critical frequencies. For a coupled boundary‐element/finite element formulation of the coupled elasioacoustic problem the formulation suffers from the same numerical ill‐conditioning. However, for fluid‐filled thin shell problems the resulting coupled formulation is unique at all frequencies. In this paper the condition numbers of the coupled and uncoupled formulations are calculated and the uniqueness of the coupled formulation is demonstrated for submerged fluid‐filled thin shells.