Elastoplastic analysis with adaptive boundary element method (original) (raw)
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On the Adaptive Coupling of Finite Elements and Boundary Elements for ElastoPlastic Analysis
The purpose of this paper is to present an adaptive FEM-BEM coupling method that is valid for both two- and three-dimensional e lasto-plastic analyses. The method takes care of the evolution of the elastic a nd plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub-domains in the standard FEM-BEM coupling approaches. The method estimates the FEM and BEM sub-domains and automatically generates/adapts the FEM and BEM meshes/sub-domains, according to the state of computation. The results for two- and three- dimensional application s in elasto-plasticity show the practicality and the efficiency of the adaptive FEM -BEM coupling method.
On the use of the boundary element method for elastoplastic, large deformation problems
International Journal for Numerical Methods in Engineering, 1988
The boundary element method is applied to large deformation problems typical in industrial forming problems. A form of Betti's theorem relevant to an updated Lagrangian type of solution procedure is established as the basis for the boundary element formulation. Equilibrium iterations are needed in each load step. All non-linear terms are moved to the right-hand side and the boundary element method can be used. Cross-anisotropy is assumed where Hill's yield criterion is adopted together with isotropic hardening. The investigation has shown that the boundary element method is applicable to this type of problem, giving good results within reasonable computer time.
A new boundary element technique without domain integrals for elastoplastic solids
International journal for numerical …, 2005
A simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements, namely, to use the Green's functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions, respectively. In this way, domain integrals are completely avoided in the boundary integral equations. Though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation, the elastoplastic analysis reduces, in essence, to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations (the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law). Numerical examples, using J 2 -flow theory with linear hardening, demonstrate that the proposed method retains all the advantages related to boundary element formulations, is stable and performs well.
Advanced boundary element analysis of two- and three-dimensional problems of elasto-plasticity
International Journal for Numerical Methods in Engineering, 1986
An advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach. The iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment. In the present analysis the geometry and functions are represented by higher order (quadratic) shape functions to model complex geometries and rapid functional variations accurately. The methods of numerical integration of the kernels, particularly the singular type, are substantially improved by devising suitable automatic sub-segmentation routines that incorporate the recent developments in mapping procedures. The formulations have been implemented for two-dimensional plane stress, plane strain and three-dimensional elasto-plasticity problems.
International Journal for Numerical Methods in Engineering, 2009
The purpose of this paper is to present an adaptive finite element-boundary element method (FEM-BEM) coupling method that is valid for both two-and three-dimensional elasto-plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub-domains in the standard FEM-BEM coupling approaches. The method estimates the FEM and BEM sub-domains and automatically generates/adapts the FEM and BEM meshes/sub-domains, according to the state of computation. The results for two-and three-dimensional applications in elasto-plasticity show the practicality and the efficiency of the adaptive FEM-BEM coupling method.
Computers & Structures, 1992
Mesh refinement has become a standard tool in practical engineering stress analysis problems. In this paper, an algorithm is presented which combines the process of mesh refinement and redistribution in order to position the new nodes at asymptotically optimal locations. The algorithm is described in the context of a two-dimensional boundary element treatment of the equations of linear elasticity. Two examples are presented which verify the algorithm in the case of problems with and without singularities.
Elastoplastic analysis of plate with boundary element method
International Journal of Mechanical Engineering and Technology (IJMET), 2018
This work is the development of boundary element method for elastoplastic plate analysis to include elastic-linear hardening material. The plate is subjected to bending, in-plane and combined bending and in-plane. The plastic zone is evaluated by using von Mises criterion. The cell discretization is implemented to solve numerically the domain integral caused by plasticity. To evaluate the nonlinear term in the formulation of the boundary element, a total incremental technique is implemented. The capability of the development in this work will be presented by having numerical examples.
A convergent adaptive finite element method for the primal problem of elastoplasticity
International Journal for Numerical Methods in Engineering, 2006
The boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some nondifferentiable functional. This paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction and, up to higher order terms, the R-linear convergence of the stresses with respect to the number of loops. Applications include several plasticity models: linear isotropic-kinematic hardening, linear kinematic hardening, and multisurface plasticity as model for nonlinear hardening laws. For perfect plasticity, the adaptive algorithm yields strong convergence of the stresses. Numerical examples confirm an improved linear convergence rate and study the performance of the algorithm in comparison with the more frequently applied maximum refinement rule. Copyright © 2006 John Wiley & Sons, Ltd.
Computational Mechanics, 1995
This paper presents a novel method for error estimation and h-version adaptive mesh refinement for potential problems which are solved by the boundary element method (BEM). Special sensitivities, denoted as mesh sensitivities, are used to evaluate a posteriori error indicators for each element, and a global error estimator. A mesh sensitivity is the sensitivity of a physical quantity at a boundary node with respect to perturbation of the mesh. The element error indicators for all the elements can be evaluated from these mesh sensitivities. Mesh refinement can then be performed by using these element error indicators as guides. The method presented here is suitable for both potential and elastostatics problems, and can be applied for adaptive mesh refinement with either linear or quadratic boundary elements. For potential problems, the physical quantities are potential and/or flux; for elastostatics problems, the physical quantities are tractions/displacements (or tangential derivatives of displacements). In this paper, the focus is on potential problems with linear elements, and the proposed method is validated with two illustrative examples. However, it is easy to extend these ideas to elastostatics problems and to quadratic elements. 1 Introduction This paper proposes the use of mesh sensitivities as error indicators, and the use of these indicators to carry out an h-version adaptive mesh refinement procedure. The analysis method of interest here is the boundary element method (BEM). The focus here is on potential problems, which is related to