Adaptive numerical analysis in primal elastoplasticity with hardening
ثبت نشده
چکیده
The quasi-static viscoplastic resp. elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh-refining in the spatial discretization. Within one time-step of an implicit time-discretization, the finite element method leads to a minimisation problem for non-smooth convex functions on discrete subspaces. For piecewise constant resp. affine ansatz functions, the stress resp. displacement approximations are experimentally and theoretically shown to converge linearly. An a posteriori error estimate then justifies an automatic adaptive mesh-refining algorithm. Numerical examples support the superiority of the adapted mesh. © 1999 Published by Elsevier Science S.A. All rights reserved.
منابع مشابه
A Convergent Adaptive Finite Element Method for the Primal Problem of Elastoplasticity
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 non-differentiable 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−l...
متن کاملAdaptive Finite Elements in Elastoplasticity with Mechanical Error Indicators and Neumann-type Estimators
Abstract: Many interesting tasks in technology need the solution of complex boundary value problems modeled by the mathematical theory of elasticity and elastoplasticity. Error controlled adaptive strategies should be used in order to achieve a prescribed accuracy of the computed solutions at minimum cost. In this paper, locally computed residual error indicators in the primal form of the finit...
متن کاملA Newton-Krylov-FETI-DP Method with an Adaptive Coarse Space Applied to Elastoplasticity
We consider a Newton-Krylov-FETI-DP algorithm to solve problems in elastoplasticity. First, the material model and its discretization will be described. The model contains a Prandtl-Reuss flow rule and a von Mises flow function. We restrict ourselves to the case of perfect elastoplasticity; thus, there is no hardening. For more information on elastoplasticity; see, e.g., Carstensen and Klose [2...
متن کاملOn the Formulation of Closest-Point Projection Algorithms in Elastoplasticity
We present in this paper the characterization of the variational structure behind the discrete equations defining the closest-point projection approximation in elastoplasticity. Rate-independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite strain multiplicative plasticity. Primal variational prin...
متن کاملOptimal Control of Static Elastoplasticity in Primal Formulation
An optimal control problem of static plasticity with linear kinematic hardening and von Mises yield condition is studied. The problem is treated in its primal formulation, where the state system is a variational inequality of the second kind. First-order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by Hub...
متن کامل