Abstract

This paper is concerned with the analysis as well as the numerical solution of the structural optimization problem for bilateral frictional contact problem where the static elasto-plastic material model with linear kinematic hardening rather than elastic material model is assumed. The displacement and stress of the bodies in elasto-plastic contact with a given friction are governed by the system of the coupled variational inequalities. In these problems usually very high stress appear along the surfaces in contact. It leads to wear or fatigue of the contacting surfaces. Therefore the aim of the topological optimization is to find such distribution of the material filling the body in contact to minimize the contact stress. Using von Mises yield function as well as the regularization and penalization techniques the original system of variational inequalities is transformed into the system of coupled nonlinear equations. The derivative of the cost functional with respect to the perturbation of the domain occupied by the body in contact is calculated using the material derivative method. Finite element method is used as the discretization method. In the numerical computations generalized Newton method is used to solve this contact problem. The level set method is used to describe and govern the evolution of the domain shape in the design space where the direction of the evolution is determined based on the calculated shape derivative. The results of computation are provided and discussed.

Abstract

This paper is focused on a new optimization variant of the shear strength reduction (OPT-SSR) in non-associated Mohr-Coulomb plasticity. The OPT-SSR method mimics the limit analysis problem and enables to compute the factor of safety without performing an elasto-plastic analysis. It is shown that this optimization problem is well defined and closely related to recently developed Davis approaches used in combination with the standard SSR method. Next, the duality between the static and kinematic principles of OPT-SSR is introduced. For the numerical solution, a regularization method is suggested.