Development of a new integration algorithm for parallel implementation of the finite element elasto-plastic analysis

Abstract

The accurate integration of stress-strain relations is an important factor in element analysis for elasto-plastic problems. The conventional method for this problem is the Euler algorithm which divides the whole integration process into a number of smaller substeps of equal size. It is difficult to control the errors in such integration scheme. In this paper, we will present a new algorithm for integrating strain-stress relations. It is based on the third and the fourth order Runge-Kutta method. This substepping scheme controls the errors in the integration process by adjusting the substep size automatically. In order to implement the substepping scheme on parallel systems, a parallel preconditioned conjugate gradient method is developed. The resulting algorithms have been implemented on a parallel environment defined by a cluster of workstation and their performance will be presented.