Efficient parallel algorithms for elastic–plastic finite element analysis

Abstract

This paper presents our new development of parallel finite element algorithms for elastic-plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic-plastic stress-strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic-plastic problems whose size is much too large for a single workstation becomes possible.

Study of micro flexible rolling based on grained inhomogeneity

“…The analysis of such a nonlinear elastic-plastic problem can proceed in an incremental manner. Specifically, the loading is applied in successive incremental stages and an iterative approach is adopted to find the elastic-plastic equilibrium at each increment [66].…”

Analysis for Composite Material in Plate-Cone Reticulated Shell

“…the strain weight of the k layer plate, and t k is the thickness of the k layer plate. According to the method of reference [1], the multilayer plate's element stiffness matrix of plane stress problems and the equivalent elasticity stiffness matrix of multilayer plate can be deduced.…”

“…The integral of the multilayer plate's element stiffness matrix in sheet curving problems also should be ran in every layer. Refer to the Reference [1], the equivalent curve stiffness matrix [ ] D ~and the apparent formula of element stiffness matrix is can be deduced.…”