Stress Updates in Adaptive ALE (Arbitrary-Eulerian-Lagrangian) Meshes.
Abstract
The conservation laws, the constitutive equations and the equations of state for path dependent materials are formulated for an adaptive finite element method based on an arbitrary Lagrangian Eulerian description. Both the geometrical and material nonlinearities are included in this setting. A Petrov Galerkin method is developed for the stress update so that the history dependence and the resulting convective term on the stress tensor can be treated. A collocation weighted residual scheme is also developed. In addition, the tangent stiffness matrix for the equilibrium equation is derived from the principle of virtual work. Various methods for solving the finite element equations are presented and several numerical examples are analyzed to examine some features of the proposed method. The first are some elastic-plastic wave propagation problems which serve to check the correctness of the numerical scheme. The second is a flexural problem, the response of which is dominated by the formation of hinge lines. The adaptive mesh technique enables this problem to be solved with a much coarser mesh.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 02, 1986
- Accession Number
- ADA177027
Entities
People
- Hsiu-guo Chang
- T. Belytschko
- Wing K. Liu
Organizations
- Northwestern University