Arbitrary lagrangian-eulerian petrov-galerkin finite elements for nonlinear continua

Abstract

The fundamental arbitrary Lagrangian-Eulerian (ALE) mechanics and its finite element formulation are given. The tangential stiffness matrix, which is shown to be composed of the linarized material response matrix, the geometrical stiffness matrix, and the ALE transport matrix are derived from a consistent linearization procedure. Various numerical methods for the ALE finite element equations are then presented, and several examples are analyzed to examine some features of the method. © 1988.