Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua. (English) Zbl 0626.73076

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 linearized 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.


74S05 Finite element methods applied to problems in solid mechanics
76M99 Basic methods in fluid mechanics
74B20 Nonlinear elasticity
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids


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