The arbitrary Lagrangian-Eulerian (ALE) approach and its finite element formulation are implemented for the analysis of nonlinear structures. In the ALE formulation material displacement is described as the sum of mesh displacement and relative displacement. The former is the Eulerian displacement by which we control meshes to reduce the numerical errors resulted from mesh distortions during the deformation process. And the latter represents the Lagrangian displacement that is concerned with the deformation. According to the ALE description, a computer program is developed for the static analysis of elastoplastic, large deformation problems. Two mesh controllers are included in the program. One is based on the Winslow algorithm which can be applied only to regular meshes. Another is the method proposed in this thesis for irregular meshes, which is an empirical algorithm based on the measure of mesh distortion and displacements in the previous loading step.
Three examples are solved with and without mesh control. The results are in good agreement with those from the ABAQUS program but the mesh distortion is considerably reduced in case of controlled meshes. This illustrates that the ALE approach might be useful for problems where severe mesh distortion is anticipated. Further research will be required for the treatment of nonlinear boundary conditions and the refinement of the empirical algorithm.
