Abstract

The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed.

Abstract

The stability of composite material plates is being developed following basically two procedures: finite element analysis (FEA) and mathematical approaches using the energy method. The advantage of the finite element models is that they can be used with any geometry, configuration and load combination. However, it requires a significant pre-processing, computation and post-processing time of the results. On the other hand, analytical methods require much less time to obtain the results compared to them, but are limited to just basic geometries, such as rectangular panels without lightening holes. In this work, an analytical approach based on the energy method for buckling analysis of composite panels with holes has been developed. The innovation of this method is the inclusion of holes with different shapes in any position of a trapezoidal panel submitted to any in-plane loads combination. An exhaustive validation has been performed using FEA models and test results.