Local adaptive refinement method applied to solid mechanics

A good spatial discretization is of prime interest in the accuracy of the Finite Element Method. This paper presents a new refinement criterion dedicated to an h-type refinement method called Conforming Hierarchical Adaptive Refinement MethodS (CHARMS) and applied to solid mechanics. This method produces conformally refined meshes and deals with refinement from a basis function point of view. The proposed refinement criterion allow adaptive refinement where the mesh is still too coarse and where a strain or a stress field has a large value or a large gradient. The sensitivity of the criterion to the value or to the gradient ca be adjusted. The method and the criteria are validated through 2-D test cases. One limitation of the h-adaptive refinement method is highlighted: the discretization of boundary curves.

An Adaptive EFG-FE Computational Model for Thermal Elasto-Plastic Frictional Contact Problems

An adaptive meshless element-free Galerkin-finite element (EFG-FE) coupling model for thermal elasto-plastic contact problems is developed to investigate the influences of the steady-state frictional heating on the contact performance of two contacting bodies. The thermal elasto-plastic contact problems using the initial stiffness method is presented. The local adaptive refinement strategy and the strain energy gradient-based error estimation for EFG-FE coupling method are combined. The adaptive meshless model takes into account the temperature variation, micro plastic flow, and the coupled thermo-elasto-plastic behavior of the materials, considering the strain-hardening property of the materials and temperature-dependent yield strength. The adaptive model is verified through the contact analysis of a cylinder with an elasto-plastic plane. The thermal effects on the contact pressure, stresses distributions with certain frictional heat inputs are studied. The results show that the accuracy of the solutions from the adaptive refinement model is satisfactory but the cost of the CPU time is much less than that for the uniform refinement calculation.