Inverse Pre-Deformation of Finite Element Mesh for Large Deformation Analysis

In the finite element analysis that deals with large deformation, the process usually produces distorted elements at the later stages of the analysis. These distorted elements lead to analysis problems, such as inaccurate solutions, slow convergence and premature termination of the analysis. This paper proposes a new mesh generation algorithm to mesh the input part for pure Lagrangian analysis, where our goal is to improve the shape quality of the elements during the analysis in order to reduce the number of inverted elements as well as to decrease the chance of premature termination of the analysis. One pre-analysis is required to collect the geometric information and stress information in the analysis. The proposed method then uses the deformed shape boundary known from the pre-analysis, finds the optimal node locations, considers the stress information to control the mesh sizes as well as control the mesh directionality, generates meshes on the deformed boundary, and finally, maps the elements back to the undeformed boundary using inverse bilinear mapping. The proposed method has been tested on two forging example problems. The results indicate that the method can improve the shape quality of the elements during the analysis, and consequently extend the life of the analysis, which reducing the chance of premature analysis termination.