Currently, the main tool for the simulation of forming processes is the finite element method. Unfortunately, for processes involving very large deformations, finite elements based on a Lagrangian formulation are problematic due to mesh distortion. Results become inaccurate and might even lose their physical meaning. In the 1980s, a new group of numerical methods emerged. This group is entitled meshless methods, and aims at avoiding problems related to the use of a mesh. The nodal-based approach of these methods does not restrict the relative motion of nodes by shape criteria related to elements. The goal of the research as presented in this thesis is to develop a meshless method for solving large deformations more efficiently than currently possible with finite elements. The first step in this research was to select a single meshless method for further developments. Therefore, three meshless shape functions and two numerical integration schemes were investigated in a comparative study. It can be concluded that diffuse meshless shape functions, like moving least squares and local maximum entropy approximations, are more accurate than simple linear interpolation upon a Delaunay triangle. However, the computational effort for these two diffuse functions is considerably higher. Concerning the numerical integration, a nodal integration scheme performs very well. Volumetric locking is absent and good accuracy is obtained. Therefore the linear triangle interpolation in combination with a nodal integration scheme was chosen for further development. For this combination, an extension to large deformations was presented. The new method, named Adaptive Smoothed Finite Elements (ASFEM), is based on a cloud of nodes following a Lagrangian description of motion and a triangulation algorithm that sets up the connectivity between nodes for each increment. The method was successfully tested on the simulation of a forging process and an extrusion process. No failure of the algorithm as a result of mesh distortion was encountered. Results compared accurately to reference solutions made with finite elements.
|Award date||7 Oct 2011|
|Place of Publication||Enschede, The Nejherlands|
|Publication status||Published - 7 Oct 2011|