Rapid stress analysis of geometrically complex domains using implicit meshing

Abstract

In an economically competitive industrial setting, it is advantageous to generate accurate engineering analysis results as rapidly as possible in order to minimize the design cycle time. For many structural problems, the goal of the computational analysis is to obtain the stress field. The standard tool for obtaining the stress field is the finite-element method. The task of obtaining the stress field using finite-element analysis is complicated by the fact that many industrial problems are geometrically complex and thus require a significant number of man hours to generate a finite-element mesh appropriate for stress analysis. This mesh generation task can be greatly simplified by using the method of implicit meshing. In conventional finite-element analysis, the given domain is explicitly meshed. In the implicit meshing method, the geometrically complex domain is embedded into a geometrically simpler domain. The finite-element method is then applied to the embedding domain. The original domain inherits its discretization from that of the embedding domain. Herein, the implicit meshing method is applied to the stress analysis of linear elasto-static problems. It is shown that with the appropriate choice of finite element and integration technique, the implicit meshing method can provide accurate stress fields with only moderate mesh refinement.