Finite element mesh optimization using genetic algorithms

Abstract

In finite element analysis, structures are modeled as meshes of elements and nodes appropriate for the geometry, boundaries and loading of each structure. Typically, it is desirable to have a mesh which is finer in parts of the structure where stress gradients are high and coarser where such gradients are low. This is usually done by experienced engineers using intuition and previous experience. Otherwise, a fine mesh throughout the structure can be used which results in high computational costs. In this work, the possibility of using genetic algorithms for optimizing finite-element meshes is studied. The method is implemented on a number of simple loaded structures. The meshes used are generated using a number of parameters that can be varied randomly. Then the parameters are varied using operators appropriate to genetic algorithms such that the value of an objective function is minimized within a defined precision and iteration limit. The objective function used in this study is an energy-based error norm. The results obtained with this method are compared to those obtained from a commercial finite element package that incorporates its own mesh optimization algorithms.