Topology optimization by minimizing the geometric average displacement

Abstract

Abstract On the problem of maximum stiffness design of linear elastic structural topology optimization, the objective of most existing models is to achieve minimum mean compliance. However, in most applications the desired results are ones that achieve minimum maximum displacement. In this article, the comparison of the optimum design results between the maximum displacement and the conventional mean compliance is carried out by an example of optimal cross-sectional design of a continuous beam. The result emphasizes the limitations of the conventional minimum compliance method. An improved index, geometric average displacement (GAD), is introduced in the article for linear elastic structural optimization models, with a GAD-based design model. Several examples are provided to demonstrate the effectiveness of the new proposed formulation. Keywords: topology optimizationgeometric average displacement (GAD)finite elements Acknowledgements This research is supported by the National Basic Research Program (973 Program) of China (no. 2011CB610304), National Natural Science Foundation of China (nos 11172052, 90816025) and the Research Fund for the Doctoral Program of Higher Education of China (grant no. 20090041110023). The financial support is gratefully acknowledged.