Comparison of Sensitivity Analysis Methods for Structural Shape Optimization

摘要

The primary motivation of this research is to compare different sensitivity analysis methods used in structural shape optimization. Gradient based optimization schemes are often driven by the accuracy of the gradients or sensitivities. If the sensitivities at each design point are accurate, the optimizer converges to the expected logical optimum solution. Sizing optimization as well as shape optimization routines are considered here because if the shape design variables are involved, sensitivity analysis is more challenging because most of the sensitivity analysis schemes require calculation of mesh sensitivities which are computationally expensive and tend to be less accurate. In this work, a cantilevered hollow circular rod problem is used to compare sensitivity analysis methods such as finite difference method, discrete analytic method and continuum sensitivity analysis. It is expected that continuum sensitivity analysis would be the most promising among these methods since it is proven to be more accurate than the other methods. The best scheme however would be an acceptable tradeoff between accuracy and computation cost and ease of implementation of the sensitivity analysis method within the optimization framework.