On design sensitivity analysis based on EFG method in mechanical shape optimization

The sensitivity analysis is a fundamental requirement for shape optimization. In this paper, the design sensitivity analysis based on element free Galerkin method is proposed, and the derivative of shape function with respect to design variable is obtained by utilizing the ideas of direct differential approach and semi-analytical method. The accuracy and consistency, computational costs and implementations efforts of building computation approaches is discussed. The most advantage of the approach presented is that the calculating process of DSA is similar to the solving process of EFG method. This approach can also be easily extended to 3-D. The example, which has the exact solution, is presented to test the derived arithmetic. The results obtained that there exists excellent agreement between the analytical solution and numerical results.