Numerical method for shape optimization using meshfree method

A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element-based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.