Simultaneous optimization of the material properties and the topology of functionally graded structures

A level set based method is proposed for the simultaneous optimization of the material properties and the topology of functionally graded structures. The objective of the present study is to determine the optimal material properties (via the material volume fractions) and the structural topology to maximize the performance of the structure in a given application. In the proposed method, the volume fraction and the structural boundary are considered as the design variables, with the former being discretized as a scalar field and the latter being implicitly represented by the level set method. To perform simultaneous optimization, the two design variables are integrated into a common objective functional. Sensitivity analysis is conducted to obtain the descent directions. The optimization process is then expressed as the solution to a coupled Hamilton-Jacobi equation and diffusion partial differential equation. Numerical results are provided for the problem of mean compliance optimization in two dimensions.