Level set based method for simultaneous optimization of material property and topology of functionally graded structures

ABSTRACT

A level set based method is proposed for simultaneous optimization of material property and topology of functionally graded structures. The objective is to determine the optimal material property (via material volume fraction) and structural topology to maximize the performance of the structure in a given application. In the proposed method volume fraction and structural boundary are considered as design variables, with the former being discretized as a scaler field and the latter being implicitly represented by 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.

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INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

Keywords:
dynamic implicit boundary, functionally graded materials, heterogeneous objects, level set method, topology optimization