Theory and simulation of topology optimization design for anisotropic structure

A new theoretic model of the topology optimization for the anisotropic continuum structure was established, and the augmented Lagranian method was employed firstly to solve the problem of the inequality constraint. By the combination of material derivative, level set function and augmented Lagrangian multipliers method, a novel topology optimization approach of the sensitivity analysis was proposed. The evolution of the structural design boundary could be controlled by the artificial velocity which makes the objective functional descent. The level set surface of a higher-dimensional function could be moved up and down without changing its topology structure, but the optimization boundaries embedded on level set function could automatically modify the topology structure by the boundaries merging and breaking. The extensively studied 2D examples were employed to demonstrate the validity of the present methodologies. The conclusions indicate this investigation will provide an important theoretic foundation for the topological optimization of the complex constructive relationship material.