Dynamic shape optimization based on continuum derivatives

Material derivatives of structural volume and natural frequencies are obtained based on continuum derivatives. In order to carry out dynamic shape optimization for continuum structure, virtual displacements of control point are selected as the design variables, approximate model is constructed by Taylor series expansion, move limit of design variables are adopted to ensure algorithmic reliability. The method can be implemented not by modifying source program of finite element method and by less finite element analysis. Numerical examples are shown to demonstrate the efficiency and generality of the method, the method is fit for some kinds of dynamic shape optimization problem.