基于材料场级数展开的结构动力学拓扑优化

Structural dynamic response optimization under steady-state and transient excitations is of major concern in the design of aerospace structures. Traditional gradient based topology optimization methods usually require complex sensitivity derivations, which makes the selection of dynamic optimization index limited, and the complicated dynamic response often makes the optimization problem fall into the local optimal solution. In this paper, therefore, the steady-state and transient dynamic topology optimization problems are formulated and solved effectively with the material-field series expansion strategy and non-gradient optimization algorithm, In the implementation of dynamic topology optimization, the material-field series expansion technique is used to reduce the dimension of the structure topology in the mapping space, which greatly reduces the design variables, and then the sequential Kriging surrogate model algorithm is adopted to solve the optimization problem. The examples show that the proposed method can effectively deal with the topology optimization problems of structural steady-state and transient dynamics without structural dynamic response sensitivity analysis.