如何通过结构优化实现稳态与瞬态动力载荷下动力学响应的有效抑制是航空航天结构设计中关心的重要问题之一。传统基于梯度的拓扑优化方法因需要复杂的灵敏度推导使得动力学优化指标选择受限,并且复杂的动力学响应也使得优化问题往往陷入局部最优解。本文基于材料场级数展开策略和非梯度优化算法有效实现了结构稳态和瞬态动力学拓扑优化问题的求解。在动力学拓扑优化问题中,采用材料场级数展开技术将结构拓扑在特征映射空间进行降维表征,大幅度减少设计变量,进而采用序列Kriging代理模型算法求解。通过给出的拓扑优化算例,验证了该方法能够在不需要结构动响应灵敏度分析的前提下有效地处理结构稳态与瞬态动力学拓扑优化问题。
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.
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