组合结构的残余振动最小化结构优化设计

摘要

External impact on engineering structure generates residual vibration, which may deteriorate structural performance. This paper studies optimum design of combined structure subject to impact for minimization of residual vibration. The objective function of the optimization problem is a performance index in the form of the integral of a quadratic function, which measures the residual vibration response globally. The design variables are geometric parameters of combined structure including size, shape and layout of the structure and its members. Due to the complexity of the stiffness matrix and mass matrix of the combined structure, a semi analytical sensitivity approach was implemented to overcome the difficulty of adjoint sensitivity evaluation. Both commercial software Matlab and Ansys were adopted to realize the semi-analytical sensitivity analysis and the optimization process. One numerical example demonstrates the effectiveness of the proposed method.%为了解决残余振动直接影响结构性能的问题，研究了最小化残余振动为目标的组合结构优化设计，目标函数为能够总体衡量结构残余振动响应的二次型积分形式的性能指标，设计变量为组合结构参数化描述时采用的形状尺寸等参数。采用半解析法灵敏度分析克服了将这一方法应用于包含多种单元、多种类型设计变量的组合结构优化的困难，实现了采用Matlab将Ansys作为黑箱调用进行结构优化设计。数值算例展示了该方法的有效性。