关键词: 节点位置不确定, 灵敏度, 稳健拓扑优化, 优化准则法, 桁架结构

Abstract: An algorithm is presented for solving truss structural robust topology optimization problems with small uncertainty in the location of the structural nodes. This type of uncertainty would typically arise from fabrication or assembly errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. The design variable of the truss structural robust topology optimization is the sectional areas of the truss elements. The objective is to minimize the weighted sum of expectation and standard deviation of compliance. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads based on Neumann expansion and Taylor series expansion. Sensitivity of the objective is derived based on adjoint method, and then the method of Optimality criteria can be used to solve the problem. Simple examples are presented to verify the effectiveness of the proposed method, and the results demonstrate that nodal location uncertainties can have dramatic impact on optimal design.

Key words: optimality criteria method, robust topology optimization, sensitivity, uncertain nodal location, truss structure