针对结构节点位置存在小范围不确定性，提出了一种桁架结构稳健拓扑优化方法。由于工程制造或者装配误差，桁架结构节点位置常常存在误差，且此误差尺寸相对于结构单元尺寸很小。该桁架结构稳健拓扑优化问题的设计变量为各单元截面积，优化目标是结构柔度均值和标准差的加权和。优化过程中需要计算结构刚度矩阵的逆，由于结构存在节点位置不确定性，刚度矩阵是变化的，使得计算刚度矩阵的逆变得十分困难。然而，基于纽曼展开和泰勒级数展开，可将该小不确定量问题转化为较为简单的等效不确定载荷结构优化问题。为了利用优化准则法进行求解，利用伴随法进一步推导了目标函数的灵敏度信息。通过数值算例验证了该方法的有效性，并说明桁架结构节点位置不确定对结构优化结果有很大影响。

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.