• CN：11-2187/TH
• ISSN：0577-6686

• 运载工程 •

### 节点位置不确定下桁架结构稳健拓扑优化

1. 1. 北京航空航天大学机械工程及自动化学院 北京 100191;
2. 北京航空航天大学虚拟现实技术与系统国家重点实验室 北京 100191
• 出版日期:2017-01-20 发布日期:2017-01-20
• 作者简介:

付志方，男，1987年出生，博士研究生。主要研究方向为结构优化。

E-mail：zhifang_fu@buaa.edu.cn

王春洁(通信作者)，女，1955年出生，博士，教授，博士研究生导师。主要研究方向为机械设计、优化、仿真。

E-mail：wangcj@buaa.edu.cn

### Robust Topology Optimization of Truss Structure under Uncertain Nodal Locations

FU Zhifang1, WANG Chunjie1, 2

1. 1. School of Mechanical Engineering and Automation， Beihang University， Beijing 100191;
2. State Key Laboratory of Virtual Reality Technology and Systems， Beihang University， Beijing 100191
• Online:2017-01-20 Published:2017-01-20

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.