节点位置不确定下桁架结构稳健拓扑优化

发布时间：2018-07-18 21:29

【摘要】：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。
[Abstract]:A robust topology optimization method for truss structures is presented in this paper. Due to engineering manufacturing or assembly errors, there is often an error in the position of truss joints, and the size of the error is very small compared with the size of the structural element. The design variable of the robust topology optimization problem of the truss structure is the sectional area of each element and the optimization objective is the weighted sum of the mean value and standard deviation of the structural flexibility. It is necessary to calculate the inverse of the stiffness matrix in the optimization process. Due to the uncertainty of the node position of the structure, the stiffness matrix is changed, so it is very difficult to calculate the inverse of the stiffness matrix. However, based on Newman expansion and Taylor series expansion, the small uncertainty problem can be transformed into a simple equivalent uncertain load structure optimization problem. In order to solve the problem by using the optimization criterion, the sensitivity information of the objective function is further derived by the adjoint method. The effectiveness of the method is verified by numerical examples, and it is shown that the uncertainty of the joint position of truss structure has a great influence on the optimization results.
【作者单位】：北京航空航天大学机械工程及自动化学院;北京航空航天大学虚拟现实技术与系统国家重点实验室;
【分类号】：TB12

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