连续体结构屈曲约束的ICM方法拓扑优化

基于ICM(独立、连续、映射)方法解决具有屈曲约束的连续体拓扑优化问题。建立以结构重量为目标,以屈曲临界力为约束的拓扑优化模型;采用独立的连续拓扑变量,借助泰勒展式将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将约束化为近似显函数,避免了灵敏度的计算;将优化模型转化为对偶规划,并利用序列二次规划求解,减少了设计变量的数目,缩小了模型的求解规模。给出三个算例,结果表明:该方法可有效地解决屈曲约束的连续体拓扑优化问题,能够得到合理的拓扑结构,并有较高的计算效率。

Topological optimization of the continuum structure subjected to the buckling constraints with ICM method

In this paper,according to the ICM(Independent Continuous Mapping) method,the topology optimization problem of continuum structures with the buckling constraints are solved.The topology optimization model for the continuum structure is constructed,which has the minimized weight as the objective function subjected to the buckling constraints.The continuous independent topological variables are used in this problem.Based on the Taylor expansion,the filtering function and the Rayleigh quotient,the objective function is approximately expressed as a second-order expressions and the buckling constraint is approximately expressed as an explicit function.Thus the analysis of the sensitivity is avoided.The optimization model is translated into a dual programming and solved by the sequence second-order programming.The number of the variable is reduced and the model's scale is minified.Finally,three examples are presented.They show that this method can solve the topology optimization problem of continuum structures with the buckling constraints efficiently and give more reasonable structural topologies.