连续体结构屈曲约束下拓扑优化的ICM方法

用独立、连续、映射(ICM)方法解决具有屈曲约束的连续体拓扑优化问题．引入独立、连续的拓扑变量,建立以质量为目标,屈曲临界力为约束的连续体结构拓扑优化模型．借助Taylor expansion将目标函数作二阶近似展开;借助Rayleigh’s quotient,Taylor expansion,过滤函数将约束化为近似显函数,减少了灵敏度的计算量将优化模型用对偶规划方法求解,减少了设计变量的数目,缩小了模型的求解规模,得到较为理想的拓扑优化结果．算例表明,ICM方法在屈曲约束的连续体结构拓扑优化中可行性好、效率较高．

ICM Method With Topological Optimization of the Continuum Structure Subjected to the Buckling Constraints

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 continuous independent topological variables are used in this problem. The topology optimization model for the continuum structure is constructed, which has the minimized weight as the objective function subjected to the buckling constraints. Based on the Taylor expansion, the filtering function and the Rayleigh' s 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 was decreased. The optimization model is translated into a dual programming and solved. The number of the variable is reduced and the model's scale is minified. Finally, the examples show that this method can solve the topology optimization problem of continuum structures with the buckling constraints feasibly and efficiently.