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中文摘要：
基于ICM（独立、连续、映射）方法建立了以结构重量最小为目标,以屈曲临界力、应力同时为约束的连续体拓扑优化模型：采用独立的连续拓扑变量,借助泰勒展式、过滤函数将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将屈曲约束化为近似显函数;将应力这种局部性约束采用全局化策略进行处理,即借助第四强度理论、过滤函数将应力局部性约束转化为应变能约束,大大减少了灵敏度分析的计算量;将优化模型转化为对偶规划,减少了设计变量的数目,并利用序列二次规划求解,缩小了模型的求解规模。数值算例表明：该方法可以有效地解决屈曲与应力约束共同作用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。
英文摘要：
In this paper, the topology optimization model for continuum structures was developed based on the ICM （Independent Continuous Mapping） method. The objective function of this model is the minimized weight, which is subjected to both the buckling constraints and stress constraints. Using continuous independent topological variables, adopting Taylor expansion and the filtering function, the objective function was expressed approximately as a second-order expression. Based on the Rayleigh quotient, Taylor expansion and the filtering function, the buckling constraints were expressed approximately and explicitly. Using the globalization method of stress constraints and the von Mises＇ yield criterion, the local stress constraints were converted into strain energy constraints of the whole structure. Thus, the sensitivity analysis was facilitated. The optimization model was converted to be a dual problem, and then solved by the sequence second-order programming. Thus, the number of the variable was reduced and the model＇s scale was minified. Numerical examples show that this method can solve the topology optimization problem of continuum structures with both the buckling and displacement constraints efficiently and give more reasonable structural topologies.
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