连续体结构拓扑优化应力约束凝聚化的ICM方法

THE ICM METHOD FOR CONTINUUM STRUCTURAL TOPOLOGY OPTIMIZATION WITH CONDENSATION OF STRESS CONSTRAINTS

为克服应力约束下拓扑优化问题约束数目多、应力敏度计算量大的困难,提出了应力约束化凝聚化的ICM方法．在利用Mises强度理论将应力约束转换成应变能约束后,提出了应力约束凝聚化的两条途径:其一为应力全局化的方法,其二为应力约束集成化的方法．由此建立了多工况下以重量为目标、以凝聚化应变能为约束的连续体结构优化模型,并利用对偶理论对优化模型进行了求解．4个数值算例表明:该方法具有较高的计算效率,得到的拓扑结构比较合理,不仅适用于二维连续体结构,也适用于三维连续体结构．

In order to overcome the difficulties of large number of stress constraints and high cost in calculating the stress sensitivities in the topology optimization with stress constraints, this paper proposes the ICM method for structural topology optimization with condensation of stress constraints. Using the theory of Mises strength to transform stress constraints into strain energy constraints, two approaches are proposed for condensation of stress constraints. One is globalization of stress constraints, the other is integration of stress constraints. Then the optimal model with a weight objective and condensed strain energy constraint is established, and the dual theory is used in the optimal model of continuum structure to obtain the numerical solution. Four examples show that the method has high computational efficiency and a reasonable optimal topology can be obtained. In addition, this method is valid not only for two dimensional continuum structure but also for three dimensional continuum structure.