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将导重法引入两类多工况拓扑优化问题的求解.首先介绍了导重法及其拉格朗日乘子的求法,并用对偶方法对多约束优化问题的拉格朗日乘子求法进行了改进;然后推导了用导重法求解最小柔度拓扑问题和最小质量拓扑优化问题的迭代公式并计算了相应的算例.算例计算结果表明,采用导重法求解多工况拓扑优化问题具有迭代公式简单、收敛速度快、求解效果好的优点.通过与Ansys中采用的SCP方法的计算结果进行比较可以看出,导重法是求解拓扑优化问题的一个行之有效的方法,它为拓扑优化问题的求解提供了一条新的途径.
This paper introduces the method of guide-weighted method to solve two kinds of multi-condition topology optimization problems.Firstly, we introduce the method of weight-bearing method and its Lagrange multiplier, and use the dual method to solve the Lagrange multiplier problem of multi-constrained optimization problem Then deduces the iterative formula to solve the minimum compliance topological problem and the minimum quality topological optimization problem by using the guide-and-weight method, and calculates the corresponding examples.Experimental results show that the guidance method is used to solve the multi-service topology optimization problem It has the advantages of simple iterative formula, fast convergence speed and good solution effect.Comparing with the calculation results of SCP method used in Ansys, it can be seen that the guide weight method is an effective method to solve the topology optimization problem, which is Topology optimization problem solving provides a new way.