Binary Discrete Method of Topology Optimization
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摘要: 单元敏度的不准确估计是离散拓扑优化算法数值不稳定的原因之一，特别是添加材料时，传统的敏度计算公式给出的估计误差较大，甚至有时估计符号都是错误的．为了克服这一问题，通过对弹性平衡增量方程的摄动分析构造了新的增量敏度估计公式．这一新的公式无论是添加材料还是删除材料都能较准确地估计出目标函数增量，它可以看作是通过非局部单元刚度阵对传统敏度分析公式的修正．以此为基础构建了一种基于离散变量的拓扑优化算法，它可以从任意单元上添加或删除材料以使目标函数减小，同时为避免优化过程中重新划分网格，采用了单元软杀策略以小刚度材料模拟空单元．这一方法的主要优点是简单，不需要太多的数学计算，特别有利于工程实际的应用．Abstract: The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities,especially,when material is added to elements.The estimation of element sensitivities is very inaccurate.Even their sign are also estimated wrongly.In order to overcome the problem,a new incremental sensitivity analysis formula was constructed based on the perturbation analysis of the elastic equilibrium increment equation,which can provide us with a good estimate of the change of the objective function whether material is removed from or added to elements.Meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix.As a consequence,a binary discrete method of topology optimization was established,in which each element is assigned either a stiffness value of solid material or a small value indicating no material.And the optimization process can remove material from elements or add material to elements so as to make the objective function decrease.And a main advantage of the method is simplicity,no need of much mathematics,and particularly engineering application.
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Key words:
- discrete variable /
- topology optimization /
- sensitivity analysis /
- matrix perturbation
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