基于Heaviside密度和灵敏度过滤的多位移约束结构拓扑优化

Structural topological optimization with multiple displacement constraints based on Heaviside density and sensitivity filtering

针对位移约束重量最小的有限元结构优化问题,结合独立、连续、映射(ICM)方法和体积不变的Heaviside密度过滤技术以及灵敏度过滤方法,建立了一套高效的位移近似表达式.结合多位移约束措施和对偶理论,形成了一种基于Heaviside密度和灵敏度过滤的多位移约束结构拓扑优化方法.算例的结果证明了此方法的有效性和高效性,并且能够得到清晰的0/1分布.

For the structure topological optimization problem with the objective function being the weight and displacement constraints,incorporating the method of independent,continuous,mapping（ICM）,and the technique of volume-preserving Heaviside density and sensitivity filtering,a set of efficient displacement approximation functions of the finite element model structure with large dimensions had been built.Integrating the multiple displacement constraints measurement and the dual planning method,a new structural topological optimization method with multiple displacement constraints based on Heaviside density and sensitivity filtering is proposed.Two typical examples verify that the proposed method is effective and may be used to obtain 0/1 solutions.