基于节点密度插值的多材料柔顺机构拓扑优化

Topology Optimization of Multi-material Compliant Mechanisms Using Node-density Interpolation Scheme

基于弹簧模型和节点密度插值的固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)方法,给出了一种用于多材料柔顺机构拓扑优化设计的分层优化方法。首先,以输出端位移最大化为目标以各种材料相应的体积占比为约束,建立了多材料柔顺机构拓扑优化模型;其次,采用节点密度插值,构造了设计区域内具有C^(0)连续性的密度场函数,给出了目标函数和约束的敏度解析表达式,使用过滤半径自适应迭代的敏度过滤方案,消除了节点密度插值法中的层化现象;再次,给出了一种分层优化策略用于求解多材料柔顺机构拓扑优化问题;最后,分别用典型的二维和三维柔顺机构拓扑优化问题验证了所提出方法的有效性,并分析了设计参数对优化结果的影响机制。

Based on the spring model and node density interpolation SIMP(Solid Isotropic Material with Penalization)method,a layered optimization strategy for topology optimization of multi-material compliant mechanism is given.Firstly,with the objective of maximizing the displacement at the output port and constraining the corresponding volume fractions of the each considered material,a model for the topology optimization of multi-material compliant mechanism is established.Secondly,the C^(0) continuity of the density field in the design area is constructed by using node density interpolation.The analytical expressions of sensitivities of the objective function and constraints are given.A sensitivity filtering scheme with adaptive filtering radius is employed to eliminate the stratification phenomenon in the node density interpolation method.Then,a laid optimization strategy is given to solve the topology optimization problem of a multi-material compliant mechanism.Finally,the typical two-dimensional and three-dimensional compliant mechanisms topology optimization problems are used to verify the effectiveness of the proposed method,and the influence of design parameters on the optimization results was analyzed.