考虑混合约束的柔顺机构拓扑优化设计

为了满足制造工艺和静强度要求,提出一种综合考虑最小尺寸控制和应力约束的柔顺机构混合约束拓扑优化设计方法。采用改进的固体各向同性材料插值模型描述材料分布,利用多相映射方法同时控制实相和空相材料结构的最小尺寸,采用最大近似函数P范数求解机构的最大应力,以机构的输出位移最大化作为目标函数,综合考虑最小特征尺寸控制和应力约束建立柔顺机构混合约束拓扑优化数学模型,利用移动渐近算法求解柔顺机构混合约束拓扑优化问题。数值算例结果表明,混合约束拓扑优化获得的柔顺机构能够同时满足最小尺寸制造约束和静强度要求,机构的von Mises等效应力分布更加均匀。

Topological design of compliant mechanisms with hybrid constraints

To satisfy manufacturing constraints and static strength requirements,a method for hybrid constrained topology optimization of compliant mechanisms considering both minimum length scale control and stress constraints was proposed.The improved solid isotropic material with a penalization model was adopted to describe the material distribution.The two-phase projection method was applied to simultaneously achieve minimum length scale control on both solid and void phases.The P norm approach was used to calculate approximately the maximum value of the element stress.The maximization of the output displacement of the compliant mechanism was developed as the objective function.The minimum length scale control and the maximum stress were used as the constraints.The model for hybrid constrained topology optimization of compliant mechanisms was established.The method of moving asymptotes was used to solve the optimization problem.The results of several numerical examples show that the compliant mechanism obtained by hybrid constrained topology optimization can meet both manufacturing constraints and strength requirements,and the von Mises equivalent stresses are more uniformly distributed.