考虑屈曲约束的无铰链多输入多输出柔性机构拓扑优化设计方法

TOPOLOGY OPTIMIZATION DESIGN METHOD FOR HINGE-FREE MULTI-INPUT MULTI-OUTPUT COMPLIANT MECHANISMS UNDER BUCKLING CONSTRAINTS

针对柔性机构的稳定性要求,基于Heaviside三场映射方案和柔顺度变化率约束措施,研究了屈曲约束下无铰链多输入多输出柔性机构柔度最小化的拓扑优化问题。首先,为解决低密度单元引起的伪屈曲模态和计算效率等问题,构建了单元刚度矩阵和应力矩阵的光滑惩罚函数,提出了解决低阶伪屈曲模态问题的综合措施。其次,结合Pian混合应力单元公式、凝聚函数法、Heaviside三场映射方案和柔顺度变化率约束措施,构建了考虑屈曲的无铰链多输入多输出柔性机构拓扑优化模型。而后,推导了目标函数和屈曲约束的灵敏度,并利用MMA(Method of Moving Asymptotes)算法进行优化求解。最后,给出的数值算例,说明了此方法的可行性和有效性。

In view of stability requirements of compliant mechanisms, based on the Heaviside three-field mapping scheme and the compliance change rate constraint measure, the topology optimization problem of the compliance minimization of hinge-free multi-input multi-output compliant mechanisms with buckling constraints is investigated. Firstly, in order to solve the problem of pseudo-buckling modes and calculation efficiency caused by low-density elements, smooth penalty functions of the element stiffness matrix and stress matrix are constructed, and comprehensive measures to solve the corresponding problem are proposed. Furthermore, cooperating with the Pian mixed stress element formula, the aggregation function method, the Heaviside three-field mapping scheme and the compliance change rate constraint measure, the topology optimization model of hinge-free multi-input multi-output compliant mechanisms considering buckling is constructed. Then, the sensitivities of the objective function and buckling constraints are derived, and the MMA algorithm is adopted to optimize the topology optimization model. Finally, the numerical examples are given to illustrate the feasibility and effectiveness of this method.