考虑全局应力约束的大变形柔顺机构拓扑构型设计

Topological Design of Large-displacement Compliant Mechanisms Considering Global Stress Constraints

摘要:

为了避免大变形引起静强度失效，提出一种考虑全局应力约束的大变形柔顺机构拓扑优化设计方法。采用Total-Lagrangian描述方法和增量式Newton-Raphson法求解机构的大变形响应问题；采用基于假设密度场的单元势能插值法，从而避免几何非线性拓扑优化出现的数值不收敛问题；以输出位移最大化作为优化目标，采用改进的P范数将机构所有单元局部应力约束转换为一个全局应力约束，构建考虑全局应力约束的柔顺机构几何非线性拓扑优化模型，采用移动渐近线算法求解优化问题。数值算例结果表明，采用本文方法获得的大变形柔顺机构能够有效满足应力约束。随着允许应力约束值的减小，机构构型中的铰链区域逐渐扩大，使机构的柔度分布更加均匀，但是输出位移逐渐减小。

Abstract:

To avoid static strength failure caused by large deflection, a design method for topology optimization of large-displacement compliant mechanisms considering global stress constraints was proposed. The Total-Lagrangian formulation and the incremental Newton-Raphson method were applied to solve the geometrically nonlinear response of the mechanisms. The element energy interpolation scheme for fictitious domain techniques was adopted to circumvent the non-convergence problem in the topology optimization of geometrical nonlinear problems. The maximum of the output displacement of the compliant mechanisms was developed as the optimization objective. The local stresses constraints for all elements were aggregated into a global stress constraint using the improved P-norm method. The optimization model for topology optimization of compliant mechanism with geometrical nonlinearities considering global stress constraints was established. The method of moving asymptotes was applied to solve the topology optimization problem for the design of large-displacement compliant mechanisms with global stress constraints. The results of numerical examples showed that large-displacement compliant mechanisms obtained by topology optimization with global stress constraint can effectively satisfy the stress constraints. As the allowable stress limit was decreased, the hinge area in the compliant mechanism configurations was gradually elongated, which can make the compliance of the mechanisms be more uniformly distributed. However, the output displacement of the mechanisms was gradually decreased.