柔顺机构几何非线性多目标拓扑优化设计

MULTIOBJECTIVE TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS WITH GEOMETRICAL NONLINEARITY

给出一种柔顺机构几何非线性多目标拓扑优化设计的新方法。首先,建立增量形式平衡方程,采用Total-La-grange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应。其次,建立适合求解几何非线性的多目标拓扑优化数学模型,目标函数以平均柔度最小和几何增益最大来满足机构的刚度和柔度需求,提出用标准化方法建立多目标函数,利用决定函数得到最优妥协解。目标函数敏度分析采用伴随求解技术,拓扑优化采用固体各向同性材料插值方法,并用移动近似算法进行迭代求解。最后,通过算例说明以上方法的正确性和有效性。研究结果表明,运用该柔顺机构几何非线性多目标拓扑优化方法能够在刚度和柔度之间找到最优妥协解,不但提高机构柔度,而且提高机构刚度,同时也说明对柔顺机构进行几何非线性拓扑优化的必要性。

A new multiobjective topology optimization method for compliant mechanisms with geometrical nonlinearity is presented.Geometrically nonlinear structural response is calculated using a Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations.The multiobjective topology optimization problem is established by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements,respectively.The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions,and the decision function is set to select the preferred solution.The solid isotropic material with penalization approach is used in design of compliant mechanisms.The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the method of moving asymptotes.These methods are further investigated and realized with the numerical examples,which are simulated to show the availability of this approach.