多输入多输出柔顺机构几何非线性拓扑优化

Topology Optimization of Multiple Inputs and Outputs Compliant Mechanisms with Geometrically Nonlinearity

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,柔顺机构拓扑实际上是一个几何非线性问题,因而研究多自由度柔顺机构几何非线性拓扑优化就显得十分必要。基于此,给出一种多输入多输出柔顺机构几何非线性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-Lagrange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,推导描述多输入多输出柔顺机构柔性的几何增益公式和描述机构刚性的应变能公式,研究抑制耦合输出策略,给出描述输出耦合效应的计算公式,在此基础上建立考虑抑制输出耦合效应时多输入多输出柔顺机构的多目标几何非线性拓扑优化数学模型。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,拓扑优化后柔顺机构可以按照预定要求运动,输出耦合现象得到了有效抑制,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性。

Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation, and the topology optimization of compliant mechanisms is actually a geometrically nonlinear problem. So it is very necessary to study the topology optimization of multiple inputs and outputs compliant mechanisms undergoing large deformation. A new topology optimization method of multiple inputs and multiple outputs compliant mechanisms with geometrical nonlinearity is presented. The multi-objective function is developed by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements, respectively. The suppression strategy of input and output coupling terms is studied, and the expression of the output coupling terms is further developed. 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. Geometrically nonlinear structural response is calculated by using a total Lagrange finite element formulation and the equilibrium is found by using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material interpolation method is used in design of compliant mechanisms. The sensitivity of objective functions is analyzed by using the adjoint solution technique and the optimization problem is solved by using the method of moving approximation algorithm. These methods are further investigated and realized with the numerical examples, which are simulated to show the availability of this approach.