This paper proposes a topology optimization method integrating the variable trajectory constraints to design rigid and compliant hybrid mechanisms. The variable trajectory constraints are distributed in the design domain and are uniformly modeled by nonlinear spring model. Each of the variable trajectory constraints has an active or inactive state and different states map various mechanical properties of the nonlinear springs. The nonlinear relation between force and displacement of the spring is formulated. A new group of design variables denoting the states of the springs is introduced into the traditional density-based topology optimization model. The design variables representing the element density of the continuum structure and the states of the variable trajectory constraints are uniformly penalized to avoid intermediate values in order to obtain a physically realizable mechanism. Sensitivity analysis is performed by the adjoint equation method. To demonstrate the versatility and the generality of the proposed method, the typical numerical examples including linear, spline and circular trajectory constraints were implemented. The numerical comparisons between the nonlinear spring model and the actual trajectory constraints verify the accuracy. The proposed method expands the application of topology optimization and can be extensively employed to design the mechanisms integrating both the compliant members and rigid parts.

中文翻译：

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刚性和柔顺混合机构的拓扑优化

本文提出了一种集成可变轨迹约束的拓扑优化方法来设计刚性和柔性混合机构。可变轨迹约束分布在设计域中，并通过非线性弹簧模型统一建模。每个可变轨迹约束都具有活动或非活动状态，不同的状态映射非线性弹簧的各种机械特性。公式化了弹簧的力和位移之间的非线性关系。一组新的表示弹簧状态的设计变量被引入到传统的基于密度的拓扑优化模型中。表示连续体结构的单元密度和可变轨迹约束的状态的设计变量被统一惩罚以避免中间值，以获得物理上可实现的机构。敏感性分析采用伴随方程法进行。为了证明该方法的通用性和通用性，实现了包括线性、样条和圆形轨迹约束在内的典型数值例子。非线性弹簧模型与实际轨迹约束之间的数值比较验证了准确性。该方法扩展了拓扑优化的应用，可广泛用于设计集成柔性构件和刚性零件的机构。