In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads and supports are often difficult to find manually. This substantially limits topology optimization's effectiveness for many mechanism design problems. We remove this limitation by developing a method which automatically determines optimal positioning of a prescribed input displacement and a set of supports simultaneously with an optimal material layout. Using nonlinear elastic physics, we synthesize a variety of compliant mechanisms with large output displacements, snap-through responses, and prescribed output paths, producing designs with significantly improved performance in every case tested. Compared to optimal designs generated using best-guess boundary conditions used in previous studies, the mechanisms presented in this paper see performance increases ranging from 47%-380%. The results show that nonlinear mechanism responses may be particularly sensitive to boundary condition locations and that effective placements can be difficult to find without an automated method.

翻译：在柔顺机构的拓扑优化中，边界条件的具体设置会强烈影响设计的材料分布和性能表现。与此同时，载荷与支撑的最优位置往往难以通过人工方式确定，这极大地限制了拓扑优化在众多机构设计问题中的有效性。我们通过开发一种方法消除了这一限制——该方法能在优化材料布局的同时，自动确定预设输入位移和一组支撑的最优位置。基于非线性弹性物理原理，我们综合了多种具有大输出位移、突跳响应和预设输出路径的柔顺机构，在所有测试案例中均生成了性能显著提升的设计方案。与以往研究中采用最佳猜测边界条件生成的优化设计相比，本文提出的机构性能提升幅度达47%-380%。结果表明，非线性机构响应可能对边界条件位置尤为敏感，且若无自动化方法，其有效布局往往难以确定。