In this work, compliant mechanisms are designed by using multi-objective topology optimization, where maximization of the output displacement and minimization of the strain are considered simultaneously. To quantify the strain, we consider typical measures of strain, which are based on the p-norm, and a new class of strain quantifying functions, which are based on the variance of the strain. The topology optimization problem is formulated using the Solid Isotropic Material with Penalization (SIMP) method, and the sensitivities with respect to design changes are derived using the adjoint method. Since nearly void regions may be highly strained, these regions are excluded in the objective function by a projection method. In the numerical examples, compliant grippers and inverters are designed, and the tradeoff between the output displacement and the strain function is investigated. The numerical results show that distributed compliant mechanisms without lumped hinges can be obtained when including the variance of the strain in the objective function.

在这项工作中，通过使用多目标拓扑优化来设计顺应性机制，其中同时考虑了输出位移的最大化和应变的最小化。为了量化应变，我们考虑基于p范数的典型应变度量，以及基于应变方差的新型应变量化函数。使用带有罚分的固体各向同性材料（SIMP）方法来确定拓扑优化问题，并使用伴随方法得出关于设计更改的敏感性。由于几乎空的区域可能会高度变形，因此通过投影方法将这些区域排除在目标函数之外。在数值示例中，设计了兼容的夹具和逆变器，并研究了输出位移与应变函数之间的折衷。数值结果表明，当在目标函数中包含应变方差时，可以获得没有集总铰链的分布式顺应机构。