The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact medium, makes the method suitable for cases with very large deformations. The proposed contact method is implemented in a second order topology optimization framework, which employs a coupled simultaneous solution of the mechanical, design update, and adjoint problems. All three problems are derived and presented in weak form, and discretized with finite elements of suitable order. The capabilities and accuracy of the developed method are demonstrated in a topology optimization problem for achieving a desired non-linear force–displacement path.

本工作提出了第三种介质接触方法的扩展，用于解决涉及并利用自接触的结构拓扑优化问题。用作接触介质的空隙区域的新规则化使该方法适用于变形很大的情况。所提出的接触方法是在二阶拓扑优化框架中实现的，该框架采用了机械，设计更新和伴随问题的耦合同时解决方案。这三个问题都以弱形式导出并给出，并用适当阶数的有限元离散化。在拓扑优化问题中证明了所开发方法的功能和准确性，以实现所需的非线性力-位移路径。