论文标题
利用Lagrange二元性进行拓扑优化，无摩擦单方面接触
Exploiting Lagrange duality for topology optimization with frictionless unilateral contact
论文作者
论文摘要
本文介绍了拓扑优化问题的可易处理的重新制定问题，这些问题受到摩擦无摩擦单方面接触条件的限制。具体而言，我们考虑了桁架和连续性的僵化最大化问题。基于拉格朗日二元性理论，我们得出不涉及互补性约束的表述。通常，与互补性约束（MPCC问题）提出了有关接触条件的结构优化问题。但是，MPCC通常需要用于数值解决方案的特殊处理，因为它不满足标准约束资格。相反，对于本文提出的公式，我们可以采用标准优化方法。进行桁架和连续性的数值实验以检查所提出的方法的效率。
This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, we consider stiffness maximization problems of trusses and continua. Based on the Lagrange duality theory, we derive formulations that do not involve complementarity constraints. It is often that a structural optimization problem with contact conditions is formulated as a mathematical programming problem with complementarity constraints (MPCC problem). However, MPCC usually requires special treatment for numerical solution, because it does not satisfy standard constraint qualifications. In contrast, to the formulation presented in this paper, we can apply standard optimization approaches. Numerical experiments of trusses and continua are performed to examine efficiency of the proposed approach.
