关于桁架结构拓扑优化中的奇异最优解

回顾了结构拓扑优化奇异最优解的研究，着重介绍了应力函数的求解问题：应力函数的不连续性可以解释受应力约束的桁架拓扑优化的奇异最优解问题；这类问题的可行区是由不同维数的可行子区域组成，奇异最优解位于退化的低维可行区的端点且和其他子可行区连通；具有不同性态约束的拓扑优化问题有本质差别，求解时需要不同的松弛处理。还介绍了可求得奇异最优解的松弛、延拓算法。

On singular optima of structural topology optimization of trusses

This paper reviews the research on singular optima of structural topology optimization. The following progresses made by the author are introduced. The singular optima of structural topology optimization problems subjected to stress constraints of trusses are caused by the discontinuity of stress functions. The feasible domain of such a problem is composed of sub domains with different lower dimension. The singular optima are located at the end points of degenerated lower feasible domains and they are connected with other parts of the feasible domain. Essential distinction can be found for topology optimization problems subjected to different behavior constraints. It is suggested that relaxed approaches should be developed respectively. This paper also introduces the relaxed and continuation method for solving singular optima as well.