The present paper addresses the robustness and convergence behavior of the direct limit analysis (LA) based methodology developed for the topology design of continuum structures subject to prescribed statically and plastically admissible loads. The design methodology, based on a direct method formulation of the static LA problem, has recently been proposed for continuous topology optimization and its merits were highlighted. One of its remarkable features is the outstanding similarity of the topology design mathematical problem with its underlying direct static form of the LA problem. Subsequently, it has been extended to solve two dimensional discrete, i.e. black-and-white, topology design problems by modifying the objective function into a square root form in a way to penalize the intermediate densities and solving a sequence of conic quadratic programming problems of identical scale and algebraic structure as the continuous design problem, leaving a number of issues to be investigated, pertaining to convergence. In the present work different families of penalization function forms are proposed and assessed as alternatives to the original square root function. The performance is evaluated in terms of robustness, accuracy in the sense of closeness of the final design to a 0–1 topology and efficiency or number of approximate problems required for convergence. Convergence of the discrete topology design is shown to be improved using higher order power functions as well as trigonometric and exponential type penalty functions. The performance of the design method in solving example problems using the various penalization schemes is compared and the factors that affect it are analyzed.

本文讨论了基于直接极限分析（LA）的方法的鲁棒性和收敛性，该方法是为承受规定的静态和塑性容许载荷的连续体结构的拓扑设计而开发的。最近提出了一种基于静态LA问题的直接方法公式化的设计方法，用于连续拓扑优化，并突出了其优点。它的显着特征之一是拓扑设计数学问题与LA问题的潜在直接静态形式的显着相似性。随后，它已扩展为求解二维离散量，即黑白 通过将目标函数修改为平方根形式以惩罚中间密度，并解决与连续设计问题相同规模和代数结构的圆锥二次规划问题序列，从而产生拓扑设计问题，还有许多问题需要研究，关于收敛。在本工作中，提出并评估了不同的惩罚函数形式系列，作为原始平方根函数的替代形式。根据鲁棒性，最终设计与0–1拓扑的紧密程度以及收敛所需的效率或近似问题的数量，对性能进行了评估。使用高阶幂函数以及三角函数和指数型惩罚函数可提高离散拓扑设计的收敛性。比较了该设计方法使用各种惩罚方案解决示例问题的性能，并分析了影响该方法的因素。