A computational strategy is proposed to circumvent some of the major issues that arise in the classical threshold-based approach to discrete topology optimization. These include the lack of an integrated element removal strategy to prevent the emergence of hair-like elements, the inability to effectively enforce a minimum member size of arbitrary magnitude, and high sensitivity of the final solution to the choice of ground structure. The proposed strategy draws upon the ideas used to arrive at mesh-independent solutions in continuum topology optimization and enables efficient imposition of a minimum size constraint onto the set of non vanishing elements. This is achieved via augmenting the design variables by a set of auxiliary variables, called existence variables, that not only prove very effective in addressing the aforementioned issues but also bring in a set of added benefits such as better convergence and complexity control. 2D and 3D examples from truss-like structures are presented to demonstrate the superiority of the proposed approach over the classical approach to discrete topology optimization.

提出了一种计算策略来规避经典的基于阈值的离散拓扑优化方法中出现的一些主要问题。这些措施包括缺乏防止毛发状元素出现的综合元素去除策略，无法有效实施任意大小的最小成员大小以及最终解决方案对地面结构选择的高度敏感性。所提出的策略借鉴了用于在连续体拓扑优化中获得独立于网格的解决方案的思想，并使最小尺寸约束有效地强加于不消失元素集上。这是通过将一组辅助变量（称为存在变量）增加设计变量来实现的，不仅证明对解决上述问题非常有效，而且还带来了一系列额外的好处，例如更好的收敛性和复杂性控制。给出了来自桁架状结构的2D和3D示例，以证明所提出的方法优于经典方法的离散拓扑优化。