A new topology optimization scheme called the projection‐based ground structure method (P‐GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P‐GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing‐oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density‐based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P‐GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self‐supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling‐induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P‐GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling‐induced mechanism design are presented and discussed in details.

中文翻译：

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基于投影的地面结构方法（P‐GSM）的线性和非线性拓扑优化设计

针对线性和非线性拓扑优化设计，提出了一种新的拓扑优化方案，称为基于投影的地面结构方法（P‐GSM）。对于线性设计，与仅限于设计细长构件的传统GSM相比，P-GSM可以有效地解决此限制并生成功能渐变的晶格结构。对于面向增材制造的设计，制造能力是限制可行设计空间的关键因素，例如最小长度和几何形状复杂性。传统的基于密度的方法（其中每个元素都作为变量）总是导致具有大量细小复杂特征的复杂几何形状，而这些细小的特征通常甚至无法通过3D打印来制造，并且在后处理之后会失去其几何精度。所提出的P‐GSM是控制几何复杂度和最小长度以进行最佳设计的有效方法，同时能够自然地设计自支撑结构。在优化过程中，某些钢筋可能会彼此断开连接（漂浮在空中）。对于屈曲诱导的设计，由于构件之间的断开导致空隙空间中的严重网格变形，因此此问题变得至关重要，而P‐GSM可以克服此问题。为了证明所提出方法的有效性，提出并详细讨论了三种不同的设计问题，从顺应性优化到屈曲诱发的机构设计。在优化过程中，某些钢筋可能会彼此断开连接（漂浮在空中）。对于屈曲诱导的设计，由于构件之间的断开导致空隙空间中的严重网格变形，因此此问题变得至关重要，而P‐GSM可以克服此问题。为了证明所提出方法的有效性，提出并详细讨论了三种不同的设计问题，从顺应性优化到屈曲诱发的机构设计。在优化过程中，某些钢筋可能会彼此断开连接（漂浮在空中）。对于屈曲诱导的设计，由于构件之间的断开导致空隙空间中的严重网格变形，因此此问题变得至关重要，而P‐GSM有能力克服此问题。为了证明所提出方法的有效性，提出并详细讨论了三种不同的设计问题，从顺应性优化到屈曲诱发的机构设计。