Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

Abstract

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. K E Y W O R D Sbuckling-induced design, functionally graded lattice, projection-based ground structure method, self-support design, topology optimization

Topology Optimisation in Structural Steel Design for Additive Manufacturing

“…Table 4 summarises those findings. [194] The TO method accounts for AM geometrical, mechanical, and machining constraints [345]…”

Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models

“…This approximation is invalid when truss members become too thick. Deng and To in [8] develop a method that projects the ground structure onto a background finite element mesh, eliminating the thin beam assumption. In a similar vein, the family of methods related to moving morphable components (MMC) [13,23] represent a structure as a collection of discrete geometric components whose shape and position are controlled by the optimization parameters, and model the resulting structure by projecting component geometries on a background mesh.…”

Multiscale design of nonlinear materials using a Eulerian shape optimization scheme

“…Some researchers have addressed geometrical nonlinearity in topology optimization. These include Jog, 23 Buhl et al, 24 Bruns et al, [25][26][27][28] Kwak and Cho, 29 Abdi et al, 30 Chen et al, 31 Deng, 32 Dunning, 33 Xu et al, 34 and Zhu et al 35 Other authors have investigated the topology optimization of nonlinear structures. [36][37][38][39][40][41][42][43][44][45][46][47][48][49] Yuge and Kikuchi, 36 Maute et al, 38 Yoon and Kim, 39 Alberdi et al, 47 and Zhao et al 49 have used topology optimization to design structures undergoing plastic deformation.…”