Topology optimization of compliant mechanisms with stress constraints and manufacturing error robustness

Abstract

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Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

“…This behavior may seem counterintuitive at first, since smaller manufacturing tolerances seem easier to achieve; however, it is not totally unexpected. A similar behavior is observed by Da Silva et al, 26 when addressing two compliant mechanism problems with same mesh and different filter radii; in that case, a stress peak was observed between dilated and intermediate designs for the case with smaller R, whereas an absolutely smooth behavior was observed for the case with larger R. Observation of these particular cases indicates that topologies with more structural details and thinner structural members are more sensitive to boundary variations when stress requirements are taken into account in the formulation. In order to handle this issue, in this article, the problem is solved again for N j = 5 and ∈ {0.2, 0.35, 0.5, 0.65, 0.8}; topology and voxel-based stress graph are shown in Figure 13.…”

“…This method has been shown to be a valid alternative to the aggregation techniques often employed to handle the large number of stress constraints in the formulation. Introduced by Pereira et al 53 in the field of stress-constrained topology optimization, the augmented Lagrangian method has been employed to address density-based 23,26,27,42,43,[54][55][56][57][58] and level-set based 20,24,59,60 problems with stress constraints. In this work, the augmented Lagrangian formulation by Birgin and Martínez 61 is employed.…”

“…Among them, there are works that focus on developing more efficient and accurate ways to handle the stress constraints, [8][9][10][11][12][13][14][15][16] and works that focus on novel applications, [17][18][19][20] as the problem of compliant mechanisms with stress constraints. [21][22][23][24][25][26][27] Although not novel, stress-constrained topology optimization has been the subject of intensive research in the literature up to the present day.…”

“…Since the seminal paper by Duysinx and Bendsøe, 7 several works addressing topology optimization with stress constraints have been developed. Among them, there are works that focus on developing more efficient and accurate ways to handle the stress constraints, 8‐16 and works that focus on novel applications, 17‐20 as the problem of compliant mechanisms with stress constraints 21‐27 . Although not novel, stress‐constrained topology optimization has been the subject of intensive research in the literature up to the present day.…”

“…Most of the research in the field of stress‐constrained topology optimization, however, is focused on deterministic problems. Although there are some recent works that propose formulations to handle uncertainty in stress‐constrained topology optimization (see, e.g., References 26,27,38‐43), these are applied to small scale problems, with less than 600 thousand elements. The combination of stress constraints and manufacturing tolerances, despite its great importance for practical applications, is hence an unexplored topic in very large scale three‐dimensional topology optimization.…”