Garcke, Harald and Lam, Kei Fong and Nurnberg, Robert and Signori, Andrea (2023) Overhang Penalization in Additive Manufacturing via Phase Field Structural Topology Optimization with Anisotropic Energies. APPLIED MATHEMATICS AND OPTIMIZATION, 87 (3): 44. ISSN 0095-4616, 1432-0606
Full text not available from this repository. (Request a copy)Abstract
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during construction) with anisotropic energy functionals. Convex and non-convex examples are provided, with the latter showcasing oscillatory behavior along the object boundary termed the dripping effect in the literature. We provide a rigorous mathematical analysis for the structural topology optimization problem with convex and non-continuously-differentiable anisotropies, deriving the first order necessary optimality condition using subdifferential calculus. Via formally matched asymptotic expansions we connect our approach with previous works in the literature based on a sharp interface shape optimization description. Finally, we present several numerical results to demonstrate the advantages of our proposed approach in penalizing overhang developments.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; SELF-SUPPORTING STRUCTURES; SINGULAR PERTURBATIONS; VARIATIONAL-PROBLEMS; STRUCTURE DESIGN; ANGLE CONTROL; FUNCTIONALS; SHARP; CONSTRAINTS; MODEL; Topology optimization; Phase field; Anisotropy; Linear elasticity; Optimal control; Additive manufacturing; Overhang penalization |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Mar 2024 11:49 |
| Last Modified: | 16 Mar 2024 11:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/60153 |
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