Body‐fitted topology optimization via integer linear programming using surface capturing techniques

• Published in: International Journal for Numerical Methods in Engineering Vol. 125; no. 13
• Main Authors: Soares da Costa Azevêdo, Anderson, Li, Hao, Ishida, Naouyuki, Siqueira, Lucas Oliveira, Cortez, Rômulo Luz, Nelli Silva, Emílio Carlos, Nishiwaki, Shinji, Picelli, Renato
• Format: Journal Article
• Language: English; Japanese
• Published: Hoboken, USA Wiley 15.07.2024; John Wiley & Sons, Inc; Wiley Subscription Services, Inc
• Subjects: Benchmarks; body‐fitted mesh; Computational efficiency; Computing costs; Density; discrete methods; Energy dissipation; finite element method; Fluid dynamics; Fluid flow; geometry trimming; Grid refinement (mathematics); Integer programming; Linear programming; Optimization; Reynolds number; Software; Topology optimization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7480

Recent advancements in computational tools and additive manufacturing have expanded design possibilities on fluid devices and structures to also include aesthetics. However, traditional discrete density‐based topology optimization methods usually use square and cubic regular meshes, resulting in jagged contour patterns that require mesh refinement and post‐processing to numerical solution steps of complex physics problems. In this article, we propose a new isosurface boundary capture strategy for topology optimization in structural and fluid flow problems. The capture of smoothed boundaries is done via a simple strategy through element splitting and analysis domain remeshing. The smoothing procedure novelty lies on the optimizer regular mesh decomposition into smaller triangular or tetrahedral elements with a pseudo‐density nodal function that produces implicit geometry boundaries. We employ the TOBS‐GT (topology optimization of binary structures with geometry trimming) method to solve optimization problems for mean compliance and fluid flow energy dissipation, subject to a volume fraction constraint. Since, we perform discrete body‐fitted optimization, the material interpolation models are expressed in linear form without penalty factors. Our method produces a lower computational cost topology evolution with high resolution and mitigated sharp details, achieved via smooth edges and surfaces, as demonstrated through benchmark numerical examples in two‐ and three‐dimensional space. In addition, the proposed strategy facilitates the optimization of benchmark fluid flow examples for moderate Reynolds numbers.