
Christiansen AN Bærentzen JA Nobel-Jørgensen M Aage N Sigmund O Combined shape and topology optimization of 3D structures Comput Graph 2015 46 25 35 Google Scholar Digital Library.Christiansen AN Nobel-Jørgensen M Aage N Sigmund O Bærentzen JA Topology optimization using an explicit interface representation Struct Multidisc Optim 2014 49 3 3117 Google Scholar Digital Library.Burman E Claus S Hansbo P Larson MG Massing A CutFEM: discretizing geometry and partial differential equations Int J Numer Methods Eng 2015 1352.65604 Google Scholar Cross Ref.Bruggi M Venini P A mixed FEM approach to stress-constrained topology optimization Int J Numer Methods Eng 2008 73 12 1693 1714 2397968 1159.74397 Google Scholar Cross Ref.Bendsøe MP Optimal shape design as a material distribution problem Struct Optim 1989 1 4 193 202 Google Scholar Digital Library.Struct Multidisc Optim 1–23 Google Scholar Andreasen CS, Elingaard MO, Aage N (2020) Level set topology and shape optimization by density methods using cut elements with length scale control.Amstutz S Novotny AA Topological optimization of structures subject to von Mises stress constraints Struct Multidisc Optim 2010 41 3 4132 1274.74053 Google Scholar.Allaire G Dapogny C Frey P Shape optimization with a level set based mesh evolution method Comput Methods Appl Mech Eng 2014 282 22 53 3269890 1423.74739 Google Scholar Cross Ref.Allaire G Dapogny C Frey P Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh CR Math 2011 349 17– 2838253 1368.74045 Google Scholar.Allaire G Jouve F Toader A-M Structural optimization using sensitivity analysis and a level-set method J Comput Phys 2004 1136.74368 Google Scholar Digital Library.Allaire G Jouve F Minimum stress optimal design with the level set method Eng Anal Boundary Elem 2008 32 11 9.74104 Google Scholar Cross Ref.The applicability of the proposed approach, as well as its relative advantages compared to density-based approaches is demonstrated on several benchmark cases of stress-constrained topology optimization. Utilizing the smooth IGA solution, the stress is limited in the domain as well as in precise computation points on the boundaries. Consistent analytical sensitivity analysis is formulated for the entire procedure. This leads to accurate stress computations and smooth stress fields, which are critical for constraining the stresses in regions that exhibit high concentrations.
Geometric boundary iso#
The governing state equations are solved using Iso Geometric Analysis (IGA). Subsequently, a mechanical model that replicates the geometrical model precisely is constructed by mesh refinement. Untrimming techniques are used to construct the topology from the implicit boundaries defined by the level set function. The geometrical model is a spline-based topology that evolves following the level set method. In this paper, we address stress-constrained topology optimization using an explicit and precise representation of the boundaries. The solution of stress-constrained topology optimization problems is strongly affected by the accuracy of the computed stresses on the boundary of the evolving structure.
