Sensitivity analysis of key formulations of topology optimization on an example of cantilever bending beam

0542249 - ÚT 2022 RIV CH eng J - Journal Article
Šotola, Martin - Maršálek, Pavel - Rybanský, David - Fusek, M. - Gabriel, Dušan
Sensitivity analysis of key formulations of topology optimization on an example of cantilever bending beam.
Symmetry-Basel. Roč. 13, č. 4 (2021), č. článku 712. E-ISSN 2073-8994
R&D Projects: GA MŠMT(CZ) EF15_003/0000493; GA TA ČR(CZ) TN01000024
Institutional support: RVO:61388998
Keywords : topology optimization * optimization * filtering * method * penalization * weight factor * FEM * MATLAB * SIMP
OECD category: Applied mechanics
Impact factor: 2.940, year: 2021
Method of publishing: Open access
https://www.mdpi.com/2073-8994/13/4/712

Topology optimization is a modern method for optimizing the material distribution ina given space, automatically searching for the ideal design of the product. The method aims tomaximize the design performance of the system regarding given conditions. In engineering practice,a given space is first described using the finite element method and, subsequently, density-basedmethod with solid isotropic material with penalty. Then, the final shape is found using a gradient-based method, such as the optimality criteria algorithm. However, obtaining the ideal shape is highlydependent on the correct setting of numerical parameters. This paper focuses on the sensitivityanalysis of key formulations of topology optimization using the implementation of mathematicalprogramming techniques in MATLAB software. For the purposes of the study, sensitivity analysis ofa simple spatial task—cantilever bending—is performed. This paper aims to present the formulationsof the optimization problem—in this case, minimization of compliance. It should be noted that thispaper does not present any new mathematical formulas but rather provides an introduction intothe mathematical theory (including filtering methods and calculating large-size problems using thesymmetry of matrices) as well as a step-by step guideline for the minimization of compliance withinthe density-based topology optimization and search for an optimal shape. The results can be used forcomplex commercial applications produced by traditional manufacturing processes or by additivemanufacturing methods
Permanent Link: http://hdl.handle.net/11104/0320165