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# Sensitivity Analysis of Key Formulations of Topology Optimization on an Example of Cantilever Bending Beam

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Department of Applied Mechanics, Faculty of Mechanical Engineering, VŠB—Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava, Czech Republic
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Institute of Thermomechanics of the Czech Academy of Sciences, Dolejskova 5, 182 00 Prague, Czech Republic
*
Author to whom correspondence should be addressed.
Academic Editors: Sun Young Cho and Aviv Gibali
Symmetry 2021, 13(4), 712; https://doi.org/10.3390/sym13040712
Received: 11 March 2021 / Revised: 9 April 2021 / Accepted: 16 April 2021 / Published: 18 April 2021
(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics)
Topology optimization is a modern method for optimizing the material distribution in a given space, automatically searching for the ideal design of the product. The method aims to maximize 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-based method 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 highly dependent on the correct setting of numerical parameters. This paper focuses on the sensitivity analysis of key formulations of topology optimization using the implementation of mathematical programming techniques in MATLAB software. For the purposes of the study, sensitivity analysis of a simple spatial task—cantilever bending—is performed. This paper aims to present the formulations of the optimization problem—in this case, minimization of compliance. It should be noted that this paper does not present any new mathematical formulas but rather provides an introduction into the mathematical theory (including filtering methods and calculating large-size problems using the symmetry of matrices) as well as a step-by step guideline for the minimization of compliance within the density-based topology optimization and search for an optimal shape. The results can be used for complex commercial applications produced by traditional manufacturing processes or by additive manufacturing methods. View Full-Text
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MDPI and ACS Style

Sotola, M.; Marsalek, P.; Rybansky, D.; Fusek, M.; Gabriel, D. Sensitivity Analysis of Key Formulations of Topology Optimization on an Example of Cantilever Bending Beam. Symmetry 2021, 13, 712. https://doi.org/10.3390/sym13040712

AMA Style

Sotola M, Marsalek P, Rybansky D, Fusek M, Gabriel D. Sensitivity Analysis of Key Formulations of Topology Optimization on an Example of Cantilever Bending Beam. Symmetry. 2021; 13(4):712. https://doi.org/10.3390/sym13040712

Chicago/Turabian Style

Sotola, Martin, Pavel Marsalek, David Rybansky, Martin Fusek, and Dusan Gabriel. 2021. "Sensitivity Analysis of Key Formulations of Topology Optimization on an Example of Cantilever Bending Beam" Symmetry 13, no. 4: 712. https://doi.org/10.3390/sym13040712

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