Oliveira, Hugo Luiz; de Castro e Andrade, Heider; Leonel, Edson Denner An isogeometric boundary element approach for topology optimization using the level set method. (English) Zbl 1481.74622 Appl. Math. Modelling 84, 536-553 (2020). Summary: Among the various types of structural optimization, topology has been occupying a prominent place over the last decades. It is considered the most versatile because it allows structural geometry to be determined taking into account only loading and fixing constraints. This technique is extremely useful in the design phase, which requires increasingly complex computational modeling. Modern geometric modeling techniques are increasingly focused on the use of NURBS basis functions. Consequently, it seems natural that topology optimization techniques also use this basis in order to improve computational performance. In this paper, we propose a way to integrate the isogeometric boundary techniques to topology optimization through the level set function. The proposed coupling occurs by describing the normal velocity field from the level set equation as a function of the normal shape sensitivity. This process is not well behaved in general, so some regularization technique needs to be specified. Limiting to plane linear elasticity cases, the numerical investigations proposed in this study indicate that this type of coupling allows to obtain results congruent with the current literature. Moreover, the additional computational costs are small compared to classical techniques, which makes their advantage for optimization purposes evident, particularly for boundary element method practitioners. Cited in 16 Documents MSC: 74P15 Topological methods for optimization problems in solid mechanics 49Q10 Optimization of shapes other than minimal surfaces 65D07 Numerical computation using splines 65N38 Boundary element methods for boundary value problems involving PDEs Keywords:isogeometric BEM; topology optimization; level set method; Peng regularization PDFBibTeX XMLCite \textit{H. L. Oliveira} et al., Appl. Math. Modelling 84, 536--553 (2020; Zbl 1481.74622) Full Text: DOI References: [1] Michell, A. G.M., Lviii. the limits of economy of material in frame-structures, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 8, 47, 589-597 (1904) · JFM 35.0828.01 [2] Bendsøe, M. P.; Sigmund, O., Topology optimization: Theory, methods, and applications (2004), Springer-Verlag Berlin Heidelberg · Zbl 1059.74001 [3] Bendsøe, M. P.; Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. 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