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dc.contributor.authorOliver Olivella, Xavier
dc.contributor.authorYago Llamas, Daniel
dc.contributor.authorCante Terán, Juan Carlos
dc.contributor.authorLloberas Valls, Oriol
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Física
dc.identifier.citationOliver, J. [et al.]. Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework. "Computer methods in applied mechanics and engineering", Octubre 2019, vol. 355, p. 779-819.
dc.description.abstractThe work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the work
dc.format.extent41 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia
dc.subject.lcshStructural optimization--Mathematics
dc.subject.otherTopological optimization
dc.subject.otherVariational approach
dc.subject.otherClosed-form solutions
dc.subject.otherPseudo-time sequential analysis
dc.subject.otherStructural topological optimization
dc.titleVariational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework
dc.subject.lemacOptimització d'estructures -- Models matemàtics
dc.contributor.groupUniversitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria
dc.description.peerreviewedPeer Reviewed
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/779611/EU/Computational catalog of multiscale materials: a plugin library for industrial finite element codes/CATALOG
upcommons.citation.authorOliver, J.; Yago, D.; Cante, J.C.; Lloberas-Valls, O.
upcommons.citation.publicationNameComputer methods in applied mechanics and engineering

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