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dc.contributor.authorCodony Gisbert, David
dc.contributor.authorMarco Alacid, Onofre
dc.contributor.authorFernández Méndez, Sonia
dc.contributor.authorArias Vicente, Irene
dc.contributor.otherUniversitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.identifier.citationCodony, D. [et al.]. An immersed boundary hierarchical B-spline method for flexoelectricity. "Computer methods in applied mechanics and engineering", 1 Setembre 2019, vol. 354, p. 750-782.
dc.description© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.description.abstractThis paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order nature of the coupled PDE system is addressed by a sufficiently smooth hierarchical B-spline approximation on a background Cartesian mesh. The domain of interest is embedded into the background mesh and discretized in an unfitted fashion. The immersed boundary approach allows us to use B-splines on arbitrary domain shapes, regardless of their geometrical complexity, and could be directly extended, for instance, to shape and topology optimization. The domain boundary is represented by NURBS, and exactly integrated by means of the NEFEM mapping. Local adaptivity is achieved by hierarchical refinement of B-spline basis, which are efficiently evaluated and integrated thanks to their piecewise polynomial definition. Nitsche's formulation is derived to weakly enforce essential boundary conditions, accounting also for the non-local conditions on the non-smooth portions of the domain boundary (i.e. edges in 3D or corners in 2D) arising from Mindlin's strain gradient elasticity theory. Boundary conditions modeling sensing electrodes are formulated and enforced following the same approach. Optimal error convergence rates are reported using high-order B-spline approximations. The method is verified against available analytical solutions and well-known benchmarks from the literature.
dc.format.extent33 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.otherStrain gradient elasticity
dc.subject.otherImmersed boundary B-spline approximation
dc.subject.otherHigh-order PDE
dc.subject.otherNitsche's method
dc.titleAn immersed boundary hierarchical B-spline method for flexoelectricity
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::74 Mechanics of deformable solids::74S Numerical methods
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/679451/EU/Enabling flexoelectric engineering through modeling and computation/FLEXOCOMP
local.citation.authorCodony, D.; Marco, O.; Fernandez, S.; Arias, I.
local.citation.publicationNameComputer methods in applied mechanics and engineering

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