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Meshfree Approximate Solution of the Cauchy-Navier Equations of Elastodynamics

2021-11Comunicação em conferência Acesso aberto
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.sdg07:Energias Renováveis e Acessíveis
datacite.subject.sdg11:Cidades e Comunidades Sustentáveis
dc.contributor.authorValtchev, Svilen S.
dc.contributor.authorMartins, Nuno F. M.
dc.date.accessioned2026-04-23T14:10:49Z
dc.date.available2026-04-23T14:10:49Z
dc.date.issued2021-11
dc.descriptionConference date - 10 November 2021 - 12 November 2021; Conference code - 175477
dc.descriptionEISBN - 978-1-6654-3981-7
dc.descriptionLink de acesso para o documento - https://scholar.google.com/scholar?q=Meshfree%20Approximate%20Solution%20of%20the%20Cauchy%E2%80%93%20Navier%20Equations%20of%20Elastodynamics
dc.description.abstractIn this study we propose a meshfree scheme for the numerical solution of boundary value problems (BVP) for the nonhomogeneous Cauchy-Navier equations of elastodynamics. The method uses the classical approach where first a particular solution for the partial differential equation (PDE) is calculated and then the corresponding homogeneous BVP is solved for the homogeneous part of the total solution. In particular, we approximate each component of the source term of the nonho-mogeneous PDE by superposition of plane wave functions with different frequencies and directions of propagation. Using these expansions, a particular solution for the PDE is derived in the form of a linear combination of elastic P-And S-waves, at no extra computational cost. In the second step of the scheme, we solve the corresponding homogeneous BVP using the classical method of fundamental solutions (MFS), with shape functions given by the Kupradze tensor. The accuracy and the convergence of the proposed technique is illustrated for a Dirichlet BVP, posed in a 2D multiply connected domain, bounded by polygonal and parametric curves.eng
dc.description.sponsorshipThe first author gratefully acknowledges the financial support from the Portuguese FCT - Fundação para a Ciência e a Tecnologia, through the projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, Portugal.
dc.identifier.citationS. S. Valtchev and N. F. M. Martins, "Meshfree Approximate Solution of the Cauchy– Navier Equations of Elastodynamics," 2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), Lipetsk, Russian Federation, 2021, pp. 149-154, doi: 10.1109/SUMMA53307.2021.9632193.
dc.identifier.doi10.1109/summa53307.2021.9632193
dc.identifier.isbn978-1-6654-3982-4
dc.identifier.isbn978-1-6654-3981-7
dc.identifier.urihttp://hdl.handle.net/10400.8/16180
dc.language.isoeng
dc.peerreviewedyes
dc.publisherIEEE Canada
dc.relationCenter for Computational and Stochastic Mathematics
dc.relation.hasversionhttps://ieeexplore.ieee.org/document/9632193
dc.relation.ispartof2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA)
dc.rights.uriN/A
dc.subjectmeshfree method
dc.subjectplane wave functions
dc.subjectmethod of fundamental solutions
dc.subjectCauchy-Navier equations of elastodynamics
dc.subjectnonhomogeneous PDE
dc.titleMeshfree Approximate Solution of the Cauchy-Navier Equations of Elastodynamicseng
dc.typeconference paper
dspace.entity.typePublication
oaire.awardNumberUIDB/04621/2020
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardURIhttp://hdl.handle.net/10400.8/13612
oaire.citation.conferenceDate2021-11
oaire.citation.conferencePlaceLipetsk, Russian Federation
oaire.citation.endPage154
oaire.citation.startPage149
oaire.citation.titleProceedings - 2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2021
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameValtchev
person.givenNameSvilen
person.identifier.ciencia-idAF1E-BD9D-A8D7
person.identifier.gsidhttps://scholar.google.com/citations?user=MtxwhiUAAAAJ&hl=en
person.identifier.orcid0000-0002-3474-2788
person.identifier.scopus-author-id8361079200
relation.isAuthorOfPublicationb6302c21-a0e4-4419-967b-0a1bac949132
relation.isAuthorOfPublication.latestForDiscoveryb6302c21-a0e4-4419-967b-0a1bac949132
relation.isProjectOfPublication9c9950fd-9a9f-4c8f-94eb-65df530d33e9
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In this study we propose a meshfree scheme for the numerical solution of boundary value problems (BVP) for the nonhomogeneous Cauchy-Navier equations of elastodynamics. The method uses the classical approach where first a particular solution for the partial differential equation (PDE) is calculated and then the corresponding homogeneous BVP is solved for the homogeneous part of the total solution. In particular, we approximate each component of the source term of the nonho-mogeneous PDE by superposition of plane wave functions with different frequencies and directions of propagation. Using these expansions, a particular solution for the PDE is derived in the form of a linear combination of elastic P-And S-waves, at no extra computational cost. In the second step of the scheme, we solve the corresponding homogeneous BVP using the classical method of fundamental solutions (MFS), with shape functions given by the Kupradze tensor. The accuracy and the convergence of the proposed technique is illustrated for a Dirichlet BVP, posed in a 2D multiply connected domain, bounded by polygonal and parametric curves.
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