Quaternion and octonion-based finite element analysis methods for computing multiple first order derivatives

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dc.citation.journalTitleJOURNAL OF COMPUTATIONAL PHYSICS
dc.contributor.authorAristizabal, Mauricio
dc.contributor.authorRamirez-Tamayo, Daniel
dc.contributor.authorGarcia, Manuel
dc.contributor.authorAguirre-Mesa, Andres
dc.contributor.authorMontoya, Arturo
dc.contributor.authorMillwater, Harry
dc.contributor.researchgroupMecánica Aplicadaspa
dc.date.accessioned2021-04-16T20:10:42Z
dc.date.available2021-04-16T20:10:42Z
dc.date.issued2019-11-15
dc.description.abstractThe complex Taylor series expansion method for computing accurate first order derivatives is extended in this work to quaternion, octonion and any order Cayley-Dickson algebra. The advantage of this new approach is that highly accurate multiple first order derivatives can be obtained in a single analysis. Quaternion and octonion-based finite element analysis methods were developed in order to compute up to three (quaternion) and up to seven (octonion) first order derivatives of shape, material properties, and/or loading conditions in a single analysis. The traditional finite element formulation was modified such that each degree-of-freedom was augmented with three or seven additional imaginary nodes. The quaternion and octonion-based methods were integrated within the Abaqus commercial finite element code through a user element subroutine. Numerical examples are presented for thermal conductivity and linear elasticity; however, the methodology is general. The results indicate that the quaternion and octonion-based methods provide derivatives of the same high accuracy as the complex finite element method but are significantly more efficient. A Fortran code to solve a simple seven variable quaternion example is given in the Appendix. (C) 2019 Elsevier Inc. All rights reserved.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=9831
dc.identifier.doi10.1016/j.jcp.2019.07.030
dc.identifier.issn00219991
dc.identifier.issn10902716
dc.identifier.otherWOS;000486433900015
dc.identifier.otherSCOPUS;2-s2.0-85083818253
dc.identifier.urihttp://hdl.handle.net/10784/29220
dc.language.isoengeng
dc.publisherElsevier Inc.
dc.publisher.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85083818253&doi=10.1016%2fj.jcp.2019.07.030&partnerID=40&md5=ce5ed6d0c27068cdb5b338dbd1d5c7e5
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0021-9991
dc.sourceJOURNAL OF COMPUTATIONAL PHYSICS
dc.subject.keywordQuaternionseng
dc.subject.keywordCayley-Dickson numberseng
dc.subject.keywordNumerical differentiationeng
dc.subject.keywordFirst order derivativeseng
dc.subject.keywordComplex stepeng
dc.titleQuaternion and octonion-based finite element analysis methods for computing multiple first order derivativeseng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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