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Hybrid FEM with fundamental solutions as trial functions for heat conduction simulation

Wang, Hui; Qin, Qing Hua

Description

A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of...[Show more]

dc.contributor.authorWang, Hui
dc.contributor.authorQin, Qing Hua
dc.date.accessioned2015-12-08T22:08:32Z
dc.identifier.issn0894-9166
dc.identifier.urihttp://hdl.handle.net/1885/28649
dc.description.abstractA new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method (HT-FEM) over the conventional finite element method (FEM) and boundary element method (BEM), and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.
dc.publisherSpringer
dc.sourceActa Mechanica Solida Sinica
dc.subjectKeywords: Boundary integrals; Domain integrals; Element stiffness matrix; FE model; fundamental solution; Fundamental solutions; Governing equations; hybrid FEM; Hybrid finite elements; Interpolation function; Linear combinations; Mesh distortion; Numerical accurac fundamental solution; heat conduction; hybrid FEM; variational functional
dc.titleHybrid FEM with fundamental solutions as trial functions for heat conduction simulation
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume22
dc.date.issued2009
local.identifier.absfor090699 - Electrical and Electronic Engineering not elsewhere classified
local.identifier.ariespublicationu4708487xPUB59
local.type.statusPublished Version
local.contributor.affiliationWang, Hui, Henan University
local.contributor.affiliationQin, Qing Hua, College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue5
local.bibliographicCitation.startpage487
local.bibliographicCitation.lastpage498
local.identifier.doi10.1016/S0894-9166(09)60300-1
dc.date.updated2016-02-24T11:20:45Z
local.identifier.scopusID2-s2.0-70350534441
local.identifier.thomsonID000273922600014
CollectionsANU Research Publications

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