Extraction of stress intensity factors of biharmonic equations with corner singularities corresponding to mixed boundary conditions of clamped, simply supported, and free (II)

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dc.contributor.authorKim, Seokchan
dc.contributor.authorPalta, Birce
dc.contributor.authorJeong, Jaewoo
dc.contributor.authorOh, Hae-Soo
dc.date.accessioned2023-04-20T08:04:13Z
dc.date.available2023-04-20T08:04:13Z
dc.date.issued2022
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractIn [13], we derived stress intensity factors (SIF) extraction formulas of a biharmonic equation delta(2)u = f in a cracked domain whose crack faces have clamped boundary conditions. In this paper, we extend our investigation to the derivation of the SIF extraction formulas of the biharmonic equation in non-convex polygonal domains containing cracks or reentrant corners when various BC such as clamped (CC), simply supported (SS), free (FF), or mixed conditions (CS, FC, SF) are imposed on the boundary. We prove that the SIF is expressed as the integral of f Psi s(k)* - u delta(2)Psi s(k)* for a cut-off function psi and a dual singular function s(k)* on a small neighborhood of the singularity. The dual singular function is determined in this paper. For a numerical approximation of u, we proposed an iteration method as well as a direct finite element method. For a finite element solution of delta(2)u = f, we have to use C-1-continuous basis functions. For continuous differentiable basis functions, we use either C-1 continuous B-spline basis functions or the conventional Hermite basis function. Because of several advantages of B-spline functions in imposing complex boundary conditions, we choose B-spline basis functions for the finite element approximation of u. Moreover, in the direct numerical method, we propose to use implicitly enriched basis functions that resemble the singularities.
dc.description.sponsorshipBasic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Education [2017R1D1A1B04030594]
dc.description.sponsorshipThis research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B04030594).
dc.identifier.doi10.1016/j.camwa.2022.01.028
dc.identifier.endpage259
dc.identifier.issn0898-1221
dc.identifier.issn1873-7668
dc.identifier.scopus2-s2.0-85123787879
dc.identifier.scopusqualityQ1
dc.identifier.startpage235
dc.identifier.urihttps://doi.org/10.1016/j.camwa.2022.01.028
dc.identifier.urihttps://hdl.handle.net/20.500.11776/11029
dc.identifier.volume109
dc.identifier.wosWOS:000789872600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorPalta, Birce
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.relation.ispartofComputers & Mathematics With Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectStress Intensity Factor
dc.subjectBiharmonic Equations With Corner Singularities
dc.subjectC-1-Continuous Basis Function
dc.subjectIterative Method
dc.subjectEnriched Galerkin Method
dc.titleExtraction of stress intensity factors of biharmonic equations with corner singularities corresponding to mixed boundary conditions of clamped, simply supported, and free (II)
dc.typeArticle

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