Multiple reciprocity boundary element analysis of two-dimensional anisotropic thermoelasticity involving an internal arbitrary non-uniform volume heat source

Shiah, Yui‐Chuin; Lin, Y.J.

doi:10.1016/j.ijsolstr.2003.08.006

Cited by 16 publications

(5 citation statements)

References 20 publications

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“…The unknown coefficients {α i } and {β} can be assessed at first by applying the application points A to Eqs (40) and (41), that provides N A equations, and subsequently by using the constraints (37) and (38), that gives N p equations. The obtained system of linear algebraic equations with the size N s can be written in the matrix form as…”

Section: E V a L U A T I O N O F T H E D O M A I N I N T E G R A L Smentioning

confidence: 99%

“…Nowak and Brebbia 36 have proposed the multiple reciprocity method (MRM), in which the domain integrals are replaced by an infinite series of boundary integrals involving higher order fundamental solutions. Shiah and Lin 37 have used the MRM in the 2D BEM analysis for thermoelasticity with non‐uniform internal heat sources. The fast multipole method (FMM) has been introduced by Greengard and Rokhlin 38 as a fast algorithm for a particle simulation.…”

Section: Introductionmentioning

confidence: 99%

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Thermoelastic crack analysis in functionally graded materials and structures by a BEM

Ekhlakov

Khay

Zhang

et al. 2012

Fatigue Fract Eng Mat Struct

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A B S T R A C T In this paper, transient thermoelastic crack analysis in two-dimensional, isotropic, continuously non-homogeneous and linear elastic functionally graded materials subjected to a thermal shock is presented. The Laplace transform technique is used to eliminate the time dependence of the governing equations of the linear coupled thermoelasticity. Fundamental solutions for isotropic, homogeneous and linear elastic solids in the Laplacetransformed domain are applied to derive boundary-domain integral equations for the mechanical and thermal fields. The radial integration method is employed to transform the domain integrals into the boundary integrals. A collocation-based boundary element method is implemented for the spatial discretization of the boundary-domain integral equations. The time-dependent numerical solutions are obtained by using Stehfest's inversion algorithm. Numerical results are presented and discussed to show the influences of the material gradation, the thermo-mechanical coupling, the crack orientation and the thermal shock loading on the dynamic stress intensity factors.Keywords boundary element method; dynamic stress intensity factors; functionally graded materials; Laplace transform; radial integration method; thermal shock. N O M E N C L A T U R Ea = half crack length a j i = unknown expansion coefficients b j = unknown expansion coefficients c (x) = specific heat at constant strain c 0 (x) = free-term coefficient c 0 jk (x) = free-term coefficients c i jkl (x) = elasticity tensor d A = support size for the application point A E(x) = Young's modulus h = semi-height of the FG plate H(t) = Heaviside step function I = identity matrix k(x) = thermal conductivitȳ K ± I (t) = normalized mode-I dynamic stress intensity factor at the crack-tips x 1 = ±ā K ± I I (t) = normalized mode-II dynamic stress intensity factor at the crack-tips x 1 = ±a N = total number of the unknown quantities N A = total number of the application points N s = total number of the approximation terms N q = total number of the boundary elements N d = total number of the internal points N w = total number of the boundary nodes N a (ξ ) = standard shape functions for quadratic elements n i = components of the outward unit normal vector Correspondence: A. Ekhlakov,

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Section: E V a L U A T I O N O F T H E D O M A I N I N T E G R A L Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermoelastic crack analysis in functionally graded materials and structures by a BEM

Ekhlakov

Khay

Zhang

et al. 2012

Fatigue Fract Eng Mat Struct

View full text Add to dashboard Cite

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“…Polynomial series f j ¼ x m y n Fourier sine series f j ¼ sin mx sin ny Fourier cosine series f j ¼ cos mx cos ny Hyperbolic sine series f j ¼ sin h mx sin h ny Hyperbolic cosine series f j ¼ cos h mx cos h ny 181,216], thermoelasticity analysis [165,166,233] and elastoplastic analysis [180]. In [180], Ochiai and Kobayashi stipulated that the conventional MRBEM is not convenient to operate in the elastoplastic problems arising from inability in determining the distribution of initial stress and initial strain analytically.…”

Section: Global Basis Functionmentioning

confidence: 99%

Development and implementation of some BEM variants—A critical review

Kadarman

Djojodihardjo

2010

Engineering Analysis with Boundary Elements

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a b s t r a c tDue to rapid development of boundary element method (BEM), this article explores the evolution of BEM over the past half century. We here summarize the overall development and implementation of several well-known BEM variants that includes collocation BEM, galerkin BEM, dual reciprocity BEM, complex variable BEM and analog equation method. Their theoretical and mathematical backgrounds are carefully described and a generalized Laplace's equation (and Poisson's equation) is utilized in demonstrating the different approaches involved. An up-to-date review on characteristics and implementation for each of the five variants is presented and also highlighted their significant contributions in boundary element research. In addition, this article tries to cover whole aspect of interests including efficiency, applicability and accuracy in order to give better understanding of BEM evolution. Comparisons and techniques of improvement for these variants are also discussed.

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“…Shiah and Tan [4,5] presented a formulation for thermo-elastic analysis of a uniformly distributed heat source in an anisotropic 2D domain using the BEM. Shiah and Lin [6] and Shiah and Huang [7] analysed thermo-elastic problems involving non-uniform heat sources in a 2D anisotropic domain using the BEM. They used the multiple reciprocity method and transformed each domain integral into an infinite series of boundary integrals.…”

Section: Introductionmentioning

confidence: 99%

Boundary element analysis of two- and three-dimensional thermo-elastic problems with various concentrated heat sources Boundary element analysis of two- and three-dimensional thermo-elastic problems with various concentrated heat sources

Hematiyan

Mohammadi

Aliabadi

2011

The Journal of Strain Analysis for Engineering Design

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A heat source can be concentrated at a point, along a line, or over an area in a domain or distributed over the whole domain. In this paper, a boundary element formulation for thermo-elastic analysis of isotropic media with point, line, or area heat sources is presented. Temperature, displacement, and stress analyses are performed without internal points or cells and without any need to find the temperature distribution through the domain. Several numerical examples are presented to show the accuracy of the presented method. It is clearly demonstrated that the proposed boundary element formulation is much more efficient in comparison with domain methods.

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Multiple reciprocity boundary element analysis of two-dimensional anisotropic thermoelasticity involving an internal arbitrary non-uniform volume heat source

Cited by 16 publications

References 20 publications

Thermoelastic crack analysis in functionally graded materials and structures by a BEM

Thermoelastic crack analysis in functionally graded materials and structures by a BEM

Development and implementation of some BEM variants—A critical review

Boundary element analysis of two- and three-dimensional thermo-elastic problems with various concentrated heat sources Boundary element analysis of two- and three-dimensional thermo-elastic problems with various concentrated heat sources

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