The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity

Mierzwiczak, Magdalena; Chen, Wen

doi:10.1016/j.ijheatmasstransfer.2015.07.051

Cited by 38 publications

(17 citation statements)

References 38 publications

(62 reference statements)

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“…Mierzwiczak et al [17] presented the singular boundary method for steady-state nonlinear heat conduction problems. Bhavani et al [26] solved thermoelastic equilibrium equations for a functionally graded beam to obtain the axial stress distribution.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Most of these researches on FGMs have been restricted to heat conduction analyses, thermal stress analyses, thermal buckling analyses, thermal vibration, and optimization problem. Various numerical techniques, such as the finite difference method (FDM) [2,3], finite element method (FEM) [4][5][6][7], boundary element method (BEM) [8], or more recently developed meshless methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], have been developed for analyzing thermal related problems and other problems. Because of the complexity of the relevant governing equation, analytical solutions are usually difficult to obtain for those arbitrary geometry and complex boundary conditions, and the exact solutions are usually obtained based on classical plate theory, first-order shear deformation theory, high-order shear deformation theory, and so on [24,25].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermal Analysis of 2D FGM Beam Subjected to Thermal Loading Using Meshless Weighted Least‐Square Method

Zhou

Zhang

Wang

2019

Mathematical Problems in Engineering

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The paper analyzed the thermal problem of the 2D FGM beam using meshless weighted least-square (MWLS) method. The MWLS as a meshless method is fully independent of mesh, and an approximate function was used to construct a series of linear equations to solve the unknown field variable, which avoided the troublesome task of numerical integration. The effectiveness and accuracy of the approach were illustrated by a clamped-clamped FGM beam which was subjected with interior heat source. The volume fraction of FGM beam was assumed to be given by a simple power law distribution. The effective material properties of the FGM beam were assumed to be temperature independent and calculated by Mori-Tanaka method. The results showed that a good agreement was achieved between the proposed meshless method and commercial COMSOL Multiphysics.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal Analysis of 2D FGM Beam Subjected to Thermal Loading Using Meshless Weighted Least‐Square Method

Zhou

Zhang

Wang

2019

Mathematical Problems in Engineering

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“…In the literature, the Kirchhoff transformation that allows to transform the nonlinear diffusive equation into a linear equation is in general presented [14,22] as…”

Section: Kirchhoff Tangent Transformationmentioning

confidence: 99%

Observer design for a nonlinear diffusion system based on the Kirchhoff transformation

Benameur

Maidi

Djennoune

et al. 2017

Int. J. Dynam. Control

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This paper deals with the state estimation for a nonlinear diffusion system. An observer that reconstructs the whole state, from the available measurements, is proposed based on an equivalent linear diffusion model obtained using the Kirchhoff tangent transformation. This bijective mapping allows to apply the available and powerful state estimation theory of linear distributed parameter systems and simplifies the observer design. Hence, an observer can be designed for the obtained equivalent linear diffusion system and by using the Kirchhoff transformation, the whole state of the original nonlinear diffusion system is recovered. The observability analysis of the nonlinear diffusion system and the convergence of the proposed observer are also investigated based on the equivalent linear diffusion system. The effectiveness of the proposed observer is shown, through numerical simulation runs, in the case of a heated steel rod by considering both an uniformly distributed and a punctual boundary sensing. Keywords distributed parameter system • nonlinear diffusion • partial differential equation • Kirchhoff tangent transformation • state estimation • observer.

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“…It was demonstrated that the numerical algorithm was accurate, computational efficient and stable. Recently, the Singular Boundary Method (SBM) was applied to investigate the inverse anisotropic heat conduction problems [27] , heat conduction in nonhomogeneous materials [28] , and steady-state nonlinear heat conduction problem with temperaturedependent thermal conductivity [29] . Yosibash and his co-workers systematically investigated the steadystate thermal conduction problems with singularities and obtained numerical solutions of the generalized flux intensity factors (GFIF) based on post process operations in conjunction with FEM [30,31,32,33] .…”

Section: Introductionmentioning

confidence: 99%

Study on steady-state thermal conduction with singularities in multi-material composites

Gao

Yao

et al. 2017

International Journal of Heat and Mass Transfer

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Increasing demand in material and mechanical properties has led to production of complex composite structures. The composite structures, made of different materials, possess a variety of properties derived from each material. This has brought challenges in both analytical and numerical studies in thermal conduction which is of significant importance for thermoelastic problems. Therefore, a unified and effective approach would be desirable. The present study makes a first attempt to determining the analytical symplectic eigen solution for steady-state thermal conduction problem of multi-material crack. Based on the obtained symplectic eigen solution (including higher order expanding eigen solution terms), a new symplectic analytical singular element (SASE) for numerical modeling is constructed. It is concluded that composite structures composed of multi-material with complex geometric shapes can be modeled by the developed method, and the generalized flux intensity factors (GFIFs) can be solved accurately and efficiently

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The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity

Cited by 38 publications

References 38 publications

Thermal Analysis of 2D FGM Beam Subjected to Thermal Loading Using Meshless Weighted Least‐Square Method

Thermal Analysis of 2D FGM Beam Subjected to Thermal Loading Using Meshless Weighted Least‐Square Method

Observer design for a nonlinear diffusion system based on the Kirchhoff transformation

Study on steady-state thermal conduction with singularities in multi-material composites

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