Numerical thermal shock analysis of functionally graded and layered materials

Hein, Jarno; Storm, Johannes; Kuna, Meinhard

doi:10.1016/j.ijthermalsci.2012.05.005

Cited by 21 publications

(5 citation statements)

References 20 publications

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“…The vibration of composite plates subjected to mechanical and thermal disturbance is studied by Gilat et al 31 using the Runge–Kutta approach. Hein et al 32 used a numerical approach to undertake a thermomechanical vibration investigation of reinforced composite materials. Li et al 33 applied the differential quadrature approach to examine the transient response characteristics of a homogeneous beam exposed to extreme temperature.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali

2023

Math Methods in App Sciences

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Nonlinear transverse vibration of a micro‐size moving beam like structure under the influence of thermal conditions is studied. Hamilton principle is used to derive the nonlinear equation of motion. The derived equation of transverse motion is discretized using the Galerkin technique. The vibration attributes of the moving beam, such as frequencies of the transverse response, time response, and stability analysis, are investigated at different temperatures. For stability analysis, bifurcation diagrams are presented under the influence of temperature, length‐scale parameter, and excitation frequencies at various axial speeds of the beam.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali

2023

Math Methods in App Sciences

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Section: Introductionmentioning

confidence: 99%

“…Other numerical schemes for multilayer diffusion can be found in papers by Hein et al [9], McGinty and Pontrelli [16,17] and Gudnason et al [8]. Hein et al [9], who considered only Type I conditions, included a finite difference equation for the flux condition (1.6) directly, which was derived using second-order forward and backward difference approximations for the left and right-hand sides of equation (1.6), respectively. McGinty and Pontrelli [16,17] presented numerical solutions to a problem involving advection-diffusion across a layered medium, applying the strategy proposed by Hickson et al [11] for treating the interface conditions.…”

Section: Introductionmentioning

confidence: 99%

Finite volume schemes for multilayer diffusion

March

Carr

2019

Journal of Computational and Applied Mathematics

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This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited number of interface conditions and do not carry out stability or convergence analysis. Our method also retains second-order accuracy in space while preserving the tridiagonal matrix structure of the classical single-layer discretisation. Stability and convergence analysis of the new finite volume method is presented for each of the three classical time discretisation methods: forward Euler, backward Euler and Crank-Nicolson. We prove that both the backward Euler and Crank-Nicolson schemes are always unconditionally stable. The key contribution of the work is the presentation of a set of sufficient stability conditions for the forward Euler scheme. Here, we find that to ensure stability of the forward Euler scheme it is not sufficient that the time step τ satisfies the classical constraint of τ ≤ h 2 i /(2D i ) in each layer (where D i is the diffusivity and h i is the grid spacing in the ith layer) as more restrictive conditions can arise due to the interface conditions. The paper concludes with some numerical examples that demonstrate application of the new finite volume method, with the results presented in excellent agreement with the theoretical analysis.

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“…In [21] the analysis of heat transfer and thermal stresses in metal/ceramic thermal barrier coatings of turbine blades has been carried out using the abilities of the both numerical packages mentioned above, but graded finite elements were not used. The numerical results and analytical solutions on distributions of the temperature and thermallyinduced stresses in a FGM plate under thermal shock loading have been obtained in [23]. Those calculations were carried out using the ABAQUS code, where material gradients were programmed by using a combination of mechanical and thermal subroutines of this package.…”

Section: Introductionmentioning

confidence: 99%

Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements

Burlayenko

Altenbach

Sadowski

et al. 2017

Applied Mathematical Modelling

113

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For better understanding of the behavior of functionally graded materials (FGM) in high temperature environment, a reliable and efficient numerical tool is required for predictions of heat transfer behavior and thermally-induced stresses in them. This study presents a finite element formulation of a coupled thermo-mechanical problem in functionally graded metal/ceramic plates. The theoretical framework considers the finite element method (FEM) which is applied to the development of a functionally graded two-dimensional plane strain finite element. The plane strain graded finite element is incorporated within the ABAQUS tm code via the combination of user-defined subroutines. The subroutines enable us to program graded mechanical and thermal properties of the FGM as continuous position-dependent functions and, then, to sample them directly at the Gauss integration points of the element. The performance of the developed graded finite element is verified by comparisons with results known in the literature and with calculated using conventional homogeneous elements in a layered model. The solutions of thermomechanical problems of functionally graded plates referring to pure mechanical and thermal tasks, and uncoupled and coupled analyses of thermoelasticity are carried out and discussed in the paper. Highlights• A finite element formulation of the coupled thermo-mechanical problem of a FGM plate is presented.• A graded plain strain element is incorporated within the ABAQUS code environment.• The performance of the graded element is validated by solving thermo-mechanical problems.• The examples reveal a high accuracy and efficiency of the developed graded finite element. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 *Highlights AbstractFor better understanding of the behavior of functionally graded materials (FGM) in high temperature environment, a reliable and efficient numerical tool is required for predictions of heat transfer behavior and thermally-induced stresses in them. This study presents a finite element formulation of a coupled thermo-mechanical problem in functionally graded metal/ceramic plates. The theoretical framework considers the finite element method (FEM) which is applied to the development of a functionally graded two-dimensional plane strain finite element. The plane strain graded finite element is incorporated within the ABAQUS tm code via the combination of user-defined subroutines. The subroutines enable us to program graded mechanical and thermal properties of the FGM as continuous position-dependent functions and, then, to sample them directly at the Gauss integration points of the element. The performance of the developed graded finite element is verified by comparisons with results known in the literature and with calculated using conventional homogeneous elements in a layered mode...

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Numerical thermal shock analysis of functionally graded and layered materials

Cited by 21 publications

References 20 publications

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Finite volume schemes for multilayer diffusion

Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements

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