Analytical study of the thermal shock problem of a half-space with various thermoelastic models

Balla, M.

doi:10.1007/bf01171248

Cited by 42 publications

(9 citation statements)

References 25 publications

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“…From the value of the temperature and normal stress, the stresses y and ´c an be determined from Equation (30). For this case, and in the absence of body forces (f i ) and heat source (r), Equations (25) and (27) can be expressed as…”

Section: Statement Of Problemsmentioning

confidence: 99%

“…An observation of Equations (28) to (30) indicate that the determination of the temperature (T ), x-direction displacement (u x ) and normal stress ( x ) are of interest for a complete analysis. From the value of the temperature and normal stress, the stresses y and ´c an be determined from Equation (30). For this case, and in the absence of body forces (f i ) and heat source (r), Equations (25) and (27) can be expressed as…”

Section: Statement Of Problemsmentioning

confidence: 99%

“…In particular, we consider here a thermal shock problem of a half‐space, which is frequently used as a test example for thermoelastic problems due to its relative simplicity. Analytical solutions of such a problem have been reported since 1950, with the pioneering work due to Danilovskaya , who was among the first to give closed‐form, uncoupled, dynamic solutions for the temperature and stress fields. The problem, which involves a sudden, step‐jump heating on the boundary, was later named after her as ‘ Danilovskaya's first problem '.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

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A novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systems

Shimada

Masuri

Tamma

2014

Numerical Meth Engineering

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SUMMARYOf fundamental interest are multidisciplinary interactions encompassing: (1) first order systems such as those encountered in parabolic heat conduction, first order hyperbolic systems such as fluid flow, and so on, and (2) second order systems such as those encountered in hyperbolic heat conduction, hyperbolic second order systems such as elastodynamics and wave propagation, and so on. After space discretization using methods such as finite differences, finite volumes, finite elements, and the like, the consequent proper integration of the time continuous ordinary differential equations is extremely important. In particular, the physical quantities of interest may need to be mostly preserved and/or the equations should be optimally integrated so that there is minimal numerical dissipation, dispersion, algorithm overshoot, capture shocks without too much dissipation, solve stiff problems and enable the completion of the analysis, and so on. To-date, practical methods in most commercial and research software include the trapezoidal family (Euler forward/backward, Galerkin, and Crank Nicholson) for first order systems and the other counterpart trapezoidal family (Newmark family and variants with controllable numerical dissipation) for second order systems. For the respective first/second order systems, they are totally separate families of algorithms and are derived from altogether totally different numerical approximation techniques. Focusing on the class of the linear multistep (LMS) methods, algorithms by design was first utilized to develop GS4-2 framework for time integration of second order systems. We have also recently developed the GS4-1 framework for integrating first order systems. In contrast to all past efforts over the past 50 years or so, we present the formalism of a generalized unified framework, termed GS4 (generalized single step single solve), that unifies GS4-1 (first-order systems) and GS4-2 (second-order systems) frameworks for simultaneous use in both first and second order systems with optimal algorithms, numerical and order preserving attributes (in particular, second-order time accuracy) as well. The principal contribution emanating from such an integrated framework is the practicality and convenience of using the same computational framework and implementation when solving first and/or second order systems without having to resort to the individual framework. All that is needed is a single novel GS4-2 framework for either second-and/or first-order systems, and we show how to switch from one to the other for illustrative applications to thermo-mechanical problems influenced by first/second order systems, respectively.

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Section: Statement Of Problemsmentioning

confidence: 99%

Section: Statement Of Problemsmentioning

confidence: 99%

Section: Numerical Illustrationsmentioning

confidence: 99%

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A novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systems

Shimada

Masuri

Tamma

2014

Numerical Meth Engineering

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“…Based on the LS theory, Balla and Hungary [6] derived the analytical solutions for the thermal shock problem of a half-space due to a sudden heating and Ramp-type heating cases. Using these solutions, the distributions of temperature, displacement and stress fields were illustrated, and the propagation of elastic and thermal waves was also investigated.…”

Section: Introductionmentioning

confidence: 99%

A unified generalized thermoelasticity solution for the transient thermal shock problem

2011

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A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem.

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“…Recently an asymptotic approach [28] is introduced to solve some generalized thermoelastic problems [26,29]. For this asymptotic approach, the Laplace transform technique and its limit theorem are used to have an analytical solution to these generalized equations, and the closed-form solutions can be obtained when the governing equations are linearized, which is very important to reveal the general phenomenon involving finite propagation speed of heat signal and expands the applicability of linearization technique to generalized thermoelastic problems.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of thermoelastic response in functionally graded thin plate subjected to a transient thermal shock

Wang

Liu

Wang

et al. 2016

Composite Structures

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This paper is concerned with the thermoelastic response of a functionally graded thin plate with an analytical approach. The governing equations are derived in the context of the Lord and Shulman theory (L-S theory), where the material properties of the thin plate are assumed to be graded along the lengthwise direction according to a power law distribution.An asymptotic approach based on the layer method and the Laplace transform technique is presented to deal with these nonlinear governing equations, and then the closed-form solutions of displacement, temperature and stresses, induced by a sudden temperature rise at the boundary, are derived. The propagation of each wave, as well as the distributions of each physical field, are plotted and discussed. The comparison is also conducted to evaluate the effect of characteristic parameter, including the thermal relaxation time and the power law index, on thermoelastic response.

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Analytical study of the thermal shock problem of a half-space with various thermoelastic models

Cited by 42 publications

References 25 publications

A novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systems

A novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systems

A unified generalized thermoelasticity solution for the transient thermal shock problem

Asymptotic analysis of thermoelastic response in functionally graded thin plate subjected to a transient thermal shock

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