Temperature response of an infinitely thick slab to random surface temperatures

Heller, R. A.

doi:10.1016/0093-6413(76)90097-5

Cited by 17 publications

(7 citation statements)

References 4 publications

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“…He obtained the response autocorrelation functions and power spectral densities of temperatures with stationary Gaussian excitation temperatures. Heller [7] developed statistical relations for the temperature response in an infinitely thick slab subjected to randomly varying surface temperatures. Lenyuk et al [8,9] investigated the case of an elastic halfspace by taking random boundary conditions and an isotropic homogeneous symmetric body by taking the external medium temperature to be an arbitrary function of time and determined the stresses.…”

Section: Introductionmentioning

confidence: 99%

Transient temperature distribution and thermal stresses in a thick plate subjected to random pulses

Bhoyar¹,

Varghese²,

Khalsa³

2019

International Journal of Thermodynamics

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This paper deals with the determination of second-order statistics (the mean of each component and correlations between components) of the quasi-static temperature distribution and thermal stresses on a thick plate under thermal load. The heated thick circular plate with random internal heat generation acting at random instants of time, in addition to sectional heat supply in the form of random impulses on the upper face, while the lower face is kept at zero temperature, and the fixed circular edge thermally insulated in considered for investigation. A type of Laplace transform method is employed to obtain the analytical solutions for the temperature and stresses statistics. The effects of the statistics of the random temperature distribution and its associated stresses are signified graphically that highlight the developments proposed in this paper.

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Section: Introductionmentioning

confidence: 99%

Transient temperature distribution and thermal stresses in a thick plate subjected to random pulses

Bhoyar¹,

Varghese²,

Khalsa³

2019

International Journal of Thermodynamics

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“…Heller [7] derived the frequency response function for the temperature of an infinite plate subjected to random heating, from which the standard deviation of the temperature was estimated. Using a similar method, Heller also addressed the stochastic analysis for twodimensional non-axisymmetric heat conduction of an infinite multilayered cylinder subjected to random heating at the outer surface [9].…”

Section: Case Of Random Surface Temperature or Ambient Temperaturementioning

confidence: 99%

Stochastic Analysis of Heat Conduction and Thermal Stresses in Solids: A Review

Chiba¹

2012

Heat Transfer Phenomena and Applications

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“…Thus, Esh(X, t) = Ksh [h (x, t) -1]. Since, however, we assume for the purpose of calculating the frequency response function that the initial value of h is 0 rather than 1, we use Esh(X,t) = Kshh(x,t) (16) The shrinkage coefficient depends on age, t. However, this dependence is not strong and has been neglected in numerical calculations, although the same type of solution would be possible even if the dependence of Ksh on t were considered.…”

Section: Finite Element Analysis Of Frequency Response Of Stressmentioning

confidence: 99%

“…Solution of a typical problem of this kind, concerned with random thermal stresses in an infinitely long cy-lindrical elastic vessel, was pioneered by Heller with co-workers (16)(17)(18)(19)(20)23) who applied the spectral method (method of power response spectra). His analytical solution is, however, inapplicable to concrete, because the drying diffusivity and creep strongly depend on age.…”

Section: Introductionmentioning

confidence: 99%

Spectral Finite Element Analysis of Random Shrinkage in Concrete

Bažant¹,

Wang

1984

J. Struct. Eng.

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The spectral method, previously generalized for aging linear systems, is applied in conjunction with the finite element method to an~lyze shrinkage stresses in aging viscoelastic structures exposed to random enVIronmental humidity. The age-dependence of both drying diffusivity and creep properties are taken into account. The solution of pore humidity is obtained from a matrix differential equation in time, with complex-valued matrices. Elastic shrinkage stresses are then obtained from the matrix equations of the finite element method, in which the matrices are also complex-valued. The stresses in presence of aging creep are detennined by a sllperposition integral in time based on the relaxation function. Numerical examples concerning a long cylindrical vessel exposed at the outer surface are given. The standard deviations of pore humidity and of stresses significantly vary with time, and their standard deviation exhibits fluctuations about a drifting mean. The solution is practically meaningful only if concrete does not crack, e.g., when a prestress sufficient to prevent cracking is introduced. For environmental fluctuations of long periods, such as one year, the computation is quite efficient; however, if shorttime fluctuations are considered, the computing time becomes very large.

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Temperature response of an infinitely thick slab to random surface temperatures

Cited by 17 publications

References 4 publications

Transient temperature distribution and thermal stresses in a thick plate subjected to random pulses

Transient temperature distribution and thermal stresses in a thick plate subjected to random pulses

Stochastic Analysis of Heat Conduction and Thermal Stresses in Solids: A Review

Spectral Finite Element Analysis of Random Shrinkage in Concrete

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