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On the three-dimensional thermostressed state of rectangular plates under nonuniform heating. (English. Russian original) Zbl 0925.73265

J. Math. Sci., New York 90, No. 1, 1811-1816 (1998); translation from Teor. Prikl. Mekh. 27, 18-26 (1997).
Summary: We consider three-dimensional boundary-value problems of the stationary theory of heat conduction and thermoelasticity for rectangular homogeneous isotropic plates of arbitrary thickness. It is assumed that the temperature or heat flux density prescribed on the top and bottom surfaces admit a representation in the form of double trigonometric series. A closed form analytic solution is obtained for the boundary-value problems of thermoelasticity in the case of plates with contacting edges along the lateral faces. Numerical computations are given for three types of boundary-value problems using the software package Mathcad PLUS 6.0 for thin and thick plates. We construct the graphs of variation of the temperature, deflection, and normal stresses over the thickness of the plate.

MSC:

74K20 Plates
80A20 Heat and mass transfer, heat flow (MSC2010)

Software:

Mathcad
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Full Text: DOI

References:

[1] A. D. Kovalenok,Foundations of Thermoelasticity [in Russian], Kiev (1970).
[2] A. V. Lykov,Theory of Heat Conduction [in Russian], Moscow (1967).
[3] A. I. Lur’e,Three-dimensional Problems of the Theory of Elasticity [in Russian], Moscow (1955).
[4] C. K. Youngdahl, ”On the completeness of a set of stress functions appropriate to the solution of elasticity problems in general cylindrical coordinates,”Int. J. Eng. Sci.,7, No. 1, 61–79 (1969). · Zbl 0167.52901 · doi:10.1016/0020-7225(69)90023-8
[5] B. F. Vlasov, ”On a case of bending of a rectangular thick plate,”Vestn. Mosk. Univ., NO. 2, 25–34 (1957).
[6] V. F. Ochkov,Mathcad PLUS 6.0 for Students and Engineers [in Russian] Moscow (1996).
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