Engineering Transactions, 23, 1, pp. 99-132, 1975

Nonstationary Temperature Distribution and Thermal Stresses in a Layered Elastic or Viscoelastic Medium

H. Bufler
Institut fur Mechanik (Bauwesen), Lehrstuhl II
Germany

G. Meier
Institut fur Mechanik (Bauwesen), Lehrstuhl II
Germany

A formal solution based on integral transforms and matrix analysis is given for the nonstationary fields of temperature, heat flux, stresses and displacements of a multilayered elastic medium. Non-linearities, inertia- and coupling effects are not taken into account. The applicability of the theory is demonstrated by means of numerically worked out examples. Extension to viscoelastic media is indicated.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

H.S. CARSLAW and J. C. JAEGER, Conduction of heat in solids, Oxford, at the Clarendon Press, 1959.

A.V. LUIKOV, Analytical heat diffusion theory, New York, Academic Press, 1968.

V. VODICKA, Steady temperature field in a composite doubly infinite strip, J. Phys. Soc. of Japan, Vol. 15, No. 7 (1960), p. 1232.

V. VODICKA, Steady temperature in an infinite multilayer plate. Stationary temperature fields in multilayer cylindrical tubes, Z. ang, Math, Mech., 40 (1960), p. 161, 165.

B.A. BOLEY and J.H. WEINER, Theory of thermal stresses, New York, John Wiley & Sons, Inc., 1967.

W. NOWACKI, Thermoelasticity, Oxford, Porgamon Press, 1962.

H. PARKUS, Thermoelasticity, Waltham, Mass., Blaisdell Publishing Comp., 1968.

E.L. McDOWELL, Thermal stresses in an infinite plate of arbitrary thickness, Proc. 3rd Midwest. Conf. on Solid Mech., (1957) p. 72.

I.N. Sneddon and F.J. LOCKETT, On the steady-state thermoelastic problem for the half-space and the thick plate, Quart. Appl. Math., 18, (1960), p. 145.

C.J. MARTIN and G. PAYTON, Thermoelastic stresses in a slab, J. Math. Mech., 13 (1964), p. 1.

M.P. HBISLER, Transient thermal stresses in slabs and circular pressure vessels, J. Appl. Mech., 20 (1953), p. 261.

W. DERSKI, On transient thermal stresses in a thin circular plate, Arch. Mech. Stos., 10 (1958), p. 551.

Z. MOSSAKOWSKA and W. NOWACKI, Thermal stresses in transversally isotropic bodies, Arch. Mech. Stos., 10 (1958), p. 569.

S. JARVIS and G. HARDY, Functions for thermal stress calculation near a transient heat source on a flat surface, J. Res. Nat. Bureau Stand., 70 B (1966), p. 265.

T. GOSHIMA, T. KOIZUMI and I. NAKAHARA, Axisymmetric quasi-static thermal stresses in an infinite slab, Int. J. Solids Structures, 9 (1973), p. 243.

F.V. POHLE and H. OLIVER, Temperature distribution and thermal stresses in Q model of a supersonic wing, J. Aeron. Sciences, 21 (1954), p. 8.

Z. PANKOWSKI, Stress and displacement fields due to a plane heat source in an infinite layered medium, Arch. Mech. Stos., 12 (1960), p. 749.

I.K. EBCIOGLU, Thermo-elastic equations for a sandwich panel under arbitrary temperature distribution, transverse load, and edge compression, Proc, 4th U.S. National Congress Appl. Mech., 1 (1962), p. 537.

JU-CHIN HUANG and I. K. EBCIOGLU, Circular sandwich plate under radial compression and thermal gradient, AIAA Journal, 3 (1965), p. 1146.

V. KOVARIK, On thermal stresses in sandwich plates, Acta technica CSAV, 4 (1967), p. 445.

A.F. RYABOV, Thermoelastic problem of multilayer plates, Prikladnaya Mekhanika, 3 (1967), p. 16 [Russian].

G. MEIER, Beitrag zur Berechnung geschichteter thermoelastischer Medien, Dissertation, Universität Stuttgart 1971,

H. BUFLER, Theory of elasticity of a multilayered medium, J. Elasticity, 1 (1971), p. 125.

H. BUFLER, Spannungs- und Stabilitätsproblem eines elastisch querisotropen Schichtsystems, Ing.-Arch., 41 (1972), p. 278.

A. PAPOULIS, A new method of inversion of the Laplace transform, Quart. Appl. Math., 14 (1956), p. 405.

W. NOWACKT, Theorie des Kriechens Lineare Viskoelastizität, Wien, Franz Deuticke, 1965.

A.I. LUR'E, Three-dimensional problems of the theory of elasticity, Moscow 1955.

V.Z. VLASOV and U.N. LEONT'EV, Beams, plates and shells on elastic foundations, Chapter 7 (translated from Russian, Moscow 1960), Jerusalem 1966.

I.N. SNEDDON, Fourier transforms, New York, Toronto, London, McGraw-Hill Book Comp., 1951.

B.C. PESTEL and F.A. LECKIE, Matrix methods in elastomechanics, New York, McGraw-Hill Book Comp., 1963.

K. MARGUERRE and R. UHRIG, Berechnung vielgliedriger Schwingerketten, Z. ang. Math. Mech., 44, (1964), p. 1.

H. BUFLER, Die Bestimmung des Spannungs- und Verschiebungszustandes eines geschichteten Körpers mit Hilfe von Übertragungsmatrizen, Ing. Arch., 31 (1962), p. 229.

E.C. TITCHMARSH, Introduction to the theory of Fourier integrals, Oxford, Clarendon Press 1937.

B.R. BAKER, Some fundamental thermoelastic problems in orthotropic slabs, J. Appl. Mech., 33 (1966), S. 45.

G. DOETSCI, Anleitung zum praktischen Gebrauch der Laplace-Transformation, München, R. Oldenbourg 1961.

V.I. KRYLOV and N.S. SKOBLYA, Handbook of numerical inversion of Laplace transforms, Jerusalem, IPST 1969 (Translation from Russian).

H. DUBNER and J. ABATE, Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform, J. Ass. Comp. Mach., 15 (1968), p. 115.

R. PIESSENS and M. BRANDERS, Numerical inversion of the Laplace transform using generalized Laguerre polynomials, Proc. IEE, 118 (1971), p. 1517.