Pergamon Int. J. Engng Sci. Vol. 34, No. 11, pp. 1259-1269, 1996 Copyright 0 1996 Elsevier Science Ltd PII: S0020-7225(96)00023-7 Printed in Great Britain. All rights reserved 0020-7225/96 $15.00+ 0.00 AN ANALYTICAL SOLUTION OF THERMOPLASTIC THICK-WALLED TUBE SUBJECT TO INTERNAL HEATING AND VARIABLE PRESSURE, TAKING INTO ACCOUNT CORNER FLOW AND NONZERO INITIAL STRESS H. WONG Laboratoire des Gdomateriaux, Ecole Nationale des Travaux Publics de l'Etat (ENTPE), Rue Maurice Audin, 69518 Vaulx-en-Velin, France O. SIMIONESCUt Department of Mechanics, Bucharest University, Str. Academiei 14,70109 Bucharest 1, Romania Abstract--An analytical model of an elastoplastic thick-walled tube subject to an internal pressure and to an axisymmetrical time dependent temperature field is presented. The subsequent thermal expansion generates plastic zones according to a precise predetermined order. Based on a set of simplifying, but realistic assumptions, we obtain a closed form solution expressed in terms of the main unknowns of the problem (i.e. the boundaries of the elastoplastic zones). These unknowns are simply the roots of a set of algebraic equations, and can easily be determined by simple numerical computations. Finally, a comparison with two-dimensional numerical results is presented. Copyright © 1996 Elsevier Science Ltd 1. INTRODUCTION In recent years the problems of thermomechanical behaviour of underground structures have received considerable attention. In this frame, the problem of a thick-walled tube subject to a thermal loading, and its equivalent homologue, the circular tunnel in an infinite medium, heated from the wall, have become of great importance in engineering applications. Many practical problems can be treated by these types of modelling, such as underground storage of nuclear wastes, underground coal gasification, or the stability of deep petroleum borings (see, for example, Refs [1-4]). However, whereas the case of mechanical loading under isothermal conditions has been treated in a large number of publications, analytical solutions which take into account thermal loads are relatively rare. The first analytical thermomechanical model of the thick-walled tube seems to be due to Bland [5], who analysed the case of a stationary temperature field and a variable internal pressure, under the hypothesis of face flow. lshikawa and Hata [6] and Schmitt [7] considered more complex theological behaviours, leading also to more extensive numerical computations. Under spherical symmetry, Berest [8] analyses the behaviour of a point source of heat in an elastoplastic medium and, later, Berest and Rousset [9] extend the model to a viscoplastic medium. In our paper the problem of a thick-walled cylindrical tube under internal pressure and subject to an axisymmetrical time dependent temperature field is presented, supposing a quasi-static evolution, small displacements, axisymmetrical plane strains, and the yield criterion of Tresca. We can show how the plastic zones with face flow and corner flow can coexist, and interact (one plastic zone may erase another one). The resulting solution depends on the boundary radii, which are the principal unknowns of our problem. Its exploitation requires little computational effort compared with the numerical approaches of this problem. Our results are compared with those obtained from its equivalent homologue problem, the thermoplastic behaviour of a circular tunnel (see Refs [10, 11]). Finally, we compare our tAuthor to whom correspondence should be addressed. 1259