An exact solution for thermal stresses in a three-phase composite cylinder under uniform heat flow

Abstract

An exact solution is given for the stress field in a three-phase composite cylinder induced by a uniform heat flow applied at infinity. Based on the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stress functions are derived explicitly in each medium of a three-phase composite cylinder. It is discovered that the stress in the inclusion is always linearly proportional to the coordinate z. Comparison is made with the special case of a two-phase composite cylinder, which shows that our results presented here are exact and general.

Interaction between a Nonuniformly Coated Circular Inclusion and a Remote Uniform Heat Flow

“…(75) and Eq. (76), can be reduced to an exact solution, which is identical to the one provided by Chao et al [12]. The angular variations of interfacial stresses for a three-phase cylinder are discussed in detail and shown in graphic form.…”

“…Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to heat conduction and thermoelasticity problems for a three-phase multilayered cylinder were first derived by Chao et al [11]. By using the same method, an exact solution for thermal stresses in a three-phase composite cylinder subject to uniform heat flow was provided by Chao et al [12]. By using the Peach-Koehler formula, the image force due to edge dislocations interacting with a nonuniformly coated circular inclusion was investigated by Chen [13].…”

Numerical Simulation of Conjugate Heat Transfer in Forced Convective Boundary Bilayered Cylindrical Pipe with Different Peclet Numbers

“…For instance, some investigations have been done on the thermo-mechanical and mechanical properties of composite laminates (Chao et al 2007;Pradeep and Ganesan, 2008). Therefore, the present work is centred on adaptation of wall-fluid interfacial temperature and heat flux distribution for the characterization of conjugate heat transfer dynamics in bilayered cylindrical pipe.…”

Heterogeneous Problems in Plane Thermoelasticity

“…It should be noted that the transformation involved must be independent of the loading considered. This methodology has been advanced and implemented recently by the authors in a series of papers [2][3][4][5][6][7][8][9]. For example, Chao and Young [2] gave an explicit general solution of an infinitely extended plate containing any number of circular inclusions under antiplane deformation.…”

“…Green's functions for the circularly cylindrical layered media under a point force and a point heat source were given by Chao et al [7] and Chao and Chen [8], respectively. An exact solution for thermal stresses in a three-phase composite cylinder under a remote uniform heat flow was provided by Chao et al [9].…”