Plane Thermal Stress at an Elliptical Elastic Inclusion Under Uniform Heat Flow

Real-form solution for an anisotropic elastic elliptical inhomogeneity under uniform heat flux

“…For a monoclinic material with the plane of symmetry at x 3 = 0 , the stresses at infinity are zero when subjected to a uniform remote heat flux due to the fact that ( t 12 ∞ ) 3 = 0 in this case. This conclusion is in agreement with that found in Chen [2].…”

“…It is seen from equation (50) that the internal stresses and strains inside the elliptical inhomogeneity are linear functions of the two in-plane coordinates x 1 and x 2 . This observation is consistent with that in Chen [2], Kattis and Meguid [5], and Chao and Shen [6]. Equations (62) and (65) provide the solution for the vectors h 1 , g 1 , h 2 , g 2 describing the distribution of stresses, strains, and displacements in the matrix.…”

“…The remote stresses are zero, however, in the case of a monoclinic material with the plane of symmetry at x 3 = 0. This conclusion is in agreement with that found in Chen [2]. Using the identities developed in the Stroh formalism, the unknown real constant vectors describing the thermoelastic fields in the elliptical inhomogeneity and in the surrounding matrix are determined in an elegant manner.…”

“…Several authors have addressed the problem concerning the deformations of an infinite elastic matrix into which is embedded an isotropic or anisotropic elastic elliptical inhomogeneity (including the two limiting cases in which the inhomogeneity takes the form of an elliptical hole or an elliptical rigid inclusion) and is subjected to prescribed remote uniform heat flux (see, for example, previous works [1][2][3][4][5][6][7][8]). In the context of thermo-anisotropic elasticity, however, certain issues remain.…”

Thermal stresses around a ribbon-like inclusion in a semi-infinite medium under uniform heat flow

“…However the majority of the investigations [1][2][3][4][5][6][7][8] in this field are confined to the problems for inhomogeneities with smooth surfaces because of the mathematical tractability. However the majority of the investigations [1][2][3][4][5][6][7][8] in this field are confined to the problems for inhomogeneities with smooth surfaces because of the mathematical tractability.…”