Coupling Effect Of Elastic Elliptical Inclusion With The Dislocation And Thermal Power

A new analytical method for the plane elastic or thermoelastic problem on complex multiply connected region based upon the complex potential theory of elastic mechanics built by Muskhelishvili. N. I. By combining the theory of sectionally holomorphic function, Cauchy model integral, the analysis of the singularity of complex function and Riemann boundary problem, the analysis relation between the complex potentials is obtained, and then the problem is transformed into solving an elementary complex potentials equation. Using this method, the coupled fields for an elastic elliptical inhomogeneity with a screw dislocation under infinite longitudinal shear is examined. The precise solutions in series form under general loads and several typical solutions in closed form are provided. The general formulas for interaction energy and the force acting on the dislocation due to the presence of an elliptical inhomogeneity under longitudinal shear are given. The force acting on the dislocation is figured out, particular discussion being given to its variation with the dislocation azimuth and other parameters. It is shown that the force acting on the dislocation first reduces and then increases with the augment of dislocation azimuth. The plane thermoelastic fields for elliptical inhomogeneity problem are studied. The coupled effect is analyzed for an elliptical inhomogeneity under plane uniform loads and linear temperature change at infinity. The complex potentials are obtained for an elliptical inhomogeneity under plane uniform mechanical loading, uniform temperature change and uniform heat flow directed at any angle. The discussion is also given to the variation of the interfacial stresses with thermal parameters. It is shown that the interfacial stresses increase with the heat conductivity of the matrix. The thermoelastic problem of a point heat source outside an elliptical inhomogeneity is studied, with the complex potentials being obtained. The general solutions in this paper include several existing solutions, and a wrong solution in a reference is corrected.