The Complex Potential Of The Entire Plane Elastic Problem Of Cyclical Thermo-elasticity And Application

In the theory of elasticity cyclical question research, all holds important status in the solid mechanics and the break theory simultaneously, in actual engineering design, also has the important application value. But, the existing research work has not considered in the cyclical plane elastic question temperature change this factor, but in actual project, because between the different material the thermal-expansion coefficient difference, in the object surely has the temperature stress, but the temperature stress can have the certain influence to the compound material performance.This article briefly was briefing the cyclical question research present situation, and in the research significance foundation, By the applications of the complex variable method, the general expression of the complex potentials in a finite multi-connected region under harmonic temperature change is derived. Then, based on the analysis for the expression and multivalue property of the periodic analytic function (the real part of which is given) and its object function, the general expression of the two complex potentials in plane elasticity for a body with a periodic set of holes under periodic harmonic temperature change is obtained; then, by the applications of the above result,the plane elastic problem of a nonhomogeneous body with a periodic set of cylindrical inclusions under periodic harmonic temperature change is dealt with, and some cylindrical inclusion with arbitrary cross section shape is included in each periodic cell; the material of the inclusions is different from that of the matrix, but with the same shear modulus. By the applications of the complex variable method and the study results for the quasi-periodic Riemann boundary value problem, the solution in closed form for the problem is obtained.