On Plane Welding Problems Of Doubly Periodic Plane Thermoelasticity

Research on doubly periodic elastic plane problems has important theoretical significance and plays an important role in rock mechanics, concrete mechanics, solid mechanics and the theory of fracture . In the actual design of the project, which also has an important value. However, the research is very weak, due to mathematical problems and the difficulty of the problem itself .At the same time, existing research has not yet considered doubly periodic elastic plane problems in the temperature change factor in the actual project, due to different coefficient of thermal expansion between the material differences between objects must exist in the thermal stress, temperature stress Composites will have some impact on material performance. On plane welding problems of doubly periodic plane thermoelasticity can be divided into two issues: First, consider the temperature of doubly periodic inclusion problem, and the other is the welding issues without temperature change. This article first studied the issue for more than two, By the application of the complex function method and district-wide function of pure theory, combined with the boundary value problem for analytic functions, the above-mentioned issues closed solution is derived, Then, as a special case, the analytical solution is given for doubly periodic single-cylinder inclusion issue. And then superimposed over the two, taken together, according to final results of the above-mentioned theories are given a further analysis of the results of specific issues. This article focuses on theoretical research.