Mixed Analytic Function Method For Anisotropic Elastic Planes With Cracks

In this paper,we study the application of the mixed analytic functions to anisotropic elastic planes containing cracks.We use the mixed analytic function to transform the cracks into Riemann value problems by taking advantage of the knowledge of complex function,and then to obtain the stress functions.After introducing the anisotropic material,fracture mechanics and the related knowledge of mixed analytic function,in Chapter 3 we first give the mixed analytic function expression of the complex stress function on the cracks-containing anisotropic elastic plane when the pairs of complex parameters are equal.And further transform the first fundamental problem into the mixed analytic function singular integral equation by using the generalization of the value problem of the analytic function.Finally we discuss the problem of collinear cracks in the anisotropic elastic plane.It is solved by the complex variable function,which leads to the corresponding complex stress function expressions.After that,in Chapter 4,we discuss the mixed analytic function expressions of the complex stress function for the crack-containing anisotropic elastic plane when the complex parameters are all not equal.And solve the first fundamental problem.We also discuss the related problem of the plane containing linear cracks,obtain the corresponding complex stress functions and stress intensity factor,and the change chart of stress intensity factor is also obtained by Matlab.Finally,we summary the whole paper and propose research directions for the subsequent development.