Force Power Failure In Study

Generally, the failures or the breakage of structures due to the convergence of local stress which was induced by disfigurements, such as cracks, holes, notches, interfaces and so on. So the problems of the body with disfigurement have gained great attention. For elastic materials, many two-dimension problems have been solved and a lot of three-dimension problems have been working on. Some problems have been solved in closed forms. On the other hand, for the piezoelectric materials, only two-dimension problems can be work out at the present.In this paper, the first part is on the basis of Kane-Mindlin theory, which was brought forward by Kane and Mindlin in their working on dynamic plate problems. The second part is on the basis of the Lekhnitskii's theory for elastic materials. The Muskhelishvili-Lekhnitskii's complex potential has been used in solving the problem. The main contents of this paper includes:(1) the work on the elastic materialsIn this paper, on the basis of the suppose of Kane-Mindlin, the stress method as well as strain method were used for seeking the solutions of the quasi three-dimensional problems of a circular hole and a cylindrical inclusion embedded in an isotropic elastic plate of finite thickness. All the audience components of stress were obtained in explicit. The stress concentration near the hole or interface was analyzed, and the three-dimensional effect has been discussed. The curves of some quantities were given. The present solutions for very thin plate are proved to be coincided very well with the plane stress solutions. This provides validation of the present works.(2) the work on the piezoelectric materialsFirst, on the basis of the Lekhnitskii's theory for elastic materials and the work of Sosa, the plane problem of piezoelectric plates with an elliptic hole has been solved. The stress concentrations near the hole were discussed. Then curves of some components were given. So the variety of the stress convergence along with the formal of elliptic has been characterization. Second, the plane strain problem of piezoelectric plate with an elliptic elastic inclusion has been solved.For the mapping function is not a one to one mapping function, we introduce an assumption, which has been proposed in Lekhnitskii's literature, without proved.Then this problem was successfully solved.