In this article, using the method of dislocation distribution and separation of variables, the mechanical fracture behavior of a thin rectangular plane made of piezoelectric material with limited length and width containing several cracks under out-of-plane mechanical and in-plane electrical loading is investigated. It is assumed that the behavior of the elastic medium is linear and the surfaces of the cracks are smooth. At first, the governing equations of the problem are solved according to the boundary conditions, and then the components of stress and electrical displacement in the body without cracks under external loading at the hypothetical crack location are presented. Then, according to Buckner's principle, the stress field obtained in the main problem and using the dislocation distribution method, the equations for analyzing the problem of several cracks are presented. By solving these equations and obtaining the distribution functions of dislocations, it is possible to obtain the stress and electric displacement factors at the tips of cracks. In this article, examples are given to verify the results and also to investigate the effects of the length, arrangement and interaction between the cracks on the field intensity factors.
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