The Analysis Of Mode Ⅲ Fracture In Elastic Material And Piezoelectric Material By HT BEM

The analysis of mode â…¢ fracture problems for elastic material and piezoelectric material are studied in the paper by Hybrid Trefftz boundary element approach. The formulations of mode â…¢ fracture problems in the direct method and indirect method, including collocation method, the lease square method and Galerkin method, are deduced by HT boundary element method using the Trefftz complete solution and the Trefftz special purpose function, then the programmes of indirect boundary element method, including collocation method and Galerkin method, are programmed by FORTRAN. Specially, auxiliary functions which satisfy exactly the specified boundary conditions along the microsize slit boundaries are also proposed to improve the accuracy of the degree. Meanwhile, both the stress intensity factor which describes the singular behavior of crack tip in the mode â…¢ fracture in the elastic material, and the energy release rate which describes the singular behavior in coupling field are determined directly by the unknown parameters of the Trefftz special purpose function. Furthermore, the examples of application in elastic material and in piezoelectric material are given to discuss the characters of HT boundary element method by the changes of the stress intensity factor and the energy release rate varying with the terms of the special function, the number of crack elements, the number of collocation points and the number of the Gauss points. Compared with the conventional finite element method and boundary element method, in which the special method such as local mesh refinement must be adopted, the higher precision is obtained by using much less number of elements and nodes. Besides the value of the stress intensity factor and the energy release rate, the value of displacement in elastic field and the value of electric potential in piezoelectric field are computed with higher precision. What's more, considering the nonlinearity of material behavior and constitutive equation, the governing equation can be deduced to Poisson equation or more complex equation, the process of computing is similar to the Laplace equation except for the corresponding the Trefftz complete solution and the special purpose solution. Namely, the HT boundary element method has the same precision, reliability and applicability to the nolinear problems.