Mode Ⅲ Crack Problems Of Orthotropic Media By Fractal Two Level Finite Element Method (F2LFEM)

In the present thesis, the fractal two-level finite element method (F2LFEM) are adopted to solve modeⅢcrack problem for orthotropic plate. In F2LFEM, the overall domain of cracked elastic body is divided into two domains D andΩby the artificial boundaryГ. The domain D is the region around the crack tip, which contains the singular field of problem. FFEM is employed in D . The domains outside D is the regular regionΩ, in which the traditional FEM is employed. In region D , infinite numbers of meshes and levels of finite element are generated in a self-similar manner with0 <ξ< 1, and the William's general solutions are adopted as the global interpolation function. As a result, the evaluation of infinite numbers of DOF is reduced the determination of the finite terms of generalized coefficients so that the computer storage and solution times are reduced significantly. And, by automatic refinement of the mesh with the ratio less than one, an infinitesimal mesh can be theoretical generated around the crack tip and it can highly improve the calculation accuracy.The fractal two-level finite element method (F2LFEM) has been successfully adopted to solve the stress intensity factor (SIF) for isotropic media problems. In this paper, this method is extended into the orthotropic media. The parameterβ= (μ_x /μ_y)^1/2 is introduced to perform coordinate transformation. The basic equations of antiplane crack problem for orthotropic media can be transformed in terms of those of isotropic media. Applying this analogy method, the William's general solutions for ModeⅢtwo-dimensional crack problem of orthotropic plates with internal and edge cracks are derived, respectively.The William's general solutions of ModeⅢcrack problems for orthotropic plate are used as the global interpolation function of fractal finite element method. The SIFs of orthotropic plate with edge, double-edge,centre crack and interior crack problems are obtained by using F2LFEM, respectively. The numerical examples are compared with the result from theory and show that the method is very efficient and accurate.At last, F2LFEM is adopted to solve the fund project concerning crack problems near crack tip buried in the rosette carbon-carbon nozzle of SPM supported by the China Aerospace Science & Technology Corporation (CASC). The SIFs of crack with differentαis obtained.