Boundary Element Method For Thin Plates Bending Problem With Crack

Thin plate is widely used in practical engineering. In virtue of the characteristic of the material and the mechanical feature, the plate is usually working with cracks. For the purpose of safety and design, it is necessary to find out the stress state of the plate with crack as important bearing member. For a static analysis of thin plates with crack, the boundary element method due to the advantages over other methods is considered to be an effective tool to the fracture analysis of the plate bending.Firstly, the thesis traces back comprehensively the development and present state of some relative subjects. Secondly, Matlab code is implemented based on the direct boundary integral equations. Thirdly, treating creatively the crack as the independent boundary, deduce the indirect boundary integral equations of thin plate with crack. The integrals in the IBEM integral equations generally contain strong kernel singularity problems. New treatment techniques are applied to the singular and hyper-singular kernels, respectively. Finally, based on the indirect boundary integral equations deduced forward, Matlab code is implemented for both thin plate and thin plate with crack.Equations deduced in this thesis and results of programs have been verified by theoretical solution and numerical solution in ANSYS.