层体边界元法在二维层体断裂分析中的应用

在刚度矩阵法的基础上建立了用于进行二维多层体结构断裂分析的边界单元法（ＢＥＭＬＭ）由于ＢＥＭＬＭ的基本方程中已经包含了层体表面和裂纹缝面的边界条件，因而不需要对这些边界进行单元离散，从而其断裂分析可望有较好的精度通过与柯西积分方程法进行结合，算例表明ＢＥ ＭＬＭ是可靠并有效的

BOUNDARY ELEMENT ANALYSIS OF CRACK PROBLEMS IN FINITE 2-D MULTILAYERED COMPOSITE 1)

On the basis of Stiffness Matrix Method (SMM), a boundary element method to 2-D layered media (BEMLM) is developed in this paper to the crack analysis problems in layered elastic media By way of introducing additional interfaces together with its dislocation connecting conditions, SMM can be modified to include unit concentrated dislocations in its basic stiffness relations, which can be served as fundamental solutions to the layered media These fundamental solutions are given either in explicit form as the layer number is one or two, or in the form of Fourier integration Because of involving of dislocations, the singularities are introduced into the stiffness relations in the mean time To improve the numerical convergence defects of Fourier integrations from these singularities, superposition method is used to take the advantage of theoretical solutions of a crack problem in an ideal condition, which is proven to be very effective by a result of a numerical example On the basis of the general stiffness equations that include surface, interface, crack and lateral boundary conditions associated with a finite muti-layered media, integral equations describing the crack surface boundary conditions can be derived In view of the singularity problems of these integral equations, asymptotic analysis is made to the singular kernel, by which, singularities can be separated from the equations, and stress intensity factors of the cracks can also be obtained numerically with the aid of Cauchy Integral Equation Method In the end of this paper, a numerical example is given to a weak interlaminar crack analysis that has lateral boundaries Comparing with the results from Yuuki, R (1987), Erdogan, F (1971), it is shown that BEMLM is reliable and more effective to the crack analysis of layered media Owing to the involvement of surfaces, interfaces and crack lips conditions in the basic relations of BEMLM, there is no need to the discretizations along these boundaries, whereupon more accurate results can be expected