The numerical solutions of the periodic crack problems of anisotropic strip are investigated in this paper. Using the complex variable method the mathematical model, boundary value problems for analytic functions, is established. After constructing appropriate integral transformations the boundary value problems are transformed into integral equations. Employing Lobotto-Chebyshev quadrature formulas and Gauss quadrature formulas, the approximate analytical expressions of the stress intensity factors are obtained. And some numerical results are performed for several special cases.

本文讨论双周期胞腔中含任意形状孔洞的不同材料弹性平面焊接的第二基本问题。引进函数，构造了推广的ⅢepMaH变换，将这类弹性平面问题归结为求解正则型的奇异积分方程，最后证明了其解的存在和唯一。所用方法简单、直观，而且由于是构造性的，因而有利于具体的数值求解。

In this paper, the mathematk: al problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated, and the interface are arbitrary smooth closed contours. At first, we establish mathematical models by using Muskhelisvili complex variable methods, change the primitive problems into searching complex stress functions whwh satisfy four boundary value problems and construct forms of the solution. then, under some general restrictions it is reduced to normal type singuiar integral equation, the unique olvability is proved mathematically.

本文讨论双周期胞腔中含任意形状裂纹的不同材料的弹性平面焊接。（焊线为任意形状的封闭光滑曲线）的第二基本问题。运用MycxenhIIbhnh复变函数方法，对这类弹性平面问题建立起了数学模型，将求解弹性平衡问题化归为寻求复应力函数满足一定边界条件的边值问题，然后构造其解的形式，再将其转化为正则型的奇异积分方程。数学上严格证明其解的存在与唯一。

本支利用复势方法讨论三维各向同性不同材料带双周期孔洞的弹性焊接混合边值问题。将三维应力系统分解为线性独立的两组二维应力系统。然后把复Airy函数法用于推广IIIepMab方法，将寻求复应力函数的问题归结为求解正则型的奇异积分方程，并证明了其解的存在唯一，由于所用方法是构造性的，故有利于数值计算。