本文给出了一类R iemann边值逆问题的正则型与非正则型情况的数学提法和解法1MR（1991）主题分类45E

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.

In this paper, we wish to use complex potential methods to solve the fundamental complete plane strain (CPS) problems of a three-dimensional nonhomogeneous elastic body with a doubly-periodic set of cracks in, the x1, x2plane. We resolve the complete plane strain state, which is a special three-dimensional elastic system, into two linearly independent two-dimensional (plane) elastic systems by the superposition principle of force. Based on a suitable modifieation of Cauchy-type integrals, which is defined by the replacement of the Cauehy kernel 1/(t-z) by the Weier.stra.s.s zeta function S (t-z), the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel, and the existence of an essentially unique solution is proved.

本文讨论双周期胞腔中含若干个任意形状裂纹的不同材料的弹性平面焊接问题，掇据路见可和Mycxoihmboib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的问题，并把路见可给出的复Airy函数用于推广ⅢepMah方法，更进一步地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，最后证明了其解存在且唯一。

The problem of embedding a periodic continous elastic gasket in a periodic cracked body is investigated by approaches using the singular integral eqution (SIE) with the Hilbert kernel, the periodic solution in closed form of the SIE and analytical experession of the stress intensity factors are obtained. Finally, some special examples are given.