The problem of compression of an isotropic medium by a periodic system of variable width slits comparable with elastic deformations is considered. The slit faces are under internal pressure. It is considered that the slits have end zones wherein material's tractions act. It is accepted that interaction of the slit's surface under applied loads may reduce the formation of contact zones of their surfaces. The formation of several contact areas of faces of each slit is studied. Therewith, it is considered that on some parts of a contact area there happens stick of the faces, on the remaining part there may happen slippage. The problem of equilibrium of a periodic system of slits with partially contacting faces under compressing load is reduced to the problem of linear conjugation of analytic functions. Determination of unknown parameters characterizing partial closing of a periodic system of variable width slits is reduced to the solution of the system of singular integro-differential equations. The contact stresses, the tractions in bonds between the slit faces in the end zones, the sizes of the contact areas, the adhesion and end zones are studied.

中文翻译：

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压缩作用下各向同性介质中可变宽度桥接狭缝周期系统的部分闭合

考虑了与弹性变形相当的可变宽度狭缝周期系统对各向同性介质的压缩问题。狭缝面处于内部压力之下。认为狭缝具有材料的牵引作用在其中起作用的端部区域。可以接受的是，狭缝表面在施加载荷下的相互作用可能会减少其表面接触区的形成。研究了每个狭缝面的几个接触区域的形成。因此，认为在接触区域的某些部分会发生面的粘连，在其余部分可能会发生滑移。压缩载荷下部分接触面的狭缝周期系统的平衡问题简化为解析函数的线性共轭问题。表征可变宽度狭缝周期系统部分闭合的未知参数的确定被简化为奇异积分微分方程组的解。研究了接触应力、端部区域狭缝面之间的结合牵引力、接触区域的大小、附着力和端部区域。