By the method of singular integral equations, we solve a plane elastoplastic problem of fracture mechanics for an isotropic plane with an infinite series of curvilinear holes and plasticity bands at their tips. We study the influence of the shapes of smooth holes and the radii of rounding of the contours at their tips on the opening displacements and lengths of the plasticity bands. The solutions of the corresponding problems for semiinfinite bilateral rounded notches whose tips serve as the origins of plasticity bands are obtained by the limit transition in the case where the relative distance between the holes tends to zero. On the basis of the deformation criterion of fracture and solutions of the periodic elastoplastic problem, we approximately determine the strength of rectangular specimens with bilateral U-shaped notches.

中文翻译：

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具有曲线孔和塑性带周期系统的各向同性板的变形

利用奇异积分方程的方法，我们解决了一个各向同性平面的断裂力学平面弹塑性问题，该平面具有无限级数的曲线孔和其尖端的塑性带。我们研究了光滑孔的形状和其尖端轮廓的圆角半径对塑性带开口位移和长度的影响。以孔尖为塑性带起点的半无限双边圆缺口对应问题的解是通过孔间相对距离趋于零时的极限过渡得到的。根据断裂变形判据和周期性弹塑性问题的求解，我们近似确定了双U形缺口矩形试件的强度。