В работе рассматривается бесконечная пластинка с центральным отверстием, форма которого весьма близка к прямоугольнику под дей­ствием гидростатического давления на гранях проема. Постав­ленная задача имеет самостоятельное значение при расчете напорных гидротехнических тоннелей и входит составной частью в задачу о напряжениях от собственного веса в массивах с проемами (плоская деформа­ция).

The presence of holes in the elements of structures and machines is known to be the cause of redistribution of stresses, which is accompanied by a significant concentration of the latter.The proposed paper investigates the redistribution of stresses on the contour of a hole in an infinite plate bending in its plane. The redistribution is caused by a curvilinear hole with a shape very close to a rectangle. Cutouts with a midline ratio are considered (see article). The problem is treated as a plane problem. The hole is assumed to be relatively small and distant from the outer edges. The boundary conditions on the inner contour are satisfied exactly, on the outer contour, where the influence of the hole is neglected, they are satisfied only approximately.

We consider a plate weakened by a central curvilinear opening, in shape very close to a rectangle with the aspect ratio a:b=2 (a is the vertical, b is the horizontal side of the opening). In the curvilinear contour (Fig. 1), the ratio a:b represents the ratio of the center lines; hereafter we will call this ratio the ratio of the sides for brevity. The plate is subjected to the following loads (see the article). We shall confine ourselves to the study of the contour stresses, which are known to have maximum values, and give general considerations on the zone of influence of the hole. The work is intended to enable designers to use in their practical work a scientifically sound solution.