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The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed. The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations) or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic problem. The stress-strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear factors Introduction. Stress analysis of simply connected and doubly connected thin and nonthin elastic shells made of metallic and composite materials was performed in [7, 8, 10, 11, 15, 16, 20, etc.]. The basic results have been obtained using analytical, variational, and numerical methods for various shells (plates) with curvilinear holes (notches).The nonaxisymmetric deformation of and stress distribution in isotropic spherical shells with an elliptic hole are studied with allowance for physical or geometrical nonlinearity in [6,7,9,12]. The stress concentration near a circular hole in both spherical and ellipsoidal shells was analyzed in [2, 7, 13] with allowance for physical nonlinearity, in [3,4,7] with allowance for geometrical nonlinearity, and in [1,6,7,14] with allowance for both nonlinear factors (plasticity and large deflections).It is of interest to solve two-dimensional nonlinear static problems for thin shells with curvilinear (noncircular) holes under high surface and contour loads.Using the method developed in [17] and tested against some linear and nonlinear elastic problems, we will numerically analyze the elastoplastic stress-strain state near an elliptic hole in flexible spherical shells. We will also analyze the influence of nonlinear factors on the stress distribution in the stress concentration zones in a shell under surface pressure of given intensity.

The elastoplastic state of thin cylindrical shells with two circular holes under axial tension is analyzed considering finite deflections. The distributions of stresses along the contours of the holes and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for either physical nonlinearity (plastic deformations) and geometrical nonlinearity (finite deflections) alone and with a numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between the holes and the nonlinear factors accounted for Stress distribution in multiply connected elastic isotropic shells (plates) was studied in [3, 4, 9, 11, etc.]. The basic theoretical and experimental results have been obtained by solving linearly elastic problems for shallow and deep thin-walled shells with two and more curvilinear or rectangular holes.Physically and geometrically nonlinear problems of stress (strain or displacement) distribution in various multiply connected thin shells under static loads (surface pressure, boundary forces, or bending moments) of high intensity were addressed in [1, 3-10, 12, etc.]. A numerical method for solving nonlinear static problems for arbitrary thin shells of complex geometry with regard for geometrical (finite or large deflections) or/and physical (plastic strains) nonlinearity is outlined in [12]. This paper also proposes an algorithm for approximate solution of doubly nonlinear two-dimensional boundary-value problems of stress concentration in multiply connected shells.Specific numerical results have been obtained in [13,14] in studying the elastoplastic stress-strain state near two circular holes in spherical and cylindrical flexible shells under uniform surface load (internal pressure) of given intensity. These results were used to study the influence of physical and geometrical nonlinearities on the stress (strain) concentration in shells, depending on the distance between the holes.Expanding upon the earlier studies [12,14], we will present numerical solutions of nonlinear problems for cylindrical shells subjected to boundary forces (axial tension) and weakened by two curvilinear (circular) holes.1. We will analyze the elastoplastic state of thin-walled flexible cylindrical shell having two circular holes with centers on a common generatrix. The shell is subject to axial tensile forces of given intensity P P = ⋅ 0 3 10 N/m (Fig. 1). These forces are assumed to induce plastic strains in the stress-concentration regions of the shell, which is made of an isotropic homogeneous material. The normal displacements become comparable to or exceed the thickness of the shell [3,12], yet remain small compared with the other linear dimensions. Considering certain boundary conditions at the contours of the holes, we will analyze the stress-strain state of a complex flexible shell with certain geometrical and physicomechanical parameters, taking plastic s...