Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

Abstract

The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account) and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities accounted for Introduction. Stress, strain, and strength analyses of isotropic and anisotropic structural members (plates and shells) of complex geometry, including multiple connectivity, under static and dynamic loads are still of importance. Of heightened interest are nonaxisymmetric problems for thin and nonthin shells and plates of various outlines and shapes under high surface and boundary loads. Solving such static and dynamic problems, in both linear and nonlinear formulations, involves severe mathematical and computational difficulties.Efficient methods developed to solve linearly elastic boundary-value problems for multiply connected shells (weakened by two or more curvilinear holes or notches) are outlined in [1,2,6,7,[11][12][13].Concrete numerical results have been obtained for metal and composite shells of spherical, cylindrical, conical, and other shapes subjected to static surface loads, axial forces, and a system of boundary forces and moments. Note that the publications [2,6,7,12] present results for elastic isotropic and orthotropic cylindrical shells with two equal or unequal circular holes (their centers are on a common generatrix or directrix) and with a finite number of circular holes, and for periodic cases.It should also be emphasized that two-dimensional static problems for shells (plates) of various shapes and purposes with a curvilinear (circular or elliptic) hole or a notch of various geometries (simply and doubly connected domains) have mostly been solved considering only the elastic stage of deformation or only geometrical (finite deflections) or physical (plastic or creep strains) nonlinearities [6,7,9,11,13]. The principles and methods of theoretical and experimental analysis of stress concentration in load-bearing structural members were developed with an eye toward solving two-dimensional boundary-value problems in various formulations [3-8, 10, 11]. Isolated results were obtained by solving nonlinear problems for shells with both finite (large) deflections and plastic strains [6,7,13].As regards nonlinear problems for multiply connected thin shells, there are only isolated theoretical results. For thin-walled...

Stress-strain state of a flexible spherical shell with an eccentric circular hole

“…In support of the method proposed earlier in [16] and of its application to the numerical solution of some two-dimensional linear elastic and nonlinear problems [15,17,18], we will present specific results on the stress-strain state of a flexible spherical shell weakened by an eccentric hole. We will analyze the effect of geometrical nonlinearity (large and finite deflections) on the distribution of stresses in regions of their concentration in a shell under a surface load.…”

Using mesh-based methods to solve nonlinear problems of statics for thin shells

“…The interaction of the holes can be neglected at the point A r r ( = 0 , q = 0), which is the farthest from the second hole. The change in the stresses at the point C r r ( , ) = = 0 q p , which is closest to the second hole, is insignificant compared with shells under internal pressure [65]. Thus, when a shell (even with closely spaced holes~, l = 2 3) is subject to axial tensile forces, the point (B) in the section As the parameterl decreases, the maximum stresses ( ) s q slightly decrease in the LP (to 7%) and GNP (to 4%) and remain almost constant (difference £0.5%) in the PNP and PGNP.…”

“…[63,65]. We will analyze the elastoplastic state of a thin-walled cylindrical shell with two equal circular holes with centers on one generatrix (Fig.…”

Physically and geometrically nonlinear deformation of thin-walled conical shells with a curvilinear hole

“…Expanding upon [10][11][12][13][14][15], we will discuss specific results on the elastoplastic stress-strain state of thin-walled flexible conical shells with a circular hole under distributed surface and edge loads.…”