Elastoplastic state of flexible conical shells with a circular hole under axial tension

Abstract

The elastoplastic state of thin conical shells with a circular hole is analyzed assuming finite deflections. The distributions of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress-strain state of shells around the hole under axial tension is analyzed taking into account two nonlinear factors. The numerical results are presented as plots and tables Introduction. The major results on the stress-strain state around curved and rectangular holes in conical metallic and composite shells were obtained with analytic, variational, and numerical methods and are most fully covered in the monographs [1, 4, 5] and reviews [9][10][11].Only few publications address nonlinear problems of stress concentration in conical shells with holes. This is because of the complexity of the system of governing equations for conical shells with holes when nonlinear factors are taken into account. For this reason, most studies of the nonlinear deformation of such shells employ grid-based methods [12]. The numerical variational-difference method made it possible to solve the elastoplastic problem for a conical isotropic shell with rectangular [2] and circular [14] holes as well as for a nonlinear elastic orthotropic shell with a circular hole [3,9].The combined effect of plastic deformation and finite deflections on the stress-state of a conical shell with an opening was analyzed in [8] for a circular hole and in [7] for an elliptical hole. The finite-element method was used for numerical analysis of shells under internal pressure. Note that numerical solutions to two-dimensional nonlinear problems for axially loaded cylindrical shells were obtained only for one [6] and two [13] circular holes.Of interest is to solve physically and geometrically nonlinear problems of statics for conical shells with curved holes under axial loading. Expanding upon the studies [7, 8], we will present the basic equations and numerical results describing the distribution of displacements, strains, and stresses around a circular hole in a flexible conical shell under axial tension beyond the elastic range.

Elastoplastic deformation of conical shells with two circular holes

“…Numerical finite-element analyses were conducted for shells subject to uniform internal pressure. Two-dimensional nonlinear problems for a shell with a circular hole under axial forces were solved numerically in [6].Most numerical results on the stress-strain state around two circular holes were obtained for spherical [11,12] and cylindrical [10] shells. The FEM was used to analyze the effect of nonlinear factors on stress concentration and the interaction of the edges of holes in shells under known uniform internal pressure.…”

“…Numerical finite-element analyses were conducted for shells subject to uniform internal pressure. Two-dimensional nonlinear problems for a shell with a circular hole under axial forces were solved numerically in [6].…”