On the stress distribution in a spherical shell with an off-center curvilinear hole

Abstract

A numerical analysis is made of the joint effect of two factors of asymmetry-ellipticity and eccentricity-on the stress distribution near a free hole in a spherical shell. The nature of deformation is determined by the predominant factor. Whether there are "fixed" points on the graphs of stress distribution around a small hole at which they intersect depends on how rigidly the outer edge is fixed. As the rigidity of fixation is increased, the points smear Introduction. The asymmetric stress-strain state (SSS) near curvilinear holes (cutouts) in isotropic [4,6,9,10] and composite [4,5,8,11] plates and shells is of theoretical and practical interest: the results of a stress-strain analysis would allow us to evaluate the stress and strain of various thin-walled structural members under various kinds of loads.Numerical stress-strain analyses were performed mainly for thin-walled spherical caps with a central elliptical hole [4,5,8,10,11].As pointed out in [1,7], in the off-center case, numerical results are mainly available only for a circular hole, with the emphasis being on the stress distribution around the bridge between the outer and inner edges, which does not give an accurate account of the maximum stresses. Most publications employ special orthogonal coordinate frames and address simply connected stress-concentration problems for elastic isotropic shells. Such problems for elastoplastic shells were analyzed in [6, 10] and for shells made of nonlinear elastic composites in [8].Note that the paper [5], where the SSS of elastic orthotropic laminates with an elliptic hole was analyzed, gives specific results only for a special case (a circular hole).Specific simply and doubly connected problems for spherical shells with a central circular hole or with two circular holes were solved in [6].We will examine the joint effect of two factors of asymmetry (ellipticity and eccentricity) on the SSS only for a rigidly fixed shell with finite mechanical and geometrical parameters.Nowadays, stress-strain studies of doubly and multiply connected thin-walled structural members are of interest. The same applies to the stress-strain analysis of spherical shells (bottoms). We will discuss below results from a stress-strain analysis of elastic isotropic spherical shells with an off-center curvilinear (elliptical or circular) hole.1. Problem Formulation. Let us consider a thin isotropic nonclosed spherical shell of radius R and thickness h with an off-center [7] curvilinear (elliptical, circular) hole. The shell is a doubly connected domain (Fig. 1); its boundaries are the outer and inner edges of the shell. The shell is subjected to surface forces { } { , , } p p p p T = 1 2 3 . The inner boundary can be free, fixed,

Inelastic deformation of flexible cylindrical shells with an elliptic hole

“…In the general case [2,15] of an arbitrary thin shell described in a coordinate system not aligned with the lines of principal curvature, the geometrical equations are derived from the theory of flexible shells (second-order theory of shells) and the physical equations from the flow theory with isotropic hardening.…”

“…To derive the governing system of equations [2,15] that describes the elastoplastic state of a shell with an elliptic hole and finite deflections, the virtual-displacement principle and approximate methods are used. The method for approximate solution of nonlinear problems used here is based on the incremental loading procedure.…”

The stress-strain state of a plate with a multilayer inclusion

“…Solid mechanics reduces such problems to a stress analysis of an elastic matrix with holes or inclusions. A fundamental contribution to the study of stress concentration around curvilinear holes was made by G. N. Savin [5,6].The stress-strain state of plates and shells with holes and inclusions of different stiffness was addressed in [7,10,11,13,16]. This paper is concerned with the stress-strain state of laminated composites with multilayer fibers that are in a plane strain state.…”

“…The stress-strain state of plates and shells with holes and inclusions of different stiffness was addressed in [7,10,11,13,16]. This paper is concerned with the stress-strain state of laminated composites with multilayer fibers that are in a plane strain state.…”

“…( ) Let us pass to a local coordinate system on each boundary element and replace the densities of potentials with their expressions, using (12) and (13). After that, we use the Somigliana formulas (6)-(8) to find the displacements and differentiate these formulas to find the strains.…”