Stress State of Thin Spherical Shells with an Off-Center Elliptic Hole

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

“…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.…”

“…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.…”

Stress state of a transversely isotropic spherical shell with a rigid circular inclusion

“…The stress distribution around holes or rigid inclusions in shallow and deep transtropic and orthotropic spherical shells was studied in [1][2][3][4][5][6][7][8][9][10][11]. The results of studies into the influence of the transverse shear stiffness of materials on the stress state of composite shells are reported in [3,7,8].…”

“…The form of solution depends on the range of the transverse shear compliance parameter. The influence of the relative radius of a rigid inclusion and transverse shear compliance on stress concentration is analyzed Keywords: transverse shear, transversely isotropic shallow spherical shell, rigid circular inclusionThe stress distribution around holes or rigid inclusions in shallow and deep transtropic and orthotropic spherical shells was studied in [1][2][3][4][5][6][7][8][9][10][11]. The results of studies into the influence of the transverse shear stiffness of materials on the stress state of composite shells are reported in [3,7,8].…”

“…Substituting these constants into (3)-(5), we find the deflections and the stress functions. Next, we use formulas (9) and (10) to determine the forces and moments.…”