Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.Issues of stress concentration near holes in transtropic shallow spherical shells made of composite materials and subjected to internal pressure are addressed in [1][2][3][4][5][6][9][10][11][12]. Studies aimed at evaluating the influence of transverse shear stiffness on the stress state of shells with holes are reviewed in [2,11]. In [10,12,13], the effect of shear stiffness in composite shells is analyzed numerically.A Problem Formulation for thin elastic shells compliant to transverse shear was first proposed in [4, 5] based on differential equations of a refined Timoshenko theory that allows for the low transverse shear stiffness of the material [5],

Analytical expressions are derived for the stresses near a rigid circular inclusion in a transversely isotropic shallow spherical shell under uniform pressure. 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].

The refined Timoshenko-type theory that takes into account the transverse shear strains is used to find an analytic solution for the stress state of transversely isotropic shallow spherical shell with two circular rigid inclusions. The case of a shell with closely spaced rigid inclusions of unequal radii under internal pressure is analyzed numerically. The stresses in the shell increase considerably with decrease in the distance between the inclusions and increase in the transverse shear parameter

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The stress state of a shallow isotropic spherical shell with circular rigid inclusions subject to a force or a moment is determined. The case of two inclusions of unequal radii is analyzed numerically. It is established that the stresses in the shell increase substantially with decrease in the inclusion radius and the distance between the two inclusions Keywords: shallow isotropic spherical shell, stress state, circular rigid inclusion, bridge between inclusions Introduction. The analysis of the stress state of shells and plates with various stress concentrators such as holes and inclusions [2][3][4][5][6][7][8][9][10][11][12], concentrated [1] and local [3] loads is still of theoretic and practical interest.Analytic and numerical solutions for a spherical shell loaded by a force or a moment through a rigid ring were obtained in [3] for a shell with one perfectly rigid inclusion. However, studies of shells and plates with two circular holes or rigid inclusions showed that the stress concentration can be very high if the stress concentrators are close to each other [2,[4][5][6][7][8][9][10][11][12]. In view of this, we will consider a spherical shell with two circular perfectly rigid inclusions loaded by a force or a moment and will analyze in detail the stress state of a shell with two unequal rigid rings, including the case where they are very close to each other.1. Problem Formulation. Consider a shallow isotropic spherical shell with m circular perfectly rigid inclusions with centers located on the Ox-axis. The following boundary conditions are defined on the rigid boundaries G q of the inclusions [2]: