Displacements and stresses in an orthotropic spherical shell joined to a cylindrical shell of the same material both loaded by a uniform internal pressure



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The solution for displacements and stresses in an orthotropic spherical shell joined to a cylindrical shell of the same material, both loaded by internal pressure, is presented in this study. Spherical and cylindrical orthotropic shell equilibrium equations are derived in terms of displacements and are based on Love's differential equilibrium equations for any orthogonal coordinates, Kirchhoff's assumptions, and small-deflection approximations. Orthotropic materials are defined by three material constants which are then related to meridional end circumferential moduli of elasticity, and Poisson's ratic. The orthotropic cylincrical shell equilibrium equations are solved in closed form and used to define the boundary conditions at the sphere-cylinder juncture. The orthotropic spherical shell equilibrium equations are transformed to linear algebraic equations by finite difference approximations and used to solve for the u and w displacements of a spherical shell joined to a cylindrical shell. Stresses are obtained from the displacements by numerical differentiation. The material constants are variec. from the isotropic numerical problem to show the effect of orthotropic materials on spherical shell stresses and displacements. Although the theoretical stresses from the developed equations correlate with experimental and momentless shell theory results for isotropic materials, the developed equations yield questionable stresses for orthotropic materials.