THE DEFORMATION OF ORTHOTROPIC SHELLS OF REVOLUTION UNDER NONSYMMETRIC EDGE LOADS.
LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF
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The deformations which occur in a thin shell of revolution subjected to slowly varying, nonsymmetric edge loads are determined. The shell is assumed to be orthotropic with the axes of elastic symmetry coinciding with the lines of principal curvature of the shell middle surface. Furthermore, the meridian curves are considered to be smooth and parabolic of degree n at the apex, but otherwise arbitrary. The problem is reduced to the study of an eighth-order system of three simultaneous, ordinary differential equations with the meridional, circumferential, and normal displacements as dependent variables. For a shell which is non-shallow, the equations are satisfied approximately by four exponentially behaving edge-effect solutions and four slowly varying algebraically behaving membrane and inextensional bending solutions. For a shallow shell however, the assumptions upon which the membrane theory is based are violated and eight rapidly varying power series solutions are obtained. Finally, by suitable transformations, uniformly valid solutions are obtained which reduce to both the previously determined shallow and non-shallow results in the appropriate region of the shell. Expressions for the stress resultants and stress couples are then given. Author