Abstract
A variational derivation is used to obtain 10th and 12th order shell theories along with the associated boundary conditions. A computer program produces the coefficients in the reductions of the sets of equilibrium equations to equivalent single 10th and 12th order equations. Exact solutions for closed shells which decay in the axial direction are obtained and compared with exact three dimensional solutions in order to assess the accuracy of the shell theory as an approximation to the elasticity theory.
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