Abstract
A simple technique for the analysis of shells of revolution is presented and its application to toroidal shells shown. The method employs the leading term of the formal asymptotic solution and the eigenvalue of the exact coefficient matrix. The one-term approximation is then used as a trial solution in an integral equation form of the problem. Through the method of successive substitutions, better approximations are obtained by numerical integration. The one-term solution provides the correct boundary-layer behavior for the steep shell and the successive integration converge to the exact solution in the shallow region. In contrast to finite element and finite difference methods, this technique becomes more efficient as the radius-to-thickness ratio of the shell increases.
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