Asymptotic Solution of Nonshallow Shells of Revolution Subjected to Nonsymmetric Loads

Summary Asymptotic solutions of Novozhilov's equations are derived for a constant-thick ness,, nonshailow shell of revolution. Two cases of loading are considered: (1) Sinusoidal loading. Two-term asymptotic solutions of Novozhilov's uncoupled second-order equations are obtained in terms of the equation of the generating curve. (2) Higher harmonic load distribution. The asymptotic solu­ tions for this case are shown to depend on a single second order differential equation. This equation may be solved exactly for three types of shells. For shells of slowly varying contour, an iterative method of solution is indicated. The asymptotic solutions are obtained by the use of smallparameter expansions and by the use of a standard method3 for the singular perturbation problem and are valid for nonshailow shells free of singularities . The series are truncated to two terms for all cases of loading. It is recommended that the second term be retained in the edge-effect solutions.