Nonlinear analysis of thick shallow spherical and conical orthotropic caps using Galerkin's method (Q1347877)

An approximate analytical solution of the moderately large deflection axisymmetric response of moderately thick conical and spherical polar orthotropic caps is presented using first-order shear deformation theory. Governing equations in terms of deflection \(w\), rotation \(\psi\) of the midsurface and stress function \(\varPhi\) are used. Rotational and inplane inertia are neglected. The rotation \(\psi\) is approximated by a one-term spatial mode shape. The moment equation of equilibrium and the compatibility equations are solved exactly for \(w\) and \(\varPhi\). Galerkin's method is applied to the transverse equation of motion to obtain governing equation for the central deflection. The effect of the radius-to-thickness ratio of the cap on the response is studied.