NONLINEAR-ANALYSIS OF UNSYMMETRICALLY LAMINATED MODERATELY THICK SHALLOW SPHERICAL-SHELLS

A Fourier-Bessel series solution is formulated for the non-linear vibr ation of an unsymmetrically laminated moderately thick shallow spheric al shell with its edge elastically restrained against rotation. The ef fects of transverse shear deformation and rotatory inertia are include d in the analysis. The equations of motion are reduced to a set of non -linear ordinary differential equations for the time-dependent coeffic ients in the series by making use of the Galerkin method. These equati ons are solved by the method of harmonic balance for undamped free vib rations. The corresponding postbuckling problem is treated as a specia l case. Numerical results in non-linear free vibration, buckling and p ostbuckling are presented for various ratios of base radius to thickne ss and shell rise to thickness, number of layers, material properties and boundary conditions. The present results are compared with availab le data.