Cs. Xu et Cy. Chia, NONLINEAR-ANALYSIS OF UNSYMMETRICALLY LAMINATED MODERATELY THICK SHALLOW SPHERICAL-SHELLS, International journal of non-linear mechanics, 29(2), 1994, pp. 247-259
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.