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The nonlinear axisymmetric static analysis of polar orthotopic, unsymmetrically laminated, cross-ply moderately thick circular plates and shallow spherical shells under uniformly distributed normal loading is carried out using an iterative Chebyshev series technique. Considering the effects of transverse shear the governing equations of equilibrium for shells are derived and expressed in terms of normal deflection, slope and stress function. The effects of transverse shear, material properties, number of layers, boundary conditions, base radius to thickness ratio are studied and the results are shown graphically. Buckling analysis has been carried out and the critical loads are estimated for spherical shells. The effects of transverse shear on static response are greatly influenced by the ratio of base radius to thickness, shell parameter, material properties and boundary conditions. [ABSTRACT FROM AUTHOR]

The axisymmetric moderately thick laminated shallow spherical shells undergoing moderately large deflection subjected to dynamic loading are analyzed. Including the effects of transverse shear and rotatory inertia, the equations of dynamic equilibrium are formulated in terms of normal deflection, slope and stress function. Nonlinear governing equations of motion are linearized using quadratic extrapolation technique and the resulting linear differential equations are discretized in space and time domain using fast converging Chebyshev polynomials and the implicit Houbolt time marching scheme, respectively. Considering step function and sinusoidal loadings, both clamped and simply supported immovable laminated spherical shells are analyzed. The effect of control space variables, viz., transverse shear, rotatory inertia, material properties, shell parameter, base radius to thickness ratio, boundary conditions, number of layer and damping on the central response have been studied. [ABSTRACT FROM AUTHOR]