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Abstract In this article, higher-order closed-form solutions are obtained for static bending and free vibration analysis of laminated composite and sandwich spherical shells using a generalized higher-order shell theory. A theory is independent of the choice of shearing stress function (polynomial/non-polynomial) which eventually results in a theoretical unification of most of the classical and higher-order shear deformation theories. The present theory yields an accurate distribution of transverse shear stresses through the shell thickness; therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived by employing Hamilton's principle. Navier type higher-order closed-form solutions are obtained for simply supported boundary conditions. Displacements, stresses and natural frequencies are presented for laminated composite and sandwich plates as well as shallow and deep spherical shells. The results of parabolic, trigonometric, hyperbolic, and exponential models are compared with each other and previously published results to verify the accuracy and efficiency of the present generalized shell theory. [ABSTRACT FROM AUTHOR]

Laminated composite and sandwich structures are lightweight structures that can be found in many diverse applications especially civil, mechanical and aerospace engineering. The rapid increase in the industrial use of these structures has necessitated the development of new theories that suitable for the bending, buckling and vibration analysis of composite structures. Many review articles are reported in the literature on laminated composite plates and shells in the last few decades. But, in the whole variety of literature very few review articles are available exclusively on laminated composite and sandwich beams. In this article, a critical review of literature on bending, buckling and free vibration analysis of shear deformable isotropic, laminated composite and sandwich beams based on equivalent single layer theories, layerwise theories, zig-zag theories and exact elasticity solution is presented. In addition to this, literature on finite element modeling of laminated and sandwich beams based on classical and refined theories is also reviewed. Finally, displacement fields of various equivalent single layer and layerwise theories are summarized in the present study for the reference of researchers in this area. This article cites 515 references and highlights, the possible scope for the future research on laminated composite and sandwich beams. [ABSTRACT FROM AUTHOR]

A geometrically nonlinear theory is developed for shells of generic shape allowing for third-order shear deformation and rotary inertia by using five parameters: in-plane and transverse displacements and the two rotations of the normal; geometric imperfections are also taken into account. The novelty is that geometrically nonlinear strain–displacement relationships are derived retaining full nonlinear terms in all the five parameters. These relationships are presented in curvilinear coordinates, ready to be implemented in computer codes. Higher order terms in the transverse coordinate are retained in the derivation so that the theory is suitable also for thick laminated shells. The theory is applied to laminated composite circular cylindrical shells complete around the circumference and simply supported at both ends. Initially static finite deformation and buckling due to lateral pressure is studied. Finally, large-amplitude forced vibrations under radial harmonic excitation are investigated by using the new theory and results are compared to another third-order shear deformation theory that neglects nonlinear terms in rotations of the normal. [ABSTRACT FROM AUTHOR]

Abstract: Based on the three-dimensional theory of elasticity, a new approach combining the state space method and the differential quadrature method (DQM) is presented in this paper for the free vibration analysis of the cross-ply laminated cylindrical panels. The panel has one pair of opposite edges with simply supported and the other pair of opposite edges arbitrary boundary conditions. Applying the differential quadrature method to the state space formulations along the axial or circumferential directions of panel, new state equations about state variables at discrete points are obtained. Eigenfrequency equation is obtained by using edges boundary condition in this state equation. Natural frequencies of the panel are obtained by solving the frequency equation. Numerical results for laminated cross-ply panel with arbitrary edges condition are performed. Results are verified by comparing for the simply supported edges with the available published results. [Copyright &y& Elsevier]

The sensitivity of laminated cylindrical shell to imperfection is considered, via the initial post-buckling analysis, on the bases of Sanders’ theory. A general code is developed and used in studying the effect of the stretching–bending coupling (B) and the flexural (D) stiffness matrices on the buckling and the post-buckling behavior of the shell, thereby improving its behavior. [Copyright &y& Elsevier]

The method of superposition is exploited to obtain accurate analytical type solutions for resonant frequencies and mode shapes of completely free symmetric cross-ply laminated rectangular plates. Verification tests are performed by comparing computed eigenvalues with known eigenvalues for the special case of thin orthotropic plates. Results of an analytical study of the free vibration behaviour of a typical symmetric cross-ply laminated completely free plate are tabulated. These results provide valuable checkpoints against which future researchers can compare their findings. This appears to be the first analytical type free vibration solution made available for the completely free laminated plate of this type. [Copyright &y& Elsevier]