Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction

A new algorithm for solving some mechanical problems

The capability to predict the nonlinear response of beams, plates and shells when subjected to thermal and mechanical loads is of prime interest to structural analysis. in fact, many structures are subjected to high load levels that may result in nonlinear load-deflection relationships due to large deformations. One of the important problems deserving special attention is the study of their nonlinear response to large deflection, postbuckling and nonlinear vibration.

A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1936&context=lkcsb_research

The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution

The behavior of thin, rectangular, orthotropic elastic plates, with immovable edges and undergoing large deflections, is investigated by the numerical technique of differential quadrature. Approximate results are obtained, using the Newton-Raphson method and, alternatively, a finite-difference-based method to solve the nonlinear systems of equations. Bending stresses, membrane stresses, and deflections are calculated for plates with fully clamped and simply supported flexural edge conditions under uniform pressure loading. Results are compared with existing analytical, numerical, and experimental ones. The present method gives good accuracy and is computationally efficient.

Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature

Postbuckling Behavior of Unsymmetrically Layered Anisotropic Rectangular Plates

A General Mode Approach to Nonlinear Flexural Vibrations of Laminated Rectangular Plates

Non-linear flexural vibrations of orthotropic rectangular plates

An analysis is presented for the post-buckling behaviour of a simply supported, rectangular, orthotropic plate subjected to biaxial compression. The solution of von Karman-type large deflection equations of the plate satisfying the prescribed boundary conditions is expressed in the form of a double Fourier series for the transverse deflection and a double series for the stress function consisting of the appropriate beam functions. The effect of plate properties on stresses and deflections has been studied for three fibre-reinforced materials. Numerical results indicate good convergence of the present series solution and are compared with the available data.

C. Y. Chia

Papers

Postbuckling Behavior of Unsymmetrically Layered Anisotropic Rectangular Plates

A General Mode Approach to Nonlinear Flexural Vibrations of Laminated Rectangular Plates

Non-linear flexural vibrations of orthotropic rectangular plates

Post-Buckling Behaviour of Rectangular Orthotropic Plates

Effect of Transverse Shear and Rotatory Inertia on Large Amplitude Vibration of Anisotropic Skew Plates: Part 1—Theory