Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)

The solution of differential equations has a great importance in the analysis of engineering systems and applied disciplines. It is not always possible to obtain the analytical solutions of these equations, which has a boundary value and/or initial value form as usual. For this purpose, it has been improved many numerical analysis method to obtain the adequate solutions up to now. All of these methods have a relative advantage and disadvantage with respect to each other because of the time aspect and the sensitivity. In this thesis, polynomial differential quadrature (PDQ) method is developed for the geometrically nonlinear static and dynamic analysis of plates and shells resting on Winkler-Pasternak elastic foundation. In the method of differential quadrature, partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The weighting coefficients for differential quadrature are obtained using the Power, Legendre, Chebyshev and Lagrange polynomials, and harmonic functions. Results are compared with existing solutions available from other analytical and numerical methods in the literature. Key Words: Plates and shells on elastic foundation, Geometrically non-linear analysis, Polynomial differential quadrature, Dynamic analysis.