An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation

Abstract

This paper is concerned with the vibration and stability analysis of thick rectangular plates resting on elastic foundation, which is distributed over the particular area of the plate. A twoparameter (Pasternak) model is considered to describe the elastic foundation. The eigenvalue problem in 3-D domain is numerically solved by a combination of the finite element and differential quadrature method (DQM). The energy principle is employed to derive the governing equations in the framework of three-dimensional, linear and small strain theory of elasticity. The in-plane domain of the problem is discretized using two-dimensional finite elements and spatial derivatives of equations in the thickness direction are discretized in strongform using DQM. As a first endeavor, the mixed FE-DQ method has been employed for 3-D buckling and free vibration analysis of rectangular thick plates partially supported by an elastic foundation. The accuracy of obtained results is validated by comparing to the few analytical solutions in the literature.

Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness

“…Torabi and Afshari (2016) used generalized differential quadrature method and presented a numerical solution for vibration analysis of cantilever trapezoidal thick plates made of functionally graded materials. In most of papers dealing with plate theories, simply supported and clamped boundary conditions are considered (Dehghan et al 2016, Samaei et al 2015, Dehghany & Farajpour 2014, Gupta et al 2016. Unfortunately meanwhile having wide industrial applications, the cantilevered beam or plate problem is one of the most difficult boundary conditions to solve for all presented theories (Torabi et al 2013).…”