Static and free vibration analysis of stiffened FGM plate on elastic foundation based on physical neutral surface and MK method

Abstract

This paper analyzes the static and free vibration problems of the stiffened functionally graded material (FGM) plate resting on Pasternak foundation by using the moving Kriging (MK) approximation and the physical neutral surface. The stiffened FGM plates are regarded as composite structures of FGM plates and stiffeners (beams). The displacement transformation relationship between stiffeners and FGM plates is obtained through the displacement compatible conditions and moving kriging interpolation. The total potential energy and kinetic energy of FGM plate resting on Pasternak foundation are derived based on the first-order shear deformation theory (FSDT) and physical neutral surface and by superimposing those energies of the stiffeners and the FGM plate. According to the principle of Minimum Potential Energy and Hamilton's Principle, the meshless governing equations on the static and free vibration of the stiffened FGM plate are obtained, respectively. The convergence and accuracy of the proposed method are demonstrated by calculating several numerical examples. Moreover, the effect of the power-law exponent, boundary conditions and foundation parameter on the static and free vibration behavior of the stiffened FGM plates resting on Pasternak foundation are discussed.