Effects of partially supported elastic foundation on free vibration of FGP plates using ES-MITC3 elements

Abstract

The main goal of this article further extends the ES-MITC3 element based on first-order shear deformation theory (FSDT) for the free vibration analysis of functionally graded porous (FGP) plates resting on the partially supported elastic foundation (PSEF). The ES-MITC3 element is the union between the mixed interpolation of tensorial components (MITC) technique and an edge-based smoothed finite element method (ES-FEM). The elastic foundation (EF) is a Winkler-Pasternak’s model with two parameters consisting of Winkler-stiffness (k1) and Pasternak-stiffness (k2). The porosity distribution in plates is assumed to vary according to the even distribution (case 1) and uneven distribution (case 2) rules. The governing equation is derived from Hamilton's principle. Numerical examples are performed to verify the accuracy and reliability of the present method. In addition, the effects of types of PSEF, material properties and geometry characteristics on the free vibration behavior of FGP plates are fully investigated.

Keywords

• ES-FEM
• Mixed interpolation of tensorial components
• Free vibration
• Functionally Graded Porous materials (FGP)
• Partially supported foundation
• Winkler-Pasternak foundation