FE Analysis of FGM Plates on Arbitrarily Orthotropic Pasternak Foundations for Membrane Effects

Abstract

In this study, the finite element analysis of sigmoid functionally graded material (S-FGM) plates resting on orthotropic Pasternak elastic foundations with different material angles is presented. For modelling, SAP2000 software package is used in which the required adjustments are made to obtain the expected behaviour of the plate-foundation system. The plate is modelled both using solid elements and layered shell elements by defining a number of solid elements and layers in the thickness direction having elastic properties equivalent to the properties of the S-FGM plate. The interaction between the plate and the foundation is treated by equalizing the vertical displacements of the plate and foundation nodal points. The orthotropic Pasternak foundation is modelled using plane strain elements with some adjustments to the elastic properties. The membrane effects of the simply supported S-FGM plate on Pasternak foundation are considered by assigning the edge boundaries of the system as pinned supports and these effects are excluded by converting all boundary nodes into roller supports except one of the corner nodes of the plate and the foundation due to the stability requirement. A number of verification examples are performed to demonstrate the convenience and robustness of the proposed model. This work can be easily extended to static and dynamic analyses of FGM plates with various geometries resting on arbitrarily orthotropic Pasternak elastic foundations for further studies.