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.

Pasternak Türü Zemine Oturan Plakların Tesir Yüzey Katsayıları

“…The first parameter of the Pasternak foundation is represented by "area springs" assigned to the surface of the foundation. The deflections of the plate and the foundation nodes are equalised in order to provide the connection between the plate and the foundation, [17]. It is seen that the results obtained are close to each other, Table 6.…”

“…In order to verify the results, the system model is also created in SAP2000 using the procedure given in [17]. The two-parameter elastic foundation is modelled using "shell" element where the section type is selected as "Plane-Strain" and the thickness of the section is assigned to a unit value.…”

Convergence studies for static analysis of thin plates on Pasternak Foundations

“…These matrix terms are added to the stiffness matrix terms of the Kirchhoff and R-M plate elements which correspond to deflections. In [21], this procedure is carried out for the Kirchhoff plate element only. Thus, the resulting system of equations is…”

On a New Method of Quasi-static and Dynamic Analysis of Viscoelastic Plate on Elastic Foundation

“…Basic concepts regarding the mechanical behavior of viscoelastic structural components are presented in the studies [15][16][17][18][19][20][21]. The investigation of ground effects on the behavior of elastic/viscoelastic plates has been the subject of many studies [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Based on our literature review, many research activities have been devoted to the development of theoretical and computational methods for elastic/viscoelastic plate -elastic/viscoelastic foundation interaction problems.…”