Vol.1, No.2, 120-123 (2009) Natural Science

http://dx.doi.org/10.4236/ns.2009.12014

Copyright © 2009 SciRes. OPEN ACCESS

An Improved Model for Bending of Thin Viscoelastic

Plate on Elastic Foundation

Zhi-Da Li1,2, Ting-Qing Yang1, Wen-Bo Luo3

1Department of Mechanics, Huazhong University of Science and Technology, Wuhan, China; zhidali@163.com

2School of transportation, Wuhan University of Technology, Wuhan, China

3College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, China

Received 10 June 2009; revised 16 July 2009; accepted 20 July 2009.

ABSTRACT

An improved model for bending of thin viscoe-

lastic plate resting on Winkler foundation is

presented. The thin plate is linear viscoelastic

and subjected to normal distributed loading, the

effect of normal stress along the plate thickness

on the deflection and internal forces is taken

into account. The basic equations for internal

forces and stress distribution are derived based

on the general viscoelastic theory under small

deformation condition. The reduced equations

for elastic case are given as well. It is shown

that the proposed model reveals a larger flex-

ural rigidity compared to that in classic models,

in which the normal stress along the plate

thickness is neglected.

Keywords: Thin Viscoelastic Plate; Deformable

Foundation; Flexural Rigidity; Winkler Foundation

1. INTRODUCTION

The analysis of soil-structure interaction has a wide

range of applications in structural and geotechnical en-

gineering, for instance, in highway asphalt pavement

engineering, the pavement is usually treated as thin elas-

tic/viscoelastic plate structure resting on elastic/viscoe-

lastic foundation. Due to the complexity of the actual

behavior of foundations, many idealized foundation mo-

dels have appeared in the literature [1]. The simplest of

those models, which was proposed in 1867 by Winkler,

assumes that the soil medium consists of a system of

mutually independent spring elements. There are many

papers dealing with the elastic beam or plates resting on

the Winkler foundation in the literature [2,3]. As com-

putational power has developed, more realistic modeling

of soil-structure interaction has become possible. Be-

cause of the importance of viscoelastic nature of the ma-

terials used for structures, e.g. asphalt layer of pavement

structure, many works have been done to deal with the

bending behaviour of thin viscoelastic plate on elas-

tic/viscoelastic foundation. Most of such works utilized

the models similar to those for bending of elastic plate.

Mase [4] directly offered the fundamental equations for

bending of viscoelastic plate by replacing the flexural

rigidity of elastic plate with the rigidity of viscoelastic

plate. Radovskii [5] discussed the problem of treating

highway and airport pavement as thin viscoelastic plate.

Pister [6], Robertson [7] and Hewitt and Mazumdar [8]

applied the elasticity-viscoelasticity correspondence pri-

nciple to get the solution of the bending problem of vis-

coelastic plate. In contrast to dealing with the viscoelas-

tic plate on elastic foundation, some attempts have also

been made to solve the bending problem of elastic plate

resting on viscoelastic foundation. Sonoda et al [9,10]

studied the circular and rectangular plate on linear vis-

coelastic foundation. Lin [11] and Yang et al. [12] ana-

lyzed the dynamic response of circular plate resting on

viscoelastic half space. All of the above studies followed

the classic model and traditional flexural rigidity for thin

plate bending, in which the Kirchhoff hypothesis was

used and

z

was neglected [13]. However, in the case

of large lateral load subjecting to thin plate resting on a

deformable foundation with relatively large rigidity, the

bearing stresses along the plate thickness,

z

, may not

be ignored. Furthermore, it is the bearing stress of the

plate that transfer the active lateral load to the founda-

tion, the boundary condition on the main surfaces of the

plate should be satisfied. Therefore it is necessary to

develop a method to consider the effect of lateral normal

stress. In this paper, we first seek to develop a modified

Kirchhoff theory for thin viscoelastic plate resting on

Winkler foundation, in which the effect of the lateral

normal stress is considered. Then we reduce the obtained

results to the problem of thin elastic plate resting on

elastic foundation, and a different elastic flexural rigidity

is obtained.