Mathematical Formulation in Bending of Rectangular Thin Plates

Main Article Content

Yos Sompornjaroensuk
Parichat Kongtong
Dusadee Sukawat


The main purpose of this paper is to review the fundamental feature of mathematical formulations involved the theory of thin elastic rectangular plates. All of the necessary equations are analytically given in terms of only one variable; namely the deflection of plate, which are the fourth-order partial differential equation governing the plate-bending behaviors, plate deformations (deflection, slope and curvature), and stress resultants of the plate. In order to obtain these equations, certain assumptions will be stated and referred to when related to any portion of the mathematical formulations and classical boundary support conditions. Therefore, a full description of the boundary conditions is also given. In addition, two classical well-known analytical solution approaches are presented in details for solving some basic problems of uniformly loaded rectangular plates.

Article Details

Research Articles


S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed., McGraw-Hill, Singapore, 1959.

A.W. Leissa, Vibration of Plates, Reprinted ed., Acoustical Society of America, Washington, DC., 1993.

D.J. Gorman, Free Vibration Analysis of Rectangular Plates, Elsevier North Holland, Inc., New York, 1982.

S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill, Singapore, 1970.

M. Cartwright, Fourier Methods for Mathematicians, Scientists and Engineers, Ellis Horwood Limited, West Sussex, 1990.

R.V. Churchill and J.W. Brown, Fourier Series and Boundary Value Problems, 3rd ed., International Student Edition, McGraw-Hill Book Company, Singapore, 1978.

J.J. Tuma, Engineering Mathematics Handbook, 2nd enlarged and revised ed., McGraw-Hill, New York, 1979.