Mathematical Formulation in Bending of

Rectangular Thin Plates

                                                                               

 

Yos Sompornjaroensuk

Ph.D., Department of Civil Engineering, Mahanakorn University of Technology,

Bangkok 10530, Thailand, This email address is being protected from spambots. You need JavaScript enabled to view it.

 

Parichat Kongtong

M.Sc., Department of Automotive Engineering, Thai-Nichi Institute of Technology,

Bangkok 10250, Thailand, This email address is being protected from spambots. You need JavaScript enabled to view it.

 

Dusadee Sukawat

Ph.D., Department of Mathematics, King Mongkut’s University of Technology Thonburi,

Bangkok 10140, Thailand, This email address is being protected from spambots. You need JavaScript enabled to view it.

 

Manuscript received March 5, 2012

Revised June 1, 2012

 

ABSTRACT

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.

 

Keywords : Analytical Solution, Boundary Conditions, Partial Differential Equation, Rectangular Plate.

 

 

 

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