General information 
Description 
The bending of thin simply supported orthotropic rectangular plate is considered. The plate is subject to transverse uniformly distributed load q applied to the rectangular area ABCD. The Navier method is used to obtain the solution of boundary value problem. The solution is used for stress and deflection analysis. The results obtained in calculation include maximum deflection of the plate and approximation formula for deflection function, maximum normal, shear, and von Mises stresses with indication of points where these stresses occur. 
Figure 1. Simply supported plate under transverse load q uniformly distributed on the rectangular area ABCD. 
Assumptions 


Methodology 
We consider the orthotropic material with the following stressstrain relationship: 
The boundary value problem for the deflection function w(x,y) is: 
The stiffness coefficients in the differential equation are given by formulas 
where h is the thickness of the plate. 
According to the Navier method the solution of the boundary value problem w(x,y) as well as load function q(x,y) could be represented as double trigonometrical series 
where 
In the case of uniformly distributed load shown in Fig. 1 we have the formula for the coefficients q_{nm} 
The number of terms of the series in our calculations is defined as (a/l_{x}+3)(b/l_{y}+3). We also provide the approximation formula for the deflection function in which the small terms were discarded under the condition a_{nm}< w_{max}/200, where w_{max} is maximum deflection of the plate. 
For calculation stresses in the bottom layer of the plate we use the following formulas: 
In addition to σ_{x} , σ_{y} , τ_{xy} the model allows to obtain maximum values of the following stresses:
principal stresses 
shear stresses 
von Mises stresses 
References 
