General information 
Description 
The buckling of thin simply supported orthotropic rectangular plate is considered. The plate is subject to uniformly distributed load N_{x} and N_{y} applied in the middle plane of the plate around its edges. The goal of calculation is to obtain the critical combination of the load. We obtain the solution of corresponding fourthorder partial differential equation with associated homogeneous boundary conditions. The minimum eigenvalue of the problem corresponds to the critical load. The solution is represented both graphically and as simple formulas. 
Figure 1. Simply supported plate compressed in two directions by uniformly distributed load N_{x} and N_{y}. 
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. 
The solution of this homogeneous boundary value problem is the deflection function 
where n and m are natural numbers. Also we have equation 
If N_{y}=0 
Minimum of the critical load occurs when m=1 and 
Similarly if N_{x}=0 
Minimum of N_{y} occurs when n=1 and 
In general case for the given value of N_{x} one can find that 
and minimum of N_{y} takes place if 
Using last formulas we created algorithm for calculation of minimal critical load N_{y} for the different values of N_{x}. 
References 
