Buckling Analysis of a Rectangular Plate

Let us consider a rectangular plate with sides a x b and thickness h (see figure).

The thickness of plate h is much smaller than the length of its sides a,b.
The plate is uniformly compressed in a transversal direction.
Consider the case when the loaded edges of plate are simply-supported; one of the non-loaded edges is clamped, another non-loaded edge is free.

Let us use the following data: plate side length a = 500 mm, b = 800 mm  thickness of plate h = 3 mm , applied distributed force P = 1 Pa.
Material characteristics assume default values: Young's modulus E = 2.1E+011 Pа, Poisson's ratio ν = 0.28.

Analytical solution for this problem is given by:

σcritical = K π2 D / b2 h ,

where E – Young’s modulus, D = E h3 / 12 (1-ν2) – cylindrical stiffness of plate, K – coefficient whose value depends on the type of the supports of the plate edges and the ratio a/b (in this case K = 1.33).
Thus, σcritical = K π2 D / a2 h = 8.9732E+006 Pa.
After carrying out calculation with the help of AutoFEM, the following results are obtained:

Table 1. Parameters of finite element mesh

Table 2. Result "Critical load"*

 

Conclusions:

The relative error of the numerical solution compared with the analytical solution not exceed 2.5% for quadratic finite elements.

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.

 

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