ABSTRACT
When a plate is subjected to uniform compressive forces applied in the middle plane of the plate, and if the forces are sufficiently small, the force-displacement response is linear. The linear relationship holds until a certain load is reached. At that load, called the buckling load, the stable state of the plate is disturbed and the plate seeks an alternative equilibrium configuration accompanied by a change in the loaddeflection behavior. The phenomenon of changing the equilibrium configuration at the same load and without drastic changes in deformation is termed bifurcation. The load-deflection curve for buckled plates is often bilinear. The magnitude of the buckling load depends, as will be shown shortly, on geometry, material properties, and the buckling mode shape, i.e., geometric configuration of the plate at buckling. In the present study, we assume that the only applied loads are the uniform
inplane forces and that all other mechanical and thermal loads are zero. Since the prebuckling deformation w0 is that of an equilibrium configuration, it satisfies the equilibrium equations, and the equation governing buckling deflection w is given by
D11 ∂4w ∂x4
+ 2Dˆ12 ∂4w
∂4w ∂y4
+ kw = Nˆxx ∂2w ∂x2
+ Nˆyy ∂2w ∂y2
(8.1.1)
where Dˆ12 = D12+2D66, and Nˆxx < 0 and Nˆyy < 0 for compressive forces. Here we wish to determine a nonzero deflection w that satisfies Eq. (8.1.1) when the inplane forces are (Figure 8.1.1)
Nˆxx = −N0, Nˆyy = −γN0, γ = Nˆyy
Nˆxx (8.1.2)
and the edges are simply supported.
