Near and far from the threshold analysis of rectangular elastic plates

We study the problem of buckling and postbuckling of a plate under in-plane loads. This system exhibits a complex phase diagram with two distinct regimes: one near the instability for buckling and the other characterized by isometric deformations. Here, we show that the equations of elasticity for this problem can be reduced to the well-known Swift–Hohenberg equation as a leading term in a Galerkin projection. Higher order terms in the expansion are also computed to illustrate the convergence of the analysis. (paper)