Asymptotic and Rayleigh-Ritz routes to localized buckling solutions in an elastic instability problem

Two complementary approximate techniques are developed to describe the subcritical (localized) deflection patterns of elastic struts resting on elastic foundations. One is a double-scale perturbation approach developed directly from the total potential energy functional; the other is an extension of traditional Rayleigh-Ritz analysis. Both make extensive use of modern symbolic computation tools and are validated against accurate independent numerical solutions. The asymptotic perturbation approach shows most accuracy at loads close to critical buckling, while the Rayleigh-Ritz procedure compares well with numerics over most of the range from zero load to critical.