This work complements recent developments concerning the buckling of beams lying on a nonlinear (non-convex) elastic foundation, and also reports on some investigations on the role of material nonlinearity. Two structural models are studied using a simple elasto-plastic constitutive relationship, and buckling problems are formulated as reversible fourth-order differential equations. It is demonstrated that modulated responses are possible under certain circumstances. Some numerical simulations are presented supporting the analytical findings.
Coman, C. D., Bassom, A., & Wadee, M. K. (2003). Elasto-plastic localised responses in one-dimensional structural models. Journal of Engineering Mathematics, 47(2), 83-100. https://doi.org/10.1023/A:1025856602682