Teaching Nonlinear Mechanics: An Extensive Discussion of a Standard Example Feasible for Undergraduate Courses

Most courses on mechanics of materials use a linearized (second-order) buckling analysis of a simple elastic system as an introductory example. We propose to start with a third-order buckling analysis instead, to enable the students to understand the crucial load-response diagrams from the beginning of the course. We present an extensive mathematical discussion of an extended standard introductory example, leading to an easy-to-implement plotting routine for load-response diagrams. The resulting diagrams are interpreted in physical terms. An implementation of the plotting algorithm using Maplesoft Maple^TM is attached.