Teaching Nonlinear Mechanics: An Extensive Discussion of a Standard Example Feasible for Undergraduate Courses
Abstract
Most courses on mechanics of materials use a linearized (secondorder) buckling analysis of a simple elastic system as an introductory example. We propose to start with a thirdorder buckling analysis instead, to enable the students to understand the crucial loadresponse diagrams from the beginning of the course. We present an extensive mathematical discussion of an extended standard introductory example, leading to an easytoimplement plotting routine for loadresponse diagrams. The resulting diagrams are interpreted in physical terms. An implementation of the plotting algorithm using Maplesoft Maple^{TM} is attached.
 Publication:

International Journal for Computational Methods in Engineering Science and Mechanics
 Pub Date:
 March 2014
 DOI:
 10.1080/15502287.2014.882444
 Bibcode:
 2014IJCEM..15..172S
 Keywords:

 Educational;
 Buckling;
 Thirdorder theory;
 Bifurcation;
 Loadresponse diagrams;
 Plotting algorithm