Application of continuation methods to uniaxially loaded postbuckled plates

TitleApplication of continuation methods to uniaxially loaded postbuckled plates
Publication TypeJournal Article
Year of Publication2014
AuthorsTC Lyman, LN Virgin, and RB Davis
JournalJournal of Applied Mechanics
Volume81
Issue3
Date Published01/2014
Abstract

Continuation methods are used to examine the static and dynamic postbuckled behavior of a uniaxially loaded, simply supported plate. Continuation methods have been extensively used to study problems in mathematics and physics; however, they have not been as widely applied to problems in engineering. When paired with a Galerkin approximation, continuation methods are shown to be well suited to solving nonlinear buckling problems. In addition to providing a robust solution method for nonlinear equations, the linearized Jacobians from the continuation steps will contain natural frequency and mode shape information for mechanical systems (provided inertia terms are included). Results for the primary buckling branch are compared to previously published results. Using the open-source continuation package Auto, stable, remote secondary buckling branches were discovered. These secondary stable equilibrium persist even in the presence of geometric imperfections and their existence is confirmed by experiment. Copyright © 2014 by ASME.

DOI10.1115/1.4024672
Short TitleJournal of Applied Mechanics