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Engineering Mechanics of Deformable SolidsA Presentation with Exercises$
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Sanjay Govindjee

Print publication date: 2012

Print ISBN-13: 9780199651641

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199651641.001.0001

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Geometric Instability

Geometric Instability

Chapter:
(p.263) 12 Geometric Instability
Source:
Engineering Mechanics of Deformable Solids
Author(s):

Sanjay Govindjee (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199651641.003.0012

This chapter discusses mechanical failure via geometric instability or buckling. The problem is explained from the standpoint of stationary potential energy and the emergence of multiple equilibrium solutions at critical load values in both a linearized and non-linear setting. The classic problem of Euler buckling is presented from the governing equilibrium equations as well as from the concept of stationary potential energy. For more complex situations, the notion of approximate stationary potential energy is utilized to compute approximate buckling loads.

Keywords:   geometric instability, buckling, euler buckling, approximate buckling loads, multiple equilibrium solutions, unstable equilibria, critical values

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