Session: MSNDC-04-01 Nonlinear Dynamics of Structures

Paper Number: 71740

Start Time: August 17, 11:10 AM

71740 - Post-Buckling Stability of a Cantilever Beam With Cubic Non-Linearity in Constitutive Laws 

Buckling of slender structures under compressive loads has been a subject of interest within many engineering systems including those at micro-scale such as micro-electro-mechanical devices or nanotubes. Buckling dynamics has a functional relevance to nano-rods and nanotubes and more recently, it has gained research attention in the context of biological and biomimetic systems as well. In the post-buckling regime where deformations are large, it is both plausible and likely that the assumption of linear constitutive laws can be increasingly inaccurate. This paper investigates the sensitivity of the postbuckling response of slender structures to non-linearities of the constitutive law that capture both softening and hardening behavior of material. We analyze the buckling stability of elastic rods with cubic (softening or hardening) non-linearity in the constitutive law and subject to a conservative compressive force. A simple idealized model reveals that stable post-buckling equilibria, i.e., supercritical bifurcations, shrink gradually to unstable subcritical bifurcation and as a result, there is a range of constitutive law parameters corresponding to partially unstable post-buckling paths. Using perturbation analysis with high order of accuracy we also confirm these predictions in a continuum setting. This work also identifies high sensitivity of the post-buckling equilibria to the softening non-linearity in the constitutive law.

Presenting Author: Derek Hollenbeck University of California, Merced

Authors:

Soheil Fatehiboroujeni Cornell University
Derek Hollenbeck University of California, Merced
Anupam Mishra University of California, Merced
Sachin Goyal University of California, Merced