Some Classical Buckling Problems Revisited from a Continuum Approach

Mahadevan, P and Chatterjee, A (2007) Some Classical Buckling Problems Revisited from a Continuum Approach. In: UNSPECIFIED, pp. 179-185.

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Abstract

We reexamine some classical buckling problems using a prestress based three dimensional modal projection approach. The approach was recently developed for finding the critical speeds of arbitrary axisymmetric rotors. Both buckling and rotor whirl are problems of nonlinear elasticity, and the primary contribution of the approach is to intuitively identify key terms among all the nonlinear terms present that essentially determine the critical parameter of interest (load, for buckling; and speed, for whirl). Here, we briefly state the reduced formulation (that retains only key terms), and use modal projections to find the buckling loads for four systems. The primary contribution of the present paper lies in that the treatment of these classical and simple problems, though based on a continuum formulation, is analytical. The match obtained with known solutions to these problems suggests that the approach may be useful for a variety of other problems as well. © 13th National Conference on Machines and Mechanisms, NaCoMM 2007.

Item Type:	Conference Paper
Publication:	13th National Conference on Machines and Mechanisms, NaCoMM 2007
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Additional Information:	The copyright for this article belongs to PERGAMON-ELSEVIER SCIENCE LTD.
Keywords:	Continuum mechanics, Axi-symmetric rotors; Buckling loads; Buckling problems; Critical speed; IS problems; Modal projection; Nonlinear elasticity; Nonlinear terms; Prestress; Primary contribution, Buckling
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	24 Apr 2024 09:06
Last Modified:	24 Apr 2024 09:06
URI:	https://eprints.iisc.ac.in/id/eprint/84587

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