VAM applied to dimensional reduction of non-linear hyperelastic plates

Burela, Ramesh Gupta and Harursampath, Dineshkumar (2012) VAM applied to dimensional reduction of non-linear hyperelastic plates. In: INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 59 (SI). pp. 90-102.

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Abstract

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Additional Information:	Copyright for this article belongs to PERGAMON-ELSEVIER SCIENCE LTD
Keywords:	Asymptotically correct; Hyperelastic plate; 3-D warping; Closed-form solution; Dimensional reduction; Material nonlinearity
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	08 Jan 2013 12:29
Last Modified:	08 Jan 2013 12:29
URI:	http://eprints.iisc.ac.in/id/eprint/45256

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