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International Journal of Engineering Science, Volume 59, October 2012, Pages 90-102
Ramesh Gupta Burela, Dineshkumar Harursampath
Nonlinear Multifunctional Composites-Analysis and Design (NMCAD) Lab., Department of Aerospace Engineering, Indian Institute of Science, Bengaluru 560012, India
Abstract
This work aims at dimensional reduction of non-linear isotropic hyperelasticplates 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.
