Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 36, Issue 1, Pages 165-186Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0020-7462(00)00005-6
Keywords
non-linear elasticity; plate theory; dimensional analysis; asymptotic methods
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We present in this paper a new constructive method of classification of two-dimensional plate models from the applied forces level and the geometrical data. This approach which uses asymptotic methods is based on a dimensional analysis of the non-linear equilibrium equations. This dimensional analysis leads to dimensionless numbers which reflect the geometry of the structure and the applied forces. For a given forces level, the order of magnitude of the displacements and the corresponding two-dimensional model are deduced by asymptotic expansion of the three-dimensional equations. For decreasing forces level, we obtain successively the non-linear membrane model, another membrane model, the usual non-linear plate model and the linear Kirchhoff-Love model. (C) 2000 Elsevier Science Ltd. All rights reserved.
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