A classification of thin plate models by asymptotic expansion of non-linear three-dimensional equilibrium equations

Abstract

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.