Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Abstract

A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given.

Large Deformation Problem of Bimodular Functionally-Graded Thin Circular Plates Subjected to Transversely Uniformly-Distributed Load: Perturbation Solution without Small-Rotation-Angle Assumption

“…The problem and method presented in this study can be used for further research work. In particular, the problem concerning small-rotation-angle assumption may be extended into the establishment of mathematical models with buckling and contact phenomena for elastic plates [42], because the buckling problem of an elastic plate is usually accompanied by its large deformation. In addition, the single-parameter perturbation method based on the central deflection in this study may also be extended to the so-called multi-parameters perturbation method [43] that has been successfully used for investigating functionallygraded, thin, circular piezoelectric plates.…”