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

Aliki D. Muradova and Georgios E. Stavroulakis
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Aliki D. Muradova: School of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical University of Crete, 73100 Chania, Greece
Georgios E. Stavroulakis: School of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical University of Crete, 73100 Chania, Greece

Mathematics, 2020, vol. 8, issue 4, 1-15

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.

Keywords: elastic plate model; partial differential equation; boundary conditions; initial conditions; buckling phenomenon; contact effects; delaminated composite plate; nonlinear dynamic system; approximation techniques (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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