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.
Highlights
The present paper provides a review of existing mathematical plate models with both buckling and contact phenomena together and recent progress in this area.Plate theories have been created by reducing full three-dimensional solid mechanics problems to two-dimensional ones, taking into account a small thickness of a plate
Mechanical models for buckling of unilaterally constrained by nonlinear elastic foundations rectangular and infinite plates are given in the papers of Shahwan and Waas [67,68], respectively
Some delamination mathematical models are issued from the classical linear plate theories, namely buckling delaminations ofthe theMindlin–Reissner plate, are solved directly by finite element method (FEM) or other numerical techniques from the and Kirchhoff–Love and principles, many works related with
Summary
The present paper provides a review of existing mathematical plate models with both buckling and contact phenomena together and recent progress in this area. Solve the nonlinearof von-Kármán system is difficult in virtue of the in high plate equations work bestTofor small deflections the plate ([23]). They become not so accurate the order partial equations and presence of nonlinearity. The classical and nonlinear plate equations are the keyssystem for creating various plate in applied sciencelinear and engineering. Kármán is difficult in virtue models, including, delamination of equations compositeand plates The classical linear and nonlinear plate equations the main keys for creating plate models,. Let us consider plate which is under load q in vertical z direction as shown on Figure 1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
