Nonlinear elastic beam theory with application in contact problems and variational approaches

1996 ◽  
Vol 23 (1) ◽  
pp. 11-17 ◽  
Author(s):  
David Yang Gao
Keyword(s):  
Elastic Beam ◽  
Beam Theory ◽  
Contact Problems ◽  
Variational Approaches ◽  
Nonlinear Elastic

Solution of contact problems for Gao beam and elastic foundation

2017 ◽  
Vol 23 (3) ◽  
pp. 473-488 ◽  
Author(s):  
Jitka Machalová ◽  
Horymír Netuka
Keyword(s):  
Contact Problem ◽  
Elastic Foundation ◽  
Variational Equation ◽  
Main Idea ◽  
Axial Loading ◽  
Elastic Beam ◽  
Beam Theory ◽  
Contact Problems ◽  
Problem Formulations ◽  
Nonlinear Elastic

This paper presents mathematical formulations and a solution for contact problems that concern the nonlinear beam published by Gao (Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech Res Commun 1996; 23: 11–17) and an elastic foundation. The beam is subjected to a vertical and also axial loading. The elastic deformable foundation is considered at a distance under the beam. The contact is modeled as static, frictionless and using the normal compliance contact condition. In comparison with the usual contact problem formulations, which are based on variational inequalities, we are able to derive for our problem a nonlinear variational equation. Solution of this problem is realized by means of the so-called control variational method. The main idea of this method is to transform the given contact problem to an optimal control problem, which can provide the requested solution. Finally, some results including numerical examples are offered to illustrate the usefulness of the presented solution method.

scholarly journals Nonlinear ferro-electro-elastic beam theory

2009 ◽  
Vol 46 (11-12) ◽  
pp. 2397-2406 ◽  
Author(s):  
Uri Kushnir ◽  
Oded Rabinovitch
Keyword(s):  
Elastic Beam ◽  
Beam Theory

Variational approaches to impulsive elastic beam equations of Kirchhoff type

2016 ◽  
Vol 61 (7) ◽  
pp. 931-968 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Massimiliano Ferrara ◽  
Shahin Moradi
Keyword(s):  
Elastic Beam ◽  
Kirchhoff Type ◽  
Beam Equations ◽  
Variational Approaches ◽  
Elastic Beam Equations

scholarly journals Comparison of 1D and 2D solutions for a beam under transverse impact

2018 ◽  
Vol 148 ◽  
pp. 05005 ◽  
Author(s):  
Vítězslav Adámek
Keyword(s):  
Analytical Solution ◽  
Timoshenko Beam ◽  
Elastic Beam ◽  
Beam Theory ◽  
Two Dimensional ◽  
Transverse Impact ◽  
Dimensional Theory ◽  
Beam Geometry ◽  
Stationary Vibration ◽  
Main Factors

The problem of non-stationary vibration of an elastic beam caused by a transverse impact loading is studied in this work. In particular, two different approaches to the derivation of analytical solution of the problem are compared. The first one is based on the Timoshenko beam theory, the latter one follows the exact two-dimensional theory. Both mentioned methods are used for finding the response of an infinite homogeneous isotropic beam. The obtained analytical results are then compared and their agreement is discussed in relation to main factors, i.e. the beam geometry, the character of loading and times and points at which the beams responses are studied.

scholarly journals Positive solutions for nonlinear elastic beam models

2001 ◽  
Vol 27 (6) ◽  
pp. 365-375 ◽  
Author(s):  
Bendong Lou
Keyword(s):  
Positive Solutions ◽  
Elastic Beam ◽  
Negative Answer ◽  
Existence Of Positive Solutions ◽  
Nonlinear Elastic ◽  
Positive Results

We give a negative answer to a conjecture of Korman on nonlinear elastic beam models. Moreover, by modifying the main conditions in the conjecture (generalizing the original ones at some points), we get positive results, that is, we obtain the existence of positive solutions for the models.

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