scholarly journals On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions

2021 ◽  
Vol 6 (9) ◽  
pp. 9899-9910
Author(s):  
Ammar Khanfer ◽  
◽  
Lazhar Bougoffa ◽  
Keyword(s):  
Fourth Order ◽  
Nonlocal Conditions ◽  
Beam Equation ◽  
Nonlinear Beam ◽  
Small Deflection

An Asymptotic Solution for the Response of Face-Sheet Delaminations/Debonds Under Compression

2000 ◽  
Author(s):  
George A. Kardomateas ◽  
Haiying Huang
Keyword(s):  
Transverse Shear ◽  
Critical Strain ◽  
Linear Equations ◽  
Face Sheet ◽  
Beam Equation ◽  
System Of Linear Equations ◽  
Postbuckling Behavior ◽  
Nonlinear Beam ◽  
First Order ◽  
Higher Order Terms

Abstract The buckling and initial postbuckling behavior of face-sheet delaminations or face-sheet/core debonds is studied by a perturbation procedure. The procedure is based on the nonlinear beam equation with transverse shear included, and an asymptotic expansion of the load and deformation quantities. First the characteristic equation for the critical load is formulated and this is a nonlinear algebraic equation. Subsequently, the first order load is found from a system of linear equations and the initial postbuckling behavior can thus be studied. The procedure can be easily expanded to the higher order terms. The effect of transverse shear is illustrated with results on the critical strain and the initial postbuckling displacement.

scholarly journals Remarks on the existence and decay of the nonlinear beam equation

1994 ◽  
Vol 17 (2) ◽  
pp. 409-412 ◽  
Author(s):  
Jaime E. Mũnoz Rivera
Keyword(s):  
Weak Solution ◽  
Beam Equation ◽  
Nonlinear Beam

We will consider a class of nonlinear beam equation and we will prove the existence and decay weak solution

scholarly journals Existence of Positive Solutions of a Discrete Elastic Beam Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ruyun Ma ◽  
Jiemei Li ◽  
Chenghua Gao
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Elastic Beam ◽  
Beam Equation ◽  
Nonlinear Boundary Value Problems ◽  
Order Difference ◽  
Bifurcation Theorem ◽  
Existence Of Positive Solutions

LetTbe an integer withT≥5and letT2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equationsΔ4u(t−2)−ra(t)f(u(t))=0,t∈T2,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, whereris a constant,a:T2→(0,∞),  and  f:[0,∞)→[0,∞)is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

Blow-up of solutions for a nonlinear beam equation with fractional feedback

2011 ◽  
Vol 74 (4) ◽  
pp. 1402-1409 ◽  
Author(s):  
Soraya Labidi ◽  
Nasser-eddine Tatar
Keyword(s):  
Blow Up ◽  
Beam Equation ◽  
Nonlinear Beam

Analytical Approximations to Buckling Deformation of the Sandwich Beams Including Transverse Shear

2011 ◽  
Vol 317-319 ◽  
pp. 1783-1786
Author(s):  
Yong Ping Yu ◽  
Lin Zang ◽  
You Hong Sun
Keyword(s):  
Transverse Shear ◽  
Harmonic Balance ◽  
Approximate Solutions ◽  
Beam Equation ◽  
Sandwich Beams ◽  
Nonlinear Beam ◽  
Sandwich Construction ◽  
Analytical Approximations ◽  
Post Buckling ◽  
Approximate Procedure

This paper presents analytical approximate solutions for the initial post-buckling deformation of the sandwich beams including transverse shear. The approximate procedure is based on the nonlinear beam equation (with transverse shear included), by combining the Newton’s method with the method of harmonic balance, we establish analytical approximations to deformation of the sandwich beams. Illustrative examples are presented for a few typical sandwich construction configurations, and it is shown that these approximate solutions are excellent agreement with the “reference” solutions.

Symmetries and integrability of a fourth-order Euler–Bernoulli beam equation

2010 ◽  
Vol 51 (5) ◽  
pp. 053517 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Fourth Order ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam
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