Highly accurate algorithms endowing with boundary functions for solving a nonlinear beam equation involving an integral term

2017 ◽  
Vol 41 (5) ◽  
pp. 1855-1869 ◽  
Author(s):  
Chein‐Shan Liu ◽  
Botong Li
Keyword(s):  
Beam Equation ◽  
Integral Term ◽  
Nonlinear Beam ◽  
Boundary Functions

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

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.

scholarly journals Time decay for the nonlinear beam equation

2000 ◽  
Vol 7 (3) ◽  
pp. 479-488 ◽  
Author(s):  
Steven P. Levandosky ◽  
Walter A. Strauss
Keyword(s):  
Beam Equation ◽  
Time Decay ◽  
Nonlinear Beam
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