scholarly journals Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sen-Yung Lee ◽  
Qian-Zhi Yan
Keyword(s):  
Boundary Conditions ◽  
Function Method ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Strong Nonlinearity ◽  
Timoshenko Beams ◽  
Static Deflection ◽  
Boundary Problems ◽  
Beam System ◽  
Differential Characteristic

Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton’s principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.

scholarly journals Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yang Zhang ◽  
Mingxin Wang ◽  
Yuwen Wang
Keyword(s):  
Boundary Conditions ◽  
Positive Solution ◽  
Positive Solutions ◽  
Diffusion Coefficients ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Competition Model ◽  
Boundary Problems ◽  
Existence Of Positive Solutions

A Lotka-Volterra competition model with nonlinear boundary conditions is considered. First, by using upper and lower solutions method for nonlinear boundary problems, we investigate the existence of positive solutions in weak competition case. Next, we prove that-d1Δu=u(a1-b1u-c1v),x∈Ω;-d2Δv=v(a2-b2u-c2v),x∈Ω;∂u/∂ν+f(u)=0,x∈∂Ω;∂v/∂ν+g(v)=0,x∈∂Ω, has no positive solution when one of the diffusion coefficients is sufficiently large.

Sign in / Sign up

Export Citation Format

Share Document