On the estimation of the large deflection of a cantilever beam

2002 ◽  
Author(s):  
M.H. Ang ◽  
Wang Wei ◽  
Low Teck-Seng
Keyword(s):  
Cantilever Beam ◽  
Large Deflection

scholarly journals A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

Large deflection of constant curvature cantilever beam under follower load

2010 ◽  
Vol 52 (3) ◽  
pp. 440-445 ◽  
Author(s):  
Ashok Kumar Nallathambi ◽  
C. Lakshmana Rao ◽  
Sivakumar M. Srinivasan
Keyword(s):  
Cantilever Beam ◽  
Constant Curvature ◽  
Large Deflection ◽  
Follower Load

scholarly journals Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
H. Vázquez-Leal ◽  
Y. Khan ◽  
A. L. Herrera-May ◽  
U. Filobello-Nino ◽  
A. Sarmiento-Reyes ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Cantilever Beam ◽  
Homotopy Perturbation Method ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Follower Force ◽  
Homotopy Perturbation ◽  
Solution Methods ◽  
Nonlinear Pendulum

In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to179.99999999∘yielding a relative error of 0.01222747.

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