On the uniqueness of large deflections of a uniform cantilever beam under a tip-concentrated rotational load

2010 ◽  
Vol 45 (4) ◽  
pp. 433-441 ◽  
Author(s):  
M. Mutyalarao ◽  
D. Bharathi ◽  
B. Nageswara Rao
Keyword(s):  
Cantilever Beam ◽  
Large Deflections ◽  
Rotational Load

Large deflections of a nonuniform cantilever beam with end rotational load

1988 ◽  
Vol 54 (1) ◽  
pp. 24-26 ◽  
Author(s):  
B. Nageswara Rao ◽  
G. Venkateswara Rao
Keyword(s):  
Cantilever Beam ◽  
Large Deflections ◽  
Rotational Load

Large deflections of a cantilever beam under an inclined end load

2010 ◽  
Vol 217 (7) ◽  
pp. 3607-3613 ◽  
Author(s):  
M. Mutyalarao ◽  
D. Bharathi ◽  
B. Nageswara Rao
Keyword(s):  
Cantilever Beam ◽  
Large Deflections

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.

Series solution for large deflections of a cantilever beam with variable flexural rigidity

Meccanica ◽  
2012 ◽  
Vol 47 (7) ◽  
pp. 1787-1796 ◽  
Author(s):  
A. Kimiaeifar ◽  
E. Lund ◽  
O. T. Thomsen
Keyword(s):  
Cantilever Beam ◽  
Series Solution ◽  
Flexural Rigidity ◽  
Large Deflections

Model reduction technique for mechanical behaviour modelling: Efficiency criteria and validity domain assessment

2008 ◽  
Vol 222 (3) ◽  
pp. 493-505 ◽  
Author(s):  
K Ordaz-Hernandez ◽  
X Fischer ◽  
F Bennis
Keyword(s):  
Neural Network ◽  
Model Reduction ◽  
Linear Model ◽  
Cantilever Beam ◽  
Reduction Technique ◽  
Reduced Model ◽  
Large Displacements ◽  
Large Deflections ◽  
Non Linear ◽  
Model Reduction Technique

The current paper presents the study of a neural network-based technique used to create fast, reduced, non-linear behavioural models. The studied approach is the use of artificial neural networks (ANNs) as a model reduction technique to create more efficient models, mostly in terms of computational speed. The test case is the deformation of a cantilever beam under large deflections (geometrical non-linearity). A reduced model is created by means of a multi-layer feed-forward neural network, a type of ANN reported as ‘universal approximator’ in the literature. Then it is compared with two finite-element models: linear (inaccurate for large deflections but fast) and non-linear (accurate but slow). Under large displacements, the reduced model approximates well the non-linear model while having similar speed to the linear model. Unfortunately, the resulting model presents a shortening of its validity domain, as being incapable of approximating the deformed configuration of the cantilever beam under small displacements. In other words, the ANN-based model provides a very good compromise between accuracy and speed within its validity domain, despite the low fidelity presented: accurate for large displacements but inaccurate for small displacements.

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