ISSN:
1432-0681
Keywords:
Key words elastica
;
beam bending
;
frictional support
;
variable arc-length
;
elliptic integral solution
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Summary Treated herein is an elastica under a point load. One end of the elastica is fully restrained against translation, and elastically restrained against rotation, while the other end portion is allowed to slide over a friction support. The considered elastica problem belongs to the class of large-deflection beam problems with variable deformed arc-lengths between the supports. To solve the governing nonlinear differential equation together with the boundary conditions, the elliptic integral method has been used. The method yields closed-form solutions that are expressed in a set of transcendental equations in terms of elliptic integrals. Using an iterative scheme, pertinent bending results are computed for different values of coefficient of friction, elastic rotational spring constant and loading position, so that their effects may be examined. Also, these accurate solutions provide useful reference sources for checking the convergence, accuracy and validity of results obtained from numerical methods and software for large deflection beam analysis. It is interesting to note that this class of elastica problem may have two equilibrium states; a stable one and an unstable one.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004190050138
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