An iterative numerical solution is given for the case of a thin elastic rod whose inputs are simultaneously the positions of the two ends and an applied moment at one end. The development begins by considering the real rod as an end section of a longer fictitious rod loaded with end forces only. Newton’s method is then used to obtain both the shape of the real road and its vector restoring force. The results show that both the magnitude and the direction of the restoring force are changed considerably from the zero-moment case, especially when the percent deflection of the elastica is small. Such a model is a useful alternative to a pure force-deflection one because it accounts not only for the direct effect of the applied moment on the reaction rigid body but the indirect contribution to the reaction force as well.
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March 1980
Technical Briefs
An Iterative Numerical Solution for the Elastica With Causally Mixed Inputs
M. Hubbard
M. Hubbard
Department of Mechanical Engineering, University of California, Davis, Calif., 95616
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M. Hubbard
Department of Mechanical Engineering, University of California, Davis, Calif., 95616
J. Appl. Mech. Mar 1980, 47(1): 200-202 (3 pages)
Published Online: March 1, 1980
Article history
Received:
February 1, 1979
Revised:
September 1, 1979
Online:
July 21, 2009
Citation
Hubbard, M. (March 1, 1980). "An Iterative Numerical Solution for the Elastica With Causally Mixed Inputs." ASME. J. Appl. Mech. March 1980; 47(1): 200–202. https://doi.org/10.1115/1.3153607
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