Transient Response of a Hinged Elastica Under a Step Load
Date Issued
2012
Date
2012
Author(s)
Lin, Wei-Zhong
Abstract
Abstract
The previous research has studied the static deformation and stability analysis of hinged shallow arch by small deformation theory. In this paper, large deformation theory is first applied to research the transient response of elastic beam (elastica) under a step load Q. The energy method is used to predict dynamical critical load when the step load applied on the middle point of elastica. The number of the governing equations is reduced from 6 to 3 by Deformation Potentials, and the governing equations are discretised by Finite Difference Method and solved by Newton Method. The angle between the end of the initial shape studied in this paper and x-axis is 40 degree. The internal damping of material c_m is considered. The difference of the transient response between force Q and weight mg is compared, and the dynamical critical load is obtained by numerical simulation when the load applied on the non middle point.
If the step load Q much less than critical load, the transient response can converge by fining time increment k. If the step load Q greater than critical load, the time happening snap-through can be predicted precisely, but the transient response after snap-through cannot converge by fining time increment k. If the step load Q similar with critical load, the time happening snap-through cannot be predicted precisely by fining time increment k. Therefore we use the energy method to obtain the conservative dynamical critical load instead of numerical simulation. It is assured that the elastica would not happen snap-through if the step load Q less than the conservative dynamical critical load.
Subjects
Elastica
Dynamical Critical Load
Snap-through
Type
thesis
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