Large deflections of spatial variable-arc-length elastica under terminal forces
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Author list: Phungpaingam B., Athisakul C., Chucheepsakul S.
Publisher: Techno-press Ltd
Publication year: 2009
Journal: Structural Engineering and Mechanics (1225-4568)
Volume number: 32
Issue number: 4
Start page: 501
End page: 516
Number of pages: 16
ISSN: 1225-4568
Languages: English-Great Britain (EN-GB)
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Abstract
This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on KirchhofPs rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance (10-5). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.
Keywords
Snap-through phenomenon
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