Differential quadrature application in post-buckling analysis of a hinged-fixed elastica under terminal forces and self-weight
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- Sepahi, O., Forouzan, M.R. & Malekzadeh, P. J Mech Sci Technol (2010) 24: 331. doi:10.1007/s12206-009-1101-1
Based on geometrically non-linear theory for extensible elastic rods, governing equations of statically post-buckling of a beam with one end hinged and the other fixed, and subjected to a terminal force and a self-weight, are established. The formulation is derived from geometrical compatibility, equilibrium of forces and moments, and constitutive relations, which characterize a complex two-point boundary value problem. By using differential quadrature method (DQM), the non-linear governing equations are solved numerically and the post-buckled configurations of the deformed column are presented. Results are plotted in non-dimensional graphs for a range of density and terminal force, and are in good agreement with available references.