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ENERGY APPROACH FOR DYNAMIC BUCKLING OF AN UNDAMPED ARCH MODEL UNDER STEP LOADING WITH INFINITE DURATION

YONG-LIN PI

Faculty of Engineering and Information Technology, University of Technology, Sydney, Broadway, NSW 2007, Australia

Corresponding author.

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MARK ANDREW BRADFORD

Faculty of Engineering and Information Technology, University of Technology, Sydney, Broadway, NSW 2007, Australia

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SHUGUO LIANG

School of Civil Engineering, Wuhan University, Wuhan 430071, China

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https://doi.org/10.1142/S0219455410003555Cited by:15 (Source: Crossref)

Abstract

Performing a dynamic buckling analysis of structures is more difficult than carrying out its static buckling analysis counterpart. Some structures have a nonlinear primary equilibrium path including limit points and an unstable equilibrium path. They may also have bifurcation points at which equilibrium bifurcates from the primary equilibrium path to an unstable secondary equilibrium path. When such a structure is subjected to a load that is applied suddenly, the oscillation of the structure may reach the unstable primary or secondary equilibrium path and the structure experiences an escaping-motion type of buckling. For these structures, complete solutions of the equations of motion are usually not needed for a dynamic buckling analysis, and what is really sought are the critical states for buckling. Nonlinear dynamic buckling of an undamped two degree-of-freedom arch model is investigated herein using an energy approach. The conditions for the upper and lower dynamic buckling loads are presented. The merit of the energy approach for dynamic buckling is that it allows the dynamic buckling load to be determined without the need to solve the equations of motion. The solutions are compared with those obtained by an equation of motion approach.

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