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Mechanics Research Communications, Volume 47, January 2013, Pages 69-76.
Dongming Wei, Alejandro Sarria, Mohamed Elgindi.
Department of Mathematics, University of New Orleans, New Orleans, LA, USA and
Texas A& M University-Qatar, Qatar.
Abstract
In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Hollomon’s power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and comparisons to the classical result of the Euler–Engesser reduced-modulus loads are also presented.
Additional Information:
{Our analytic critical buckling load formula provides an alternative to the existing buckling formulas for elasto-plastic materials. This formula is derived based on the Hollomon stress-strain constitutive equation, which can not be effectively used in the reduced or double modulus type formulas due to large deviation from the linear Hookes’ law even for small strains.
There are a large number of Micro-alloyed low carbon sheet steels metals, such as DC05 DC06, H380LAD, high strength steels used in the automotive industry, new materials such as nano-crystalline tantalum, and polyimide products produced by DuPont.}
