On the plastic bifurcation and post-bifurcation of axially compressed beams |
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Authors: | Philippe Le Grognec Anh Le van |
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Institution: | a Ecole des Mines de Douai, Polymers and Composites Technology & Mechanical Engineering Department, 941 rue Charles Bourseul - BP 10838, 59508 Douai Cedex, France b GeM (Laboratory of Civil and Mechanical Engineering), Faculty of Science - University of Nantes, 2 rue de la Houssinière - BP 92208, 44322 Nantes Cedex 3, France |
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Abstract: | The paper presents two new results in the domain of the elastoplastic buckling and post-buckling of beams under axial compression. (i) First, the tangent modulus critical load, the buckling mode and the initial slope of the bifurcated branch are given for a Timoshenko beam (with the transverse shear effects). The result is derived from the 3D J2 flow plastic bifurcation theory with the von Mises yield criterion and a linear isotropic hardening. (ii) Second, use is made of a specific method in order to provide the asymptotic expansion of the post-critical branch for a Euler-Bernoulli beam, exhibiting one new non-linear fractional term. All the analytical results are validated by finite element computations. |
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Keywords: | Axially compressed beams Bifurcation Buckling Elastoplasticity Asymptotic developments |
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