Abstract
This paper is devoted to the theoretical aspects of the elastoplastic buckling and initial post-buckling of plates and cylinders under uniform compression. The analysis is based on the 3D plastic bifurcation theory assuming the J 2 flow theory of plasticity with the von Mises yield criterion and a linear isotropic hardening. The proposed method is shown to be a systematic and unified way to obtain the critical loads, the buckling modes and the initial slope of the bifurcated branch for rectangular plates under uniaxial or biaxial compression(-tension) and cylinders under axial compression, with various boundary conditions.
Highlights
Failure of thin structures which is mainly due to the buckling phenomenon implies the analysis of buckling and post-buckling behaviors for their mechanical design, namely the calculation of the critical loads, the bifurcation modes and the post-critical equilibrium branches.In elasticity, the bifurcation is related to the structural instability as shown in Koiter’s theory
This paper is devoted to the theoretical aspects of the elastoplastic buckling and initial post-buckling of plates and cylinders under uniform compression
Cimetiere et al [6,7,8,9] thoroughly solved the bifurcation problem for the Shanley discrete model and a compressed beam, and first provided the necessary theoretical ingredients such as the validity, the convergence of the previous expansion and the existence of the post-critical branches. Another significant result is the existence of continua of bifurcation points in plastic buckling problems, which was discovered by Cimetiere [10] when dealing with the case of compressed rectangular plates
Summary
Failure of thin structures which is mainly due to the buckling phenomenon implies the analysis of buckling and post-buckling behaviors for their mechanical design, namely the calculation of the critical loads, the bifurcation modes and the post-critical equilibrium branches. Cimetiere et al [6,7,8,9] thoroughly solved the bifurcation problem for the Shanley discrete model and a compressed beam, and first provided the necessary theoretical ingredients such as the validity, the convergence of the previous expansion and the existence of the post-critical branches Another significant result is the existence of continua of bifurcation points in plastic buckling problems, which was discovered by Cimetiere [10] when dealing with the case of compressed rectangular plates. Ore and Durban [14] derived semi-analytical values for the critical load of a cylinder under axial compression and various boundary conditions, with a special emphasis on axisymmetric modes They showed again the discrepancy between the results provided by the flow and deformation theories of plasticity. The interested reader can find more details on the theoretical developments and more complete states-of-art in the quoted references
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