Elastoplastic bifurcation and collapse of axially loaded cylindrical shells

Grognec, Philippe Le; van, Anh Le

doi:10.1016/j.ijsolstr.2007.07.017

Cited by 20 publications

(12 citation statements)

References 26 publications

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“…One particular cylinder geometry has been chosen to be numerically computed in [32] and the numerical initial slope obtained compares very well with the analytical one given by Eq. (85).…”

Section: Simply Supported Edge Solutionmentioning

confidence: 85%

Some new analytical results for plastic buckling and initial post-buckling of plates and cylinders under uniform compression

Grognec¹,

van²

2009

Thin-Walled Structures

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International audienceThis 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 oil 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

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“…One particular cylinder geometry has been chosen to be numerically computed in [32] and the numerical initial slope obtained compares very well with the analytical one given by Eq. (85).…”

Section: Simply Supported Edge Solutionmentioning

confidence: 85%

Some new analytical results for plastic buckling and initial post-buckling of plates and cylinders under uniform compression

Grognec¹,

van²

2009

Thin-Walled Structures

Self Cite

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“…Developed within a total Lagrangian framework, the program encompasses finite plasticity and geometric non-linearities (finite displacements and rotations) in order to deal with the plastic buckling and advanced post-critical behavior of general structures. For the computation of interest, the beam is discretized using a finite rotation shell finite element which is described in full details in Le Grognec and Le van (2008) in the context of cylindrical shells under axial compression.…”

Section: Finite Element Validationmentioning

confidence: 99%

“…Only the middle node at each tip is fixed in the z-direction, which enables a uniform stress state in the beam during the pre-critical deformations. Since the thickness is very thin, the numerical solution of the bending problem can be performed using the shell finite element described in Le Grognec and Le van (2008). One single finite element in the z-direction is used, whereas 50 elements along the length are necessary to correctly represent finite rotations.…”

Section: Finite Element Validationmentioning

confidence: 99%

On the plastic bifurcation and post-bifurcation of axially compressed beams

Grognec

van

2011

International Journal of Non-Linear Mechanics

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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 J 2 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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“…The elastoplastic thin shell finite element formulation is briefly reviewed in the following paragraphs. A more detailed description, which is outside the scope of this paper, may be found in Le Grognec and Le van (2008).…”

Section: Shell Finite Element Formulationmentioning

confidence: 99%

Influence of residual stresses and geometric imperfections on the elastoplastic collapse of cylindrical tubes under external pressure

2009

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International audienceThe buckling problem of a circular cylindrical shell has long been widely investigated due to its great importance in the design of aerospace and marine structures. Geometric imperfections and residual stresses are inevitable in practice and have been so far frequently considered in analytical and numerical predictions. But little attention has been paid until now on the combined influence of such initial defects on the critical and often unstable response of such elastoplastic structures. In this paper, a shell finite element is designed within the total Lagrangian formulation framework to deal with the elastoplastic buckling and post-buckling of thin cylindrical tubes under external pressure and axial compression. A specific experimental process will be introduced in order to measure residual stresses in the shell very accurately, so as to include them in the numerical calculations. The present formulation will enable us to describe the complete non-linear solutions, namely the critical pressures (bifurcation and limit (collapse) loads), the bifurcation modes and the bifurcated equilibrium branches up to advanced post-critical states. Comparisons will be made between numerical results and the experimental critical value and deformation patterns of a new generation profiler. Furthermore, the combined effects of geometric imperfections, residual stresses and plasticity will be analyzed

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Elastoplastic bifurcation and collapse of axially loaded cylindrical shells

Cited by 20 publications

References 26 publications

Some new analytical results for plastic buckling and initial post-buckling of plates and cylinders under uniform compression

Some new analytical results for plastic buckling and initial post-buckling of plates and cylinders under uniform compression

On the plastic bifurcation and post-bifurcation of axially compressed beams

Influence of residual stresses and geometric imperfections on the elastoplastic collapse of cylindrical tubes under external pressure

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