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Structural Engineering and Mechanics Volume 12, Number 5, November 2001 , pages 507-526 DOI: https://doi.org/10.12989/sem.2001.12.5.507 |
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On the local stability condition in the planar beam finite element |
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Igor Planinc, Miran Saje and Bojan Cas (Slovenia)
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| Abstract | ||
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In standard finite element algorithms, the local stability conditions are not accounted for in the formulation of the tangent stiffness matrix. As a result, the loss of the local stability is not adequately related to the onset of the global instability. The phenomenon typically arises with material-type localizations, such as shear bands and plastic hinges. This paper addresses the problem in the context of the planar, finite-strain, rate-independent, materially non-linear beam theory, although the proposed technology is in principle not limited to beam structures. A weak formulation of Reissner | ||
| Key Words | ||
| local stability; planar beam; finite element; numerical integration; plasticity. | ||
| Address | ||
| Igor Planinc, Miran Saje and Bojan Cas, Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, SI-1115 Ljubljana, Slovenia | ||