On the local stability condition in the planar beam finite element

In standard finite element algorithms, the local stability conditions are not accounted for in<br />the formulation of the tangent stiffness matrix. As a result, the loss of the local stability is not adequately<br />related to the onset of the global instability. The phenomenon typically arises with material-type localizations,<br />such as shear bands and plastic hinges. This paper addresses the problem in the context of the planar,<br />finite-strain, rate-independent, materially non-linear beam theory, although the proposed technology is in<br />principle not limited to beam structures. A weak formulation of Reissner