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Updated Lagrangian formulation for nonlinear stability analysis of thin-walled frames with semi-rigid connections

This paper presents a one-dimensional finite element formulation for nonlinear stability analysis of framed structures with semi-rigid connections. Applying the updated Lagrangian incremental formulation and the nonlinear displacement field of thin-walled cross-sections, the equilibrium equations of a straight beam element are firstly developed. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends. To account for the semi-rigid connection behaviour, a special transformation procedure is developed. The effectiveness of the numerical algorithm discussed is validated through the test problems.

thin-walled frames; connections; nonlinear stability; beam element; updated Lagrangian formulation

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