Nonlinear numerical model of plane frames considering semi-rigid connection and different beam theories

Résumé

This paper presents a numerical-computational model for frames with geometric nonlinear behavior, by the Finite Element Co-rotational method, considering the Euler-Bernoulli and Timoshenko beam theories. The connection between structural members is simulated by a null-length connection element, which considers the axial, translational and rotational stiffness. The nonlinear equations system that describes the structural problem is solved by the incremental and iterative procedure of Potra-Pták, with cubic convergence order, combined with the Linear Arc-Length path-following technique. The solution method algorithm is presented and the numerical examples are simulated with the free Scilab program. The numerical results show that the slenderness of the structure, geometric nonlinearity and semi-rigidity influence the behavior of the structure. Structural analysis and design procedures that consider these factors attains less conservative design thus obtaining more optimized structures.

Keywords: Shear deformation. Potra-Pták. Connection element.