An Integrated Formulation to Predict Pre and Post-Critical Behavior of Frames

Resumo

To reduce the discretization influence and allow a minimal beam subdivision in geometric nonlinear
analysis of a framed structure, using the finite element method (FEM), the present work evaluates an integrated

formulation in the pre and post-critical phases. This updated Lagrangian formulation considers the Euler-
Bernoulli beam theory with high-order terms of the strain tensor and a tangent stiffness matrix calculated with

analytical interpolation functions. These functions are obtained from the solution of the equilibrium differential

equation of a deformed infinitesimal element, which includes the influence of axial forces. In pre and post-
critical stages, the nonlinear response of the proposed integrated formulation is evaluated with robust nonlinear

solution schemes, and the results are compared with conventional formulations. Examples clearly show the
efficiency of the integrated formulation to predict the pre-critical phase using a low discretization and consistent
results with conventional formulations in the post-critical behavior.