GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF SPACE FRAMES

Resumo

In structural engineering, the von Kármán theory provides a robust framework for modeling geometric nonlinearity under moderate displacements while assuming small strains, making it adequate for thin-walled structures and slender frames. This work presents a Python-based finite element method (FEM) program for nonlinear analysis of space frames, implementing the von Kármán hypothesis for beams. An arc-length scheme solves the nonlinear equilibrium equations. Post-processing via PyVista and Matplotlib libraries enables intuitive interpretation of deformed configuration and force distributions. The program was validated using Abaqus and RFEM, comparing both displacements and internal forces. An eigenvalue buckling analysis module was also implemented, yielding results within 1.5% of Abaqus in complex scenarios and matching exactly those from RFEM. The source code is openly available on GitLab under the name SimuFrame, providing full access to all modules and examples. Its applications are relevant to civil engineering, especially in designs considering the second-order effects.