Development of a tool integrating matlab and finite element software for automatic incremental elastoplastic analysis of 2D frames

Abstract

Plastic analysis exploits the reserve of strength that framed structures retain beyond first yield, but tracing this behavior by hand, hinge by hinge, becomes impractical for structures with more than a few possible collapse mechanisms. This work presents a tool that automates the incremental, hinge-by-hinge plastic analysis of two-dimensional frames by coupling MATLAB with a commercial finite element package through its application programming interface. At each stage, MATLAB runs a linear elastic analysis in the finite element software, identifies the section closest to its plastic moment, computes the corresponding load factor increment, and inserts a new hinge in the model, repeating this cycle until the structure becomes a mechanism, detected through the ill-conditioning of the stiffness matrix. The tool was applied to beams and portal frames under concentrated and uniformly distributed loads. In every case, the collapse load factor and the sequence of hinge formation matched the theoretical solutions obtained by classical methods, including the position of hinges within members under distributed loads, without requiring the manual remodeling of the structure at each stage of plastification.