Deflected shape and internal forces of grillage structures using differential equations: PAE-Grelhas 3.0

Resumo

This paper aims to incorporate differential equations for internal forces, displacements and rotations into the processing of PAE-Grelhas 2.0, a free linear-elastic analysis software for grillage structures composed of straight and circumferential arc-shaped elements. The program, which already includes an input graphical interface and nodal calculations, was initially developed in Fortran, later transcribed into Python, and is based on the Finite Element Method. The main objective is the determination and plotting of the deflected shape and internal force diagrams, based on these differential equations, which include bending, torsion and shear force, as well as vertical displacements, and in-plane rotations throughout the domain of the respective elements. Results are compared with those obtained from grillage software where arcs are simulated through many straight elements. Finally, the expressions will be integrated into the program, and the updated version (PAE-Grelhas 3.0) will be made available to the scientific community.