Implementation of Gaussian quadrature in Python program for grillages with curved elements

Resumo

This paper demonstrates the development of a Python program for linear-elastic structural analysis of grillages featuring circumferential arc-shaped and regular straight elements subjected to concentrated and distributed loads. The algorithm is based on the Finite Element Method. The force method was employed to compute the flexibility matrix, followed by the determination of the stiffness matrix and load vectors through inversion. A Gauss-Legendre Quadrature was incorporated in order to have a better control on accuracy for displacements, rotations, forces and moments. Results were validated through comparisons with literature data and similar software where curved structures are simulated using numerous straight elements. It was demonstrated that the Python-based program yields results closer to the exact solution with simplified input data, highlighting the effectiveness of both programming language and Gauss quadrature technique in structural analysis.