Hinge joints in curved and straight elements of PAE-Grelhas 2.0

Resumo

This paper presents the development of a Python program for the linear-elastic analysis of grillage structures composed of circumferential arc-shaped and straight elements, subjected to concentrated and distributed loads, with the addition of hinge joint connections. This work represents an upgrade to the Finite Element-based program PAE-Grelhas 2.0, which previously relied exclusively on fixed-end elements. The implementation is based on the Force Method, allowing for the computation of the flexibility matrix; its inversion yields the stiffness matrix, with the code adapted to account for the specific conditions introduced by hinge joints in each bar. For curved elements, accuracy is ensured through the use of Gauss-Legendre Quadrature, applying an appropriate number of points for effective numerical approximation. The results are validated through comparisons with examples from the literature and additional cases developed by the authors, calculated using the Virtual Work Method.