DEVELOPMENT OF A PYTHON PROGRAM FOR ANALYSIS OF GRILLING STRUCTURES BY FINITE ELEMENT METHOD

Resumo

Abstract. Grid structures are commonly used in civil engineering systems such as floor slabs, bridge decks, and industrial platforms, where elements are subjected to bending in two orthogonal directions and torsion. The proper analysis of these systems requires numerical techniques capable of accurately capturing their structural behavior. This work presents the development of a computational tool in Python for the analysis of planar grid structures based on the Finite Element Method (FEM). The formulation considers structural elements with three degrees of freedom per node: two rotational and one translational, enabling the evaluation of torsional and flexural effects. The implementation involves the calculation of local stiffness matrices for each element, coordinate transformation to the global reference system, and the assembly of the global stiffness matrix. Once the structure’s geometry, boundary conditions, and loads are defined, the system of equations is solved to obtain nodal displacements. From these, internal forces such as bending moments, torsional moments, shear forces, and support reactions are derived. To verify the accuracy and reliability of the program, benchmark problems are used, and the results are compared with analytical solutions and well-established software. The main objective of this project is to offer a lightweight, open-source, and educationally oriented tool that can support engineers, students, and researchers in understanding and applying grid structure analysis, especially in academic environments where commercial solutions are not readily available.