IMPLEMENTATION OF COMPUTATIONAL ROUTINES IN PYTHON FOR NUMERICAL ANALYSIS OF DISPLACEMENTS IN PLATES USING THE FINITE DIFFERENCE METHOD

• DOI: https://doi.org/10.22533/at.ed.13176226240211

• Palavras-chave: Finite Difference Method; plate analysis; numerical methods; structural analysis; displacements; bending moments.

• Keywords: Finite Difference Method; plate analysis; numerical methods; structural analysis; displacements; bending moments.

• Abstract:

  The structural analysis of plates is an important topic in civil engineering, as it allows us to understand how these structures deform and how internal stresses are distributed when subjected to different loads. However, in many cases, analytical solutions become complex or even unfeasible, especially when considering different geometries and boundary conditions. In this context, numerical methods become fundamental tools for solving these problems. This work presents the development and implementation of a computational routine for the analysis of displacements and bending moments in plates using the Finite Difference Method (FDM). The method basically consists of dividing the plate into a mesh of nodes and, based on this discretization, transforming the differential equations of the problem into a system of algebraic equations that can be solved numerically. From the displacements obtained, it is possible to calculate the bending moments in the principal directions of the plate. To verify the reliability of the developed algorithm, seven plate examples with different support conditions, dimensions, and loading types were analyzed. The numerical results were compared with analytical solutions available in the classical literature and with results obtained using structural analysis software. In general, good agreement was observed between the results, with relatively small errors that are acceptable for engineering applications. It was also observed that the accuracy of the results is directly related to the refinement of the mesh used: the smaller the discretization step, the greater the accuracy, although this implies longer processing time. Nevertheless, the algorithm demonstrated good performance and the ability to analyze different geometric configurations of plates. Thus, it is concluded that the developed computational routine proves to be an efficient tool for the numerical analysis of plates, contributing both to practical applications and to the learning and understanding of numerical methods applied to structural engineering.