Análisis estructural de pórticos por el método de elementos finitos apoyado con Python

Abstract

Structural Analysis is a fundamental discipline in civil engineering that allows for the evaluation of structural behavior under various types of loads, support conditions, and materials. Diverse tools and methods are used, such as the Conjugate Beam Method, Double Integration, Castigliano's Theorem, Finite Element Method, among others, to simulate and predict structural performance under different loads or events such as Live Loads, Dead Loads, Wind, Earthquakes, Rain, and others. The results help identifies critical zones, validate designs according to current standard, such as Colombia's NSR-10, and optimize structural properties to ensure safety and efficiency. The analysis includes experimental validation or comparisons with field data, demonstrating the correlation between theoretical models and real behavior. This approach contributes to the design of safer and more sustainable structures, aligned with current engineering challenges. The method used in this work is the Finite Element Method (FEM), as it is the most precise method for performing Structural Analysis today. However, FEM involves matrix operations that require significant time due to the size of stiffness matrices and the procedures involved in such operations. For this reason, modern software analyzes highly complex structures more quickly and efficiently by applying this method. Nevertheless, most of these software tools are so expensive that, in some cases, their licensing exceeds personal budgets, and often, the underlying functionality of these tools is not fully understood. Given the above, this work aims to use Object-Oriented Programming (OOP) to perform structural analysis of two-dimensional tall frames by developing a desktop application using Python, a programming language with syntax that is easier to understand compared to other languages. To achieve this, an initial algorithm had to be implemented to apply the Finite Element Method, specifically the Stiffness Method, through a flowchart detailing the procedure for this type of analysis. This process was then translated into code to be implemented in an interpreter, which will generate the aforementioned application. Once the application has been created, the results obtained will be compared with those generated by one of the most widely used commercial software tools on the market, such as SAP2000. This comparison will verify the application's accuracy and the margin of error relative to these software tools, with the expectation that this error will be as close to zero as possible.