Desarrollo de una aplicación computacional para el análisis de estructuras utilizando elementos finitos

Abstract

This project addresses the growing need for tools that enable the efficient and pedagogical resolution of complex structural problems, given the complexity of current commercial solutions. By facilitating the learning of the finite element method, it aims to promote an understanding of the fundamentals of structural analysis and their application to real-world problems. Additionally, it focuses on offering an interactive experience that fosters the development of skills for solving complex problems in both academic and professional settings. An application was designed using matrix calculation algorithms in Python, complemented by specialized libraries of this programming language to handle matrices, generate visualizations, and produce detailed reports. Validation was carried out through experimental tests and comparisons with specialized software, analyzing practical cases of bar structures, trusses, and frames. Simultaneously, bibliographic references were consulted to support the mathematical formulation and the design of the graphical interface, ensuring that users can understand and replicate the calculations performed by the program. The results obtained demonstrate that the application is capable of accurately calculating stiffness matrices, nodal displacements, and stress diagrams, maintaining a minimal difference compared to results generated by commercial tools. Furthermore, the application offers a unique pedagogical approach, explaining the internal processes of the FEM and providing detailed reports of the structural analysis. In conclusion, this proposal represents an accessible and educational alternative that integrates advanced calculations with an intuitive interface, contributing to both learning and professional practice in structural engineering.