Finite element method applied to plane frames

Resumo

The calculation of displacements and forces in structural models is of great relevance in structural design and provides information about the behavior of the structure under different loading conditions. Due to the complexity of real problems and the demands of the production sector, the solution of a structural model becomes unfeasible without the aid of computational tools. The direct stiffness method, also known as matrix structural analysis, can be considered as a particular case of the finite element method. This article presents a computer software for structural analysis of plane frames using the direct stiffness method. The software considers the presence of hinged nodes and elastic supports in the structural model. The computational code was developed in Python language. Excel files are used as data input and output. Results include information such as nodal displacements, internal forces, and support reactions in the structure. Variations of internal forces along the frame axis, i.e. internal force diagrams, are presented in graphical manner. The influence of considering rigid or elastic supports on the results is investigated in the article.