Implementação computacional de uma formulação baseada no método dos elementos finitos para análises elástico-lineares de pórticos acoplados a elementos de rigidez axial

Abstract

This work aims to develop a computational approach for analyzing the linear elastic behavior of frames coupled with axial stiffness elements using the Finite Element Method (FEM). Structural discretization was performed with linear elements, adopting linear shape functions to approximate the displacement in the longitudinal direction of the element and cubic shape functions for the displacement in the transverse direction. Throughout the work, the deduction of the element stiffness matrix and the formulation of the equivalent force vector in local coordinates are presented. The computational implementation of the formulation was performed in MATLAB software. Finally, to validate the results obtained, three examples of frames coupled with axial stiffness elements are presented, whose results are compared and validated with those provided by Ftool software, demonstrating the effectiveness of the computational formulation with different types of loads and connections. The results demonstrate that the proposed approach is capable of accurately representing the structural behavior of frames coupled with axial stiffness elements, highlighting the consistency of the formulation and the reliability of the computational implementation developed. The study reinforces the applicability of FEM combined with MATLAB as a robust tool for structural analysis, contributing to the advancement of computational solutions for dimensioning and understanding. The results demonstrate that the proposed approach is capable of accurately representing the structural behavior of frames coupled with axial stiffness elements, highlighting the consistency of the formulation and the reliability of the computational implementation developed. The study reinforces the applicability of FEM combined with MATLAB as a robust tool for structural analysis, contributing to the advancement of computational solutions for the design and understanding of more complex structural systems.