Desenvolvimento de ferramenta computacional para análise de estabilidade de treliças tridimensionais

Abstract

This work aims to develop a computational program for the linear stability analysis of structures modeled with three-dimensional truss elements based on the finite element method. The method is based on the discretization of the structural system into finite elements and the formulation of a system of algebraic equations using physical and variational concepts. To achieve this objective, the formulations relating to three-dimensional truss elements were first studied. Then, an algorithm was developed for the computational implementation of the truss element based on the concepts of matrix analysis of structures. Subsequently, an algorithm was implemented for performing the linear stability analysis, which consists of obtaining critical loads and instability modes via eigenvalue problem solving. After the computational implementation of the developed formulations, the results provided by the developed program were compared with those provided by the commercial software MASTAN2 using three examples to verify its functionality and accuracy. The results were considered satisfactory, with little or no divergence observed between the values.