Estudo de algoritmos de integração temporal na análise dinâmica de pórticos planos com o Método dos Elementos Finitos

Abstract

This work is based on studying Temporal Integration Algorithms applied to two-dimensional bodies subjected to dynamic, mechanical loading and their respective interactions. That is, to analyze the behavior of these bodies in both static and dynamic problems. For that, computational routines must be developed that uses the Finite Element Method (FEM) as a structural analysis tool and applies a certain Temporal Integration Algorithm. Thus, the numerical results of these codes should be compared with examples found in the specialized literature in order to validate the result of these codes. In summary, the work will have, respectively, the following steps: Develop a computer program in the FORTRAN language capable of solving linear static problems of two-dimensional structures using the Finite Element Method, implementing algorithms that allow this code to solve dynamic problems and, finally, compare the responses in order to highlight the effects of dynamics on structural behavior; And also compare and analyze the different types of Temporal Integration algorithms for solving dynamic problems. Therefore, through this study it was found that the implicit temporal integration algorithms, in relation to the explicit methods, present a great superiority, and these explicit methods need relatively shorter time intervals, to present the same results as the implicit algorithms.