Implementação de código computacional para análise dinâmica linear de treliças planas via método dos elementos finitos

Abstract

The development of materials with greater mechanical strength and refinements in the structural calculation allowed the design of more slender constructions and, consequently, more susceptible to vibrations. In these cases, it is necessary to evaluate the dynamic behavior and the safety of the structure subjected to dynamic loads. The Dynamic Analysis of Structures aims to evaluate both the serviceability limit state and the ultimate limit state of a structure subject to dynamic actions. Such analyzes are possible and feasible thanks to the advancement of computing, allowing the application of numerical solutions such as the Elements Method Finites, developed in the 1940s and improved in the following decades, being used in several areas of engineering and allowing complex solutions of problems with innumerable degrees of freedom. In this work it was proposed the development of a computational code using MATLAB Student R2021a software to linear dynamic analyze of free and forced vibrations undamped in structures of plane trusses through the Finite Element Method. The proposed methodology consisted of implement an algorithm to analyze three distinct plane trusses, one of which is subject to the free vibration, and the others requested to a forced vibration, where they were analyzed a dynamic loading of the bounce type and other exponential. The results obtained by the code implemented were compared with the results obtained by the ADINA Structures software version 9.6 (900 nodes) with student licence. From the analysis of the results, it was observed that the code developed produces results compatible with those obtained from the commercial software. Thus it is concluded that the program developed in this work presents satisfactory results.