THE TIME-DEPENDENT BOUNDARY ELEMENT METHOD FORMULATION APPLIED TO DYNAMIC ANALYSIS OF EULER-BERNOULLI BEAMS: THE LINEAR THETA METHOD
Raphael Fernando Scuciato1; José Antonio Marques Carrer1; Webe Mansur2
1 Universidade Federal do Paraná; 2 Universidade Federal do Rio de Janeiro
Baixar PDF doi:10.20906/CPS/CILAMCE2015-0233
Resumo
In this paper, the dynamic analysis of Euler-Bernoulli beams is performed with the Time-Dependent Boundary Element Method Formulation (TD-BEM). In the standard formulation, the variables related to the essential boundary conditions (displacement and rotation) are assumed to vary linearly in time, i.e., within each time interval, whereas the variables related to the natural boundary conditions (shear force and bending moment) are assumed to have a constant time variation. Different hypothesis concerning the time behaviour of these quantities lead to unstable and inaccurate results. In the linear theta method, on the other hand, all the variables are assumed to have a linear time variation and reliable results are achieved. These results can be seen in the examples presented in the article, which contains the four usual types of beams under the two more frequently found types of loading.
Palavras-chave: Time-dependent BEM; Dynamic analysis; Euler-Bernoulli beams