The time-dependent boundary element method formulation applied to dynamic analysis of Euler-Bernoulli beams: the linear θ method

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 behavior of these quantities lead to unstable and inaccurate results. In the linear θ 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 this article, which contain the four usual types of beams under continuously distributed and concentrated loadings.