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The time-dependent boundary element method formulation applied to dynamic analysis of Euler-Bernoulli beams: the linear \(\theta\) method. (English) Zbl 1403.74222

Summary: 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 \(\theta\) 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 this article, which contain the four usual types of beams under continuously distributed and concentrated loadings.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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