Finite element for non-stationary problems of viscoelastic orthotropic beams

The main aim of this work is to derive a finite beam element especially for solving of non-stationary problems of thin viscoelastic orthotropic beams. Presented approach combines the Timoshenko beam theory with the consideration of nonzero axial strain. Furthermore, the discrete Kelvin-Voight material model was employed for the description of beam viscoelastic material behaviour. The presented finite beam element was derived by means of the principle of virtual work. The beam deflection and the slope of the beam have been determined by the analytical and numerical (FEM) approach. These studies were made in detail on the simple supported beam subjected to the non-stationary transverse continuous loading described by the cosine function in space and by the Heaviside function in time domain. The study shows that beam deformations obtained by using derived finite element give a very good agreement with the analytical results