DOWNLOAD previous article 2. article - 2013/2next article Vedran Jagodnik, Gordan Jelenić
and Željko Arbanas

On the application of a mixed finite-element approach to beam-soil interaction

Abstract

In this paper the deformation of a Bernoulli beam resting on Winkler's soil is reviewed in terms of the mixed finite-element methodology. While the stiffness matrix of the Bernoulli beam problem utilizing the standard displacement-based approach, in which only the displacement field is interpolated, may be alternatively obtained using a mixed-type approach to the absolutely shear-stiff second-order Timoshenko beam (in which the rotation and shear-stress resultant fields are additionally interpolated), the two approaches lead to different Winkler-type soil-stiffness contributions. Furthermore, extending the mixed-type formalism to both of these elements by additionally interpolating the distributed soil-reaction field, the soil-stiffness contributions also differ. In this way four different elements are obtained, with one, two, three or four independently interpolated fields, in which the beam-stifness matrix is equal, but the soil-stiffness matrices are different. It is demonstrated that the displacement-based one-field element is the least convergent, while the mixed-type element with four interpolated fields is the most convergent.

Keywords

Bernoulli beam, Winkler soil, mixed finite-element method