engleski

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

In this paper deformation of a Bernoulli beam resting on Winkler's soil is reviewed in light of the mixed finite-element methodology. While the stiffness matrix of the Bernoulli beam problem utilising 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 into both of these elements by additionally interpolating the distributed soil-reaction field, the soil-stiffness contributions differ additionally. In this way four different elements are obtained, with one, two, three or four independently interpolated fields, in which the beam stiffness 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.

Bernoulli beam; Winkler soil; mixed finite-element method

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