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On the application of a mixed finite-element approach to beam-soil interaction
Vedran Jagodnik, Gordan Jelenić, Željko Arbanas, 2013, original scientific article

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
Published in DKUM: 14.06.2018; Views: 1592; Downloads: 76
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Analysis of cracked slender-beams on Winkler's foundation using a simplified computational model
Matjaž Skrinar, Boris Lutar, 2011, original scientific article

Abstract: This paper discusses the coupling of Winkler's soil model with a simplified computational model that is widely used for the calculation of transverse displacements in transversely cracked slender beams. The bending problem of a cracked beam embedded in Winkler's soil is addressed by means of an analytical approach. The solving of the corresponding differential equation solutions is studied in order to obtain exact analytical expressions for the transverse displacements of the simplified computational model. After the solutions for the displacements of the beam are obtained, the inner bending moment and the shear force distributions within the beam can be calculated, either by using known, established relationships from the Euler-Bernoulli beam theory or by implementing two mechanical equilibrium conditions. Numerical examples covering several load situations are briefly presented in order to support the discussed approach. The results obtained with the presented approach are then further compared with the values from huge 2D finite-element models, where a detailed description of the crack was achieved using the discrete approach. It is evident that any drastic difference in the computational effort is not reflected in the significant differences in the results between the models.
Keywords: beams with transverse cracks, simplified computational model, elastic foundation, Winkler's soil, transverse displacements, bending moment, shear forces
Published in DKUM: 01.06.2012; Views: 2262; Downloads: 58
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