Finite Volume Based Formulations for the Analysis of Bernoulli and Timoshenko Beams

In this paper two finite volume based formulations for the bending analysis of beam type structures are presented. The first formulation, which is a mixed type one, deals with the analysis of Bernoulli beam in which shear deformations are neglected. The second formulation, displacement based formulation, concerns with the analysis of Timoshenko beam in which shear effects are included in the analysis. Capability of both formulations in terms of accurate predictions of displacement field is investigated in several test problems. The numerical results reveal that: the predictions of both approaches show monotonic convergence to the analytical solutions, the shear locking is not observed in the analysis of thin Timoshenko beam models by using the second approach and finally in the tapered beam test problems of Bernoulli beam models the first method predicts more accurate results than the finite element counterpart with the same mesh.