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Using metis model to solve the torsion problem of a prismatic bar

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This paper uses the metis displacement model to solve the torsion problem of a prismatic bar after transform this problem from 3D into 2.5D. The agreement of the results in this method with those in exact solution by the analytical method indicated the exactitude of this new model. | Vietnam Journal of Mechanics, VAST, Vol. 27, No. 3 (2005), pp. 149-157 USING M ETIS M ODEL TO SOLVE THE TORSION P ROBLEM OF A PRISMATIC BAR 1 NGUYEN TIEN DUONG, 2 NGUYEN DANG HUNG 1 Hanoi University of Technology, Vietnam 2 University of Lige, Belgium Abstract. Based on Lekhnitskiis elastici~y theory [l], the formulae of gener~lized plane strain state for the torsion problem of a prismatic bar are established. By this way, this problem in 3 dimensions (3D) is transformed into the problem in 2.5D. Metis models [3] constitute a bridge between the classical models in one field and the hybrid models in two fields. They have the advantage properties of two parents: the dual and monotonous properties of the pure models and the fast convergence of hybrid models. This paper uses the metis displacement model to solve the torsion problem of a prismatic bar after transform this problem from 3D into 2.5D. The agreement of the results in this method with those in exact solution by the analytical method indicated the exactitude of this new model. 1. INTRODUCTION The classical (pure displacement and pure equilibrium) models have the dual properties and monotonic convergence very interesting. But the convergence of these models is very slowly. The hybrid displacement and stress models permit the relaxation of the continuity conditions of unknown fields to make easier and more flexible the choice of the hypothesis and the numerical development of the finite elements. The convergence of these models is generally fast but non monotonous. The metis displacement and stress models have the advantage of two parents: the dual and monotonous properties of the pure models and the fast convergence of hybrid models. This paper uses the metis displacement model to solve the torsion problem ofa prismatic bar. This problem is transformed to the problem with geometry in 2D by using Lekhitskii 's elasticity theory. The metis displacement elements are used to calculat e the displacement and .