A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams

The purpose of this paper is to simplify the numerical implementation of the exact elastic beam theory in order to allow an inexpensive and large use of it. A finite element method is proposed for the computation of the beam operators involved in this theory. These operators are required for the calculation of the one-dimensional structural beam behavior and the three-dimensional Saint–Venant solution. The method is derived from a three-dimensional characterization of the beam operators and consists in solving seven particular elasticity problems defined on a longitudinal slice of beam. The computation is immediate when using standard three-dimensional elasticity softs that afford the quadratic 15-node triangular prism element or the 20-node rectangular prism element. The discretization is reduced since only one element is required in the longitudinal direction of the beam. The proposed method is applied to homogeneous and composite beams made of isotropic materials, and to symmetric and antisymmetric laminated beams made of transversely isotropic materials. Structural beam rigidities, elastic couplings, warpings, and three-dimensional stresses are provided and compared to available results. � 2003 Elsevier Ltd. All rights reserved.

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