On the structural behavior and the Saint Venant solution in the exact beam theory: Application to laminated composite beams

Based on the exact beam theory, the paper focuses on the effective calculation of the characteristic operators involved in beamʹs structural behavior and Saint Venant solution. It is shown that these operators can be derived from the solutions of six characteristic beam elasticity problems. These solutions are determined by minimizing potential energy functionals which allow a finite element computation technique where only the cross-section has to be discretized. This computation technique is applied to typical symmetric laminated composite beams, and to antisymmetric ones. Structural beam rigidities and couplings, warpings, and 3D stresses (including interlaminar stresses and free edge-effects) are provided and compared to available results. The proposed computation technique appears as an accurate and easy tool allowing an effective use of the exact beam theory.