Non-linear pre and post buckling behaviour of a Timoshenko beam
Résumé
Plane bending of a Timoshenko beam is derived using Cosserat formulation by the mean of a material curve and a moving director frame. Equilibrium relations are derived in the case of linear stress-strain relations and for both large strains and large displacements. Beam bending is controlled by magnitude and direction of a force and a bending moment. By a series of transformations, equilibrium equations are rearranged where pre and post buckling solutions are given in terms of Jacobi elliptic functions. From our knowledge this is the first attempt where such solution are derived by taking account a control of the bending moment.
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