Simple Mechanical Model of Curved Beams by a 3D Approach

Starting from three-dimensional (3D) continuum mechanics, a simple one-dimensional model aimed at analyzing the whole static behavior of nonhomogeneous curved beams is proposed. The kinematics is described by four one-dimensional (unknown) functions representing radial, tangential, and out-of-plane displacements of the beam axis, which are due to flexures and extension, and the twist of the cross section due to torsion. The flexural and axial displacements fit with the classical Euler–Bernoulli beam theory of straight beams, and nonuniform torsion is also considered. The relevant elastogeometric parameters have been determined, and the system of governing equilibrium equations is obtained by means of the principle of minimum potential energy. Finally, the general theory is illustrated with examples.