A refined beam theory with only displacement variables and defromable cross-section

This paper proposes several refined theories for the linear static analysis of beams made of orthotropic materials. A hierarchical scheme is obtained by extending Carrera’s Unified Formulation (CUF), which has previously been proposed for plates and shells, to beam structures. An N-order approximation via Mac Laurin’s polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formu-lation. Classical beam theories, such as Euler-Bernoulli’s and Timoshenko’s, are obtained as particular cases. According to CUF, the governing differential equations and the bound-ary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Poisson’s locking correction is assumed for the first-order and classi-cal models. Rectangular and I-shaped cross-sections are considered. Beams are considered to undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons to three-dimensional exact solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensiona