Recent developments on refined theories for beams with applications

This paper is a review of the most influential approaches to developing beam models that have been proposed over the last few decades. Essentially, primary attention has been paid to isotropic structures while a few extensions to composites have been given for the sake of completeness. Classical models - Da Vinci, Euler-Bernoulli, and Timoshenko - are described first. All those approaches that are aimed at the improvement of classical theories are then presented by considering the following main techniques: shear correction factors, warping functions, Saint-Venant based solutions and decomposition methods, variational asymptotic methods, the Generalized Beam Theory and the Carrera Unified Formulation (CUF). Special attention has been paid to the latter by carrying out a detailed review of the applications of 1D CUF and by giving numerical examples of static, dynamic and aeroelastic problems. Deep and thin-walled structures have been considered for aerospace, mechanical and civil engineering applications. Furthermore, a brief overview of two recently introduced methods, namely the mixed axiomatic/asymptotic approach and the component-wise approach, has been provided together with numerical assessments. The review presented in this paper shows that the development of advanced beam models is still extremely appealing, due to the computational efficiency of beams compared to 2D and 3D structural models. Although most of the techniques that have recently been developed are focused on a given number of applications, 1D CUF offers the breakthrough advantage of being able to deal with a vast variety of structural problems with no need for ad hoc formulations, including problems that can notoriously be dealt with exclusively by means of 2D or 3D models, such as complete aircraft wings, civil engineering constructions, as well as multiscale and wave propagation analyses. Moreover, 1D CUF leads to a complete 3D geometrical and material modeling with no need of artificial reference axes/surfaces, reduced constitutive equations or homogenization techniques