Recent developments on refined theories for beams with applications

Abstract

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.Key words : Beams, Refined theories, Structural analysis, Carrera Unified Formulation. Historical review of beam theories starting from Leonardo da VinciBeam models have been developed and exploited extensively over the last few decades for the structural analysis of slender bodies, such as columns, arches, blades, aircraft wings and bridges. The three-dimensional (3D) problem, in a beam model, is reduced to a set of one-dimensional (1D) variables, which only depend on the beam-axis coordinate. 1D structural elements, or beam elements, are simpler and computationally more efficient than 2D (plate/shell) or 3D (solid) elements. For instance, in a finite element (FE) scenario, beam models have no aspect ratio constraints. These features make beams still very appealing for the static and dynamic analyses of structures. Over the years, many beam models have been developed according to different approaches. The main contributions to the development of the beam theory are ...

Dynamic response of aerospace structures by means of refined beam theories

“…For a comprehensive review about classical and modern 1D modelling techniques, the reader is referred to [34].…”

“…Şimşek and Kocatürk [33] studied the free vibration of beams with different boundary conditions within the framework of the third-order shear deformation theory. For further details about modern models for beam structures and a comprehensive review, the reader is referred to [34].…”

Extension of MITC to higher‐order beam models and shear locking analysis for compact, thin‐walled, and composite structures

“…To overcome the limitations of the classical theories and to capture these effects, many enhanced 1D theories of structures have been proposed. A comprehensive review of the most remarkable contributions in the field can be found in Kapania and Raciti 32,33 and in Carrera et al 34 Most of these refined beam models are built based on some physical assumptions, which limit their use to particular classes of problems. In this context, the Carrera Unified Formulation (CUF) 35,36 was presented as a general structural formulation in which the order and the mathematical assumptions of the theory are introduced as input of the analysis.…”

Unified formulation of geometrically nonlinear refined beam theories

“…The analysis of more complicated problems, such as thin-walled beams subjected to coupling, local effects and other higher-order phenomena, may require the use of evolute and refined beam theories. A comprehensive discussion about higher-order beam models for the linear analysis of metallic structures can be found in the review paper by Carrera et al [30]. Moreover, some detailed expositions of the theories of thin-walled beams before the 1980s can be consulted in the reference texts from Vlasov [31], Bleich [32], Timoshenko and Gere [3] and Murray [33].…”