Beamlike (Saint–Venant) solutions for fully anisotropic elastic tubes of arbitrary closed cross section

Ladevèze, Pierre; Sanchez, Ph.; Simmonds, J. G.

doi:10.1016/j.ijsolstr.2003.11.006

Cited by 41 publications

(20 citation statements)

References 7 publications

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“…Yoon and Lee (2014) have formulated the entire warping displacement field as a combination of the three basic warping functions (one free warping function and two interface warping functions). Ladéveze and Simmonds (1996), Ladéveze et al (2004), and Ladevze and Simmonds (1998) have built 3D solutions for beam problems by adding enrichment terms to the Saint Venant solution. In such a framework, the displacement field can be written as…”

Section: Warping Functionsmentioning

confidence: 99%

Recent developments on refined theories for beams with applications

Carrera

Pagani

Petrolo

et al. 2015

Mechanical Engineering Reviews

100

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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 ...

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Section: Warping Functionsmentioning

confidence: 99%

Recent developments on refined theories for beams with applications

Carrera

Pagani

Petrolo

et al. 2015

Mechanical Engineering Reviews

100

View full text Add to dashboard Cite

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“…. , 9 are constant constitutive coefficients. The equilibrium equations in the absence of assigned body loads are…”

Section: Cosserat Shellsmentioning

confidence: 99%

“…. , 9 for the Cosserat surface in terms of the elasticity constants that appear in the classical theory of shells. Different approaches to the theory of shells have been discussed in the book of Libai and Simmonds [22].…”

Section: Classical Shell Theory Viewpointmentioning

confidence: 99%

Minimum Energy Characterizations for the Solution of Saint-Venant's Problem in the Theory of Shells

Bîrsan¹

2005

J Elasticity

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The linear theory of Cosserat surfaces is employed to study Saint-Venant's problem for cylindrical shells of arbitrary cross-section. We prove minimum energy characterizations for the solution of the relaxed Saint-Venant's problem previously obtained. Then, we determine the global measures of strain appropriate to extension, bending, torsion and flexure for certain classes of solutions to the relaxed problem. (2000): 74K25, 74G05. Mathematics Subject Classifications

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“…Ould Larbi et al [21] recently developed a shear deformation beam theory based on neutral surface position for bending and free vibration analysis of functionally graded beams. 3D elasticity equations were reduced to a beam-like formulation by Ladevéze [22,23,24], obtaining a solution for high aspect-ratio thin-walled beams. Berdichevsky [25] proposed asymptotic type expansions based on variational methods.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of aerospace structures by means of refined beam theories

Pagani

Petrolo

Colonna

et al. 2015

Aerospace Science and Technology

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Please cite this article in press as: A. Pagani et al., Dynamic response of aerospace structures by means of refined beam theories, Aerosp. Sci. Technol. (2015), http://dx. AbstractThe present paper is devoted to the investigation of the dynamic response of typical aerospace structures subjected to different time-dependent loads. These analyses have been performed using the mode superposition method combined with refined one-dimensional models, which have been developed in the framework of the Carrera Unified Formulation (CUF). The Finite Element Method (FEM) and the principle of virtual displacements are used to compute the stiffness and mass matrices of these models. Using CUF, one has the great advantage to obtain these matrices in terms of fundamental nuclei, which depend neither on the adopted class of beam theory nor on the FEM approximation along the beam axis. In this paper, Taylor-like expan- sions (TE), Chebyshev expansion (CE) and Lagrange expansion (LE) have been employed inthe framework of CUF. In particular, the latter class of polynomials has been used to develop pure translational displacementbased refined beam models, which are referred to as Component Wise (CW). This approach allows to model each structural component as a 1D element. The dynamic response analysis has been carried out for several aerospace structures, including thin-walled, open section and reinforced thin-shells. The capabilities of the proposed models are demonstrated, since this formulation allows to detect shell-like behaviour with enhanced performances in terms of computational efforts.

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Beamlike (Saint–Venant) solutions for fully anisotropic elastic tubes of arbitrary closed cross section

Cited by 41 publications

References 7 publications

Recent developments on refined theories for beams with applications

Recent developments on refined theories for beams with applications

Minimum Energy Characterizations for the Solution of Saint-Venant's Problem in the Theory of Shells

Dynamic response of aerospace structures by means of refined beam theories

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