On Application of the Exact Theory of Elastic Beams

Sanchez, Ph.; Simmonds, J. G.

doi:10.1007/0-306-46954-5_12

Cited by 7 publications

(6 citation statements)

References 8 publications

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“…It is valid for anisotropic materials, heterogeneous and axially piecewise constant cross-sections, arbitrary loadings, and any shape ratios. The first implementations of this theory (Ladev eze et al, 2001;Sanchez, 2001;El Fatmi and Zenzri, 2002) confirmed and illustrated its pertinence for the analysis of any elastic beams, and particularly composite ones. The use of composite beams is now a real trend in many engineering applications.…”

Section: Introductionmentioning

confidence: 76%

A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams

Fatmi

Zenzri

2004

International Journal of Solids and Structures

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Section: Introductionmentioning

confidence: 76%

A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams

Fatmi

Zenzri

2004

International Journal of Solids and Structures

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“…(1) was used for free vibration results by Taweel et al (2000). There is a rather extensive extant literature on finite element analyses of Saint-Venant's flexure, viz., Mason and Herrmann (1968), Tolf (1985), Wörndle (1982), Giavotto et al (1983), Kosmatka and Dong (1991), Schramm et al (1994), Popescu and Hodges (2000), Gruttmann and Wagner (2001), Ladevéze et al (2001), El Fatmi and Zenzri (2002, 2004), and El Fatmi (2007a. The SAFE method was preferred, because of its ease in displaying displacement results.…”

Section: Introductionmentioning

confidence: 94%

Much ado about shear correction factors in Timoshenko beam theory

Dong

Alpdogan²,

Taciroğlu

2010

International Journal of Solids and Structures

132

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a b s t r a c tMany shear correction factors have appeared since the inception of Timoshenko beam theory in 1921. While rational bases for them have been offered, there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application. Herein, three-dimensional static and dynamic information and results for a beam of general (both symmetric and non-symmetric) cross-section are brought to bear on these issues. Only homogeneous, isotropic beams are considered. Semi-analytical finite element (SAFE) computer codes provide static and dynamic response data for our purposes. Greater clarification of issues relating to the bases for shear correction factors can be seen. Also, comparisons of numerical results with Timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary (Bernoulli-Euler) theory.An issue concerning principal shear axes arose in the definition of shear correction factors for non-symmetric cross-sections. In this method, expressions for the shear energies of two transverse forces applied on the cross-section by beam and three-dimensional elasticity theories are equated to determine the shear correction factors. This led to the necessity for principal shear axes. We will argue against this concept and show that when two forces are applied simultaneously to a cross-section, it leads to an inconsistency. Only one force should be used at a time, and two sets of calculations are needed to establish the shear correction factors for a non-symmetrical cross-section.

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“…However, it is worth to note that this beam theory, which is completely founded on the knowledge of the Saint Venant solution, may be extended to study the case of composite cross-section for which, as mentioned in the introduction, the warping effects can be more critical. Indeed, an extended Saint Venant solution has been established for composite beam (Ladevèze and Simmonds, 1998), and its computation is already possible with the numerical method developed by Ladevèze et al (2001) or El Fatmi and Zenzri (2002, 2004. divr ¼ 0 in X eðnÞ ¼ 1 2 ðr t n þ rnÞ in X r ¼ K : eðnÞ in X r Á n ¼ 0 on S lat 9 > > > = > > > ;…”

Section: Simplified Non-uniform Warping Theorymentioning

confidence: 99%

“…For the numerical results presented in part II (El Fatmi and Zenzri, 2002), this is achieved by using the software tool designated by SECOPE which is available within the finite elements code CASTEM (Le Fichoux, 1998). SECOPE has been developed conforming to the numerical method proposed by El Fatmi and Zenzri (2002,2004) for the computation of the 3D Saint Venant solution within the framework of the exact beam theory (Ladevèze and Simmonds, 1998;Ladevèze et al, 2001).…”

Section: Nomenclaturementioning

confidence: 99%

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Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory

Fatmi

2007

International Journal of Solids and Structures

107

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This two-part contribution presents a beam theory with a non-uniform warping including the effects of torsion and shear forces, and valid for any homogeneous cross-section made of isotropic elastic material. Part I is devoted to the theoretical developments and part II discusses analytical and numerical results obtained for torsion and shear-bending of cantilever beams made of different kinds of cross-section. The theory is based on a kinematics assuming that the cross-section maintains its shape and including three independent warping parameters associated to the three warping functions corresponding to torsion and shear forces. Starting from this displacement model and using the principle of virtual work, the corresponding beam theory is derived. For this theory, closed-form results are obtained for the cross-sectional constants and the three-dimensional expressions of the normal and shear stresses. Comparison with classical beam theories is carried out and additional effects due to the non-uniformity of the warping are highlighted. In particular, the contributions of primary and secondary internal forces and the effect of the non-symmetry of the cross-section on the structural behavior of the beam are specified. Simplified versions of this theory, wherein the number of degrees of freedom is reduced, are also presented. The analytical and numerical analyzes presented in part II give responses on the quality of this non-uniform beam theory and indicate also when its simplified versions could be applied.

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On Application of the Exact Theory of Elastic Beams

Cited by 7 publications

References 8 publications

A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams

A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams

Much ado about shear correction factors in Timoshenko beam theory

Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory

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