Out-of-plane behaviour of partially composite or sandwich beams by exact and Finite Element Methods

Challamel, Noël; Bernard, Fabrice; Casandjian, Charles

doi:10.1016/j.tws.2010.03.005

Cited by 18 publications

(11 citation statements)

References 45 publications

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“…In other words, in the double symmetrical case, the tenth-order differential equation of the differential shear Timoshenko model is reduced into a sixth-order differential equation, a fact also observed for the out-of-plane behaviour of partial composite Euler-Bernoulli beams [31]. As a main conclusion, the uniform and differential shear models for partial composite beam-columns are equivalent for double symmetrical beam-columns with material symmetry and with symmetrical boundary conditions (conditions typical for layered wood beams with two identical sub-elements).…”

Section: Buckling Solution For a General Cross-sectionmentioning

confidence: 73%

“…It should be mentioned that the equivalence between the slip modulus of shear connectors and shear modulus of glue lines of finite thickness or sandwich-type of cores was first demonstrated by McCutcheon [28]. This equivalence is also discussed by Krawczyk et al [29] for the buckling problem of laminated beam-columns, by Girhammar et al [27] for the in-plane dynamics problem, and by Challamel [30] for the out-of-plane behaviour (see also [31]). With the substitution of K according to Eq.…”

Section: Shear Interlayer and Slip Modulusmentioning

confidence: 90%

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Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects

Challamel

Girhammar

2011

Engineering Structures

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This paper is focused on elastic stability problems of partial composite columns: the conditions for the axial load not to introduce any pre-bending effects in composite columns; the equivalence, similarities and differences between different sandwich and partial composite beam theories with and without the effect of shear, with and without the effect of axial extensibility, and also the effect of eccentric axial load application. The basic modelling of the composite beam-column uses the Euler-Bernoulli beam theory and a linear constitutive law for the slip. In the analysis of this reference model, a variational formulation is used in order to derive relevant boundary conditions. The specific loading associated with no prebending effects before buckling is geometrically characterized, leading to analytical buckling loads of the partial composite column. The equivalence between the Hoff theory for sandwich beam-columns, the composite action theory for beam-columns with interlayer slip and the corresponding Bickford-Reddy theory, is shown from the stability point of view. Special loading configurations including eccentric axial load applications and axial loading only on one of the sub-elements of the composite beam-column are investigated and the similarity of the behaviour to that of imperfect ordinary beam-columns is demonstrated. The effect of axial extensibility on kinematical relationships (according to the Reissner theory), is analytically quantified and compared to the classical solution of the problem. Finally, the effect of incorporating shear in the analysis of composite members using the Timoshenko theory is evaluated. By using a variational formulation, the buckling behaviour of partial composite columns is analysed with respect to both the Engesser and the Haringx theory. A simplified uniform shear theory (assuming equal shear deformations in each sub-element) for the partial composite beam-column is first presented, and then a refined differential shear theory (assuming individual shear deformations in each sub-element) is evaluated. The paper concludes with a discussion on this shear effect, the differences between the shear theories presented and when the shear effect can be neglected.

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Section: Buckling Solution For a General Cross-sectionmentioning

confidence: 73%

Section: Shear Interlayer and Slip Modulusmentioning

confidence: 90%

Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects

Challamel

Girhammar

2011

Engineering Structures

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“…Lagrangian interpolation shape functions were used. Based on Hermitian cubic and linear interpolation functions, Challamel et al (2010) developed 10-and 12-degree-of-freedom elements for the outof-plane behavior of partially composite or sandwich beams. Pham and Mohareb (2015b) developed a finite element formulation to capture the longitudinal-transverse response of a steel beam strengthened with a GFRP plate through an adhesive layer.…”

Section: Introductionmentioning

confidence: 99%

Shear deformable super-convergent finite element for steel beams strengthened with glass-fiber reinforced polymer (GFRP) plate

2019

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The present study investigates the flexural behaviour of steel beams strengthened by adhesively bonding a glass-fiber reinforced polymer (GFRP) plate to one of the flanges. The model captures shear deformation effects and partial interaction between the steel and GFRP owing to the relative flexibility of the adhesive. A general closed form solution is first developed for the governing coupled system of differential equations. The solution is then used to formulate mechanics-based shape functions and develop a finite element with superior convergence characteristics. The model is used to investigate the response of multi-span continuous beams, determine the strength gained by GFRP strengthening, and quantify shear deformation effects on the response of strengthened beams. A technique capturing partial interaction effects is devised to characterize the flexural strength of Class 3 strengthened beams. A classification limit for strengthened Class 3 sections is also proposed within the framework of the Canadian Standard CAN-CSA S16 (2014).

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“…The effect of a viscoelastic core on damped forced oscillations has been considered, for example, in [21,22]. The problem of the interlaminar slip between constitutive layers in the nonlinear free vibration has also been discussed, for example, in [23,24]. Apart from these nonlinear problems, the dynamics of sandwich panels with debonding are another computationally challenging task, even when small displacements and a material linearity are assumed.…”

Section: Introductionmentioning

confidence: 99%

Linear and Nonlinear Dynamic Analyses of Sandwich Panels with Face Sheet‐to‐Core Debonding

Burlayenko

2018

Shock and Vibration

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A survey of recent developments in the dynamic analysis of sandwich panels with face sheet-to-core debonding is presented. The finite element method within the ABAQUS6 code is utilized. The emphasis is directed to the procedures used to elaborate linear and nonlinear models and to predict dynamic response of the sandwich panels. Recently developed models are presented, which can be applied for structural health monitoring algorithms of real-scale sandwich panels. First, various popular theories of intact sandwich panels are briefly mentioned and a model is proposed to effectively analyse the modal dynamics of debonded and damaged (due to impact) sandwich panels. The influences of debonding size, form, and location and number of such damage incidents on the modal characteristics of sandwich panels are shown. For nonlinear analysis, models based on implicit and explicit time integration schemes are presented and dynamic responses gained with those models are discussed. Finally, questions related to debonding progression at the face sheet-core interface when dynamic loading continues with time are briefly highlighted.

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Out-of-plane behaviour of partially composite or sandwich beams by exact and Finite Element Methods

Cited by 18 publications

References 45 publications

Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects

Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects

Shear deformable super-convergent finite element for steel beams strengthened with glass-fiber reinforced polymer (GFRP) plate

Linear and Nonlinear Dynamic Analyses of Sandwich Panels with Face Sheet‐to‐Core Debonding

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