Exact buckling solution for two-layer Timoshenko beams with interlayer slip

Grognec, Philippe Le; Nguyen, Quang-Huy

doi:10.1016/j.ijsolstr.2011.09.020

Cited by 37 publications

(15 citation statements)

References 24 publications

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“…Kryžanowski et al [3] developed an analytical method to evaluate exact critical forces of two-layer composite columns. Grognec et al [4] used the Timoshenko beam model for buckling analysis of two-layer composite beams with partial interaction. He and Yang [5,6] presented the finite element method and higher order beam theory for buckling and dynamic problem of the two-layer composite beam.…”

Section: Introductionmentioning

confidence: 99%

A New Efficient Modified First‐Order Shear Model for Static Bending and Vibration Behaviors of Two‐Layer Composite Plate

Nam

Vinh

et al. 2019

Advances in Civil Engineering

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A two-layer (connected by stubs) partial composite plate is a structure with outstanding advantages which can be widely applied in many fields of engineering such as construction, transportation, and mechanical. However, studies are scarce in the past to investigate this type of structure. This paper is based on the new modified first-order shear deformation plate theory and finite element method to develop a new four-node plate element with nine degrees of freedom per node for static bending and vibration analysis of the two-layer composite plate. The numerical results are compared to published data for some special cases. The effects of some parameters such as the boundary condition, stiffness of the connector stub, height-to-width ratio, thickness-to-thickness ratio between two layers, and aspect ratio are also performed to investigate new numerical results of static bending and free vibration responses of this structure.

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Section: Introductionmentioning

confidence: 99%

A New Efficient Modified First‐Order Shear Model for Static Bending and Vibration Behaviors of Two‐Layer Composite Plate

Nam

Vinh

et al. 2019

Advances in Civil Engineering

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“…Lastly, the unit cell is subjected to a compressive displacement in the thickness direction (like in experiment), which leads to buckling. The critical displacement and the associated bifurcation mode will be derived from a 3D framework: the theory is developed using a total Lagrangian formulation where the different components of the model are initially seen as 3D bodies [10][11][12].…”

Section: Problem Definitionmentioning

confidence: 99%

Analytical, numerical and experimental study of the bifurcation and collapse behavior of a 3D reinforced sandwich structure under through-thickness compression

Lainé

Grognec

Comas-Cardona

et al. 2013

International Journal of Mechanical Sciences

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International audienceThree-dimensional reinforced sandwich structures are generally designed in order to provide optimal out-of-plane mechanical properties, beside traditional sandwiches which generally display satisfactory specific flexural properties but fatally insubstantial stiffnesses in the through-thickness direction. This paper deals with sandwich structures manufactured with polymeric foam core reinforced thanks to the Napco (R) technology (which is based on transverse needling) and specially investigates the compression behavior through the thickness direction. The compressive longitudinal moduli of such sandwiches are shown to be significantly improved in the presence of fibrous orthogonal reinforcements but the experimental estimations rather differ from analytical predictions that can be easily obtained using classical mixture laws. These discrepancies are mainly due to the buckling phenomenon, inherent in the geometry of the reinforcements, and the associated imperfection sensitivity. This work is thus devoted to the prediction of the critical loading of such a sandwich structure under through-thickness compression. A closed-form analytical expression is first derived from a general 3D elastic bifurcation analysis, then compared to finite element numerical solutions (obtained by both linearized buckling and incremental post-buckling analyses) for validation purposes, and finally confronted to experimental results. The buckling phenomenon is actually proved to be mainly responsible for the final collapse of the through-thickness reinforced sandwich

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“…Kirchhoff's theorem [Knops and Payne 1971] states that there is at most one solution to the Dirichlet boundary value problems in plane elasticity provided −∞ < ν < 1 2 , ν = −1, E = 0; in the traction boundary value problem there is uniqueness to within a rigid body displacement. In the considered case of null body forces and null boundary traction, since E > 0 and −1 < ν < 1 2 , the solution is unique and it consist in a null stress field, leading to a displacement field of the form…”

Section: 3mentioning

confidence: 99%

“…In a recent paper, Xu and Wu [2007] presented a very comprehensive approach for static, dynamic and buckling behavior of composite beams with partial interaction, accounting for the influence of rotary inertia and shear deformation. Approximate formulations of this kind are particularly important for studying the problem of buckling of composite columns (e.g., [Le Grognec et al 2012;Schnabl and Planinc 2011]), applicable to various materials, including lamellar wood [Cas et al 2007].…”

Section: Introductionmentioning

confidence: 99%

The effective thickness of laminated glass plates

Galuppi

Royer-Carfagni

2012

J. Mech. Mater. Struct.

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The flexural performance of laminated glass, a composite of two or more glass plies bonded together by polymeric interlayers, depends upon shear coupling between the glass components through the polymer. This effect is usually taken into account, in the design practice, through the definition of the effective thickness, i.e., the thickness of a monolith with equivalent bending properties in terms of stress and deflection. The traditional formulas à la Bennison-Wölfel are accurate only when the deformed bending shape of the plate is cylindrical and the plate response is similar to that of a beam under uniformly distributed load. Here, assuming approximating shape function for the deformation of laminated plates variously constrained at the edges, minimization of the corresponding strain energy furnishes new simple expressions for the effective thickness, which can be readily used in the design. Comparisons with accurate numerical simulations confirm the accuracy of the proposed simple method for laminated plates.

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Exact buckling solution for two-layer Timoshenko beams with interlayer slip

Cited by 37 publications

References 24 publications

A New Efficient Modified First‐Order Shear Model for Static Bending and Vibration Behaviors of Two‐Layer Composite Plate

A New Efficient Modified First‐Order Shear Model for Static Bending and Vibration Behaviors of Two‐Layer Composite Plate

Analytical, numerical and experimental study of the bifurcation and collapse behavior of a 3D reinforced sandwich structure under through-thickness compression

The effective thickness of laminated glass plates

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