a b s t r a c tIn this paper, the linear buckling of a heterogeneous thick plate is studied using the Bending-Gradient theory which is an extension of the Reissner-Mindlin plate theory to the case of heterogeneous plates. Reference results are taken from a 3D numerical analysis using finite-elements and applied to Cross Laminated Timber panels which are thick and highly anisotropic laminates. First, it is shown that critical buckling loads are close to the material failure load which proves the necessity of a design model for the buckling of Cross Laminated Timber panels. Second, the soft simple support boundary condition is introduced as an opposition to the conventional hard simple support condition. It is shown that this distinction could be taken into account for designing timber structures depending on the accuracy needed. Third, it is observed that for varying plate geometries and arrangements, the Bending-Gradient theory predicts more precisely the critical load of CLT panels than classical lamination and first-order shear deformation theories. Finally, it is demonstrated that one of the suggested projections of the BendingGradient on a Reissner-Mindlin model gives very accurate results and could favorably allow the development of engineering recommendations for estimating properly transverse shear effects.
In this paper, a new methodology for the experimental determination of the CLT equivalent cross-layer shear elastic modulus is suggested using a wooden core sandwich beam with Carbon Fiber Reinforced Polymer skins under four-point bending. The stiffness contrast between the wooden layer and the CFRP skins ensures that the bending stiffness of the sandwich beam is mostly driven by the CFRP skins and the shear force stiffness of the beam is mostly driven by the shear modulus of the wooden core. Several measurements for the determination of the bending stiffness of the sandwich beam are investigated. Particularly, it is shown that the suggested measurement of the bending stiffness from rotation at beam ends presents more reliable results than common measurements of curvature. Then the results of a preliminary experimental study are presented using this set-up and promising results are obtained: the equivalent cross-layer shear modulus is measured at 124 MPa which lies well within literature.
The purpose of this work is to understand keyhole formation observed
during pulse Nd:YAG laser welding. An analysis of the evolution of the keyhole
geometry during a laser pulse was carried out by radiography x-ray flash, for
tantalum and a titanium alloy target. From the images obtained by x-ray
radiography, we determined the evolution of the geometry of the keyhole (depth
and width) during the laser pulse. The keyhole appears after a delay, and
increases linearly. We compare the measured creation delay with a value
obtained by an analytical thermal model. We present a calculation of the
energy deposit law by Fresnel absorption; the aim is to calculate the ray
trajectory in the keyhole to deduce the local absorption. The absorption
increases strongly during the formation of the keyhole, and tends towards a
limit value. Further, we compare the mean absorption during a pulse
with a measurement using a differential microcalorimeter.
In this paper, a closed-form approach is presented to estimate rapidly the equivalent stiffness of boards used in Cross Laminated Timber (CLT) panels from local orthotropic behavior at ring scale for varying sawing patterns.It is first assumed that narrow edges are glued. In this case, closed-form Reuss and Voigt bounds are derived for the equivalent layer behavior of CLT. An application to Norway spruce boards is presented and reveals that the cross-layer (rolling) shear behavior lies between 100 and 150 MPa with a careful selection of the board sawing pattern. Then, using finite element method, upper bounds for the cross-layer shear stiffness modulus of boards with and without glued edges are calculated and theoretical predictions are compared with recommendations and experimental data from the literature.Finally, it appears that these bounds remain relevant for CLT layer with unglued narrow edges for common aspect ratios.
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