Extension of the Bending-Gradient theory to thick plates buckling: application to Cross Laminated Timber walls

Université Paris-Est, Laboratoire Navier UMR 8205 CNRS, ENPC, IFSTTAR, 6-8 Avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée, France
olivier.perret@enpc.fr

Received: 1 March 2016
Accepted: 22 June 2016

Abstract

In this paper, the resolution of the linear buckling problem is presented using the Bending-Gradient theory which is an extension of the Reissner’s 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 walls which are thick and highly anisotropic laminates. It is observed from reference results that critical buckling load and failure load are of the same order of magnitude. Buckling effects have then to be taken into account in the design of Cross Laminated Timber walls. It is then shown that for varying plate geometries, the Bending-Gradient theory predicts precisely the critical load of Cross Laminated Timber walls contrary to classical Kirchhoff and first order shear deformation theories. Moreover, it is demonstrated that the suggested projection of the Bending-Gradient on a Reissner’s model gives very accurate results. This model could then be used in a more extensive study on the buckling of Cross Laminated Timber walls with initial geometrical imperfections and on the effects of the long term behavior of wood.