A finite element for static and dynamic analyses of cross-laminated timber floors

In this paper, a finite plate element for floorings consisting of a cross-laminated timber slab and a floating floor based on linear elastic behavior is presented. Both elemental mass and stiffness matrices are derived, allowing for static and dynamic analyses. For the cross-laminated timber plate, a higher order plate theory is employed, capturing the layer-wise zig-zag deformation of the plate and the stresses derived thereof accurately. It is augmented by an elastic layer representing the footfall sound insulation and an isotropic plate modeling the screed of a floating floor. In total, the finite element exhibits ten nodal degrees of freedom. Hence, larger structures can be analyzed efficiently, which is demonstrated by comparative finite element simulations with a commercial software package based on continuum elements.