A finite element for static and dynamic analyses of concrete-cross-laminated timber composite plates

In this paper, a finite plate element for composite plates consisting of a cross-laminated-timber panel with concrete topping is presented. A higher-order plate theory capable of capturing the zig-zag deformation in the timber layers is used. Taking into account partial interaction between concrete and timber, the finite plate element for this unsymmetric composite exhibits nine degrees of freedom per node. Elemental stiffness and mass matrices and load vector due to transverse loading are presented, assuming linear elastic material behavior. To verify the plate theory, outcomes of finite element simulations of a slab with mixed boundary conditions employing continuum elements in a commercial software package are used, which exhibits tenfold the number of degrees of freedom if compared to the proposed plate element model. An excellent agreement for static and dynamic simulations is obtained, both for low and high values of interlayer slip modulus. While displacements and normal strains are captured very accurately by the plate element, deviations are obtained for shear strains, however only incase of an unrealistically low degree of composite action. The first 15 natural frequencies and mode shapes from both simulations match excellently, again showing a tendency of slightly higher errors for weak interaction. Experimental results taken from literature are used to validate the plate theory. For a simply supported panel strip, results from modal analyses with two sets of interlayer slip moduli are compared. To validate the load-bearing capacity for these two setups, a simple non-linear model for the interface based on damage mechanics is implemented. Considering the uncertainties in the experimental data, a satisfactory overall match between experimental and numerical results is obtained.