A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

A new 3-node triangular hybrid displacement function Mindlin- Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses

A new approach to model nailed and screwed timber joints using the finite element method

International audienceThis paper presents a novel way to simulate the behaviour of nailed and screwed timber joints, using the finite element method. In order to avoid the detailed 3D modelling of nails (or screws) using solid elements, which is costly ineffective, the authors proposed and developed an approach based on beam-to-solid coupling where the nails (or screws) were modelled using one-dimensional beam element, while the assembled timber members were modelled using solid elements. To deal with the coupling between the degrees of freedom (d.o.f.) belonging to the screws and those belonging to the timber, the existing 2-node beam element has been modified involving in a 4-node beam element with only translational d.o.f. per node, leading in fact to a full compatibility with solid elements. Using the numerical approach developed, the linear elastic behaviour of a push-out shear test of a single shear timber-to-timber connection was successfully simulated

Non-linear finite element modelling of the structural behaviour of screwed timber-to-concrete composite connections

International audienceThis paper discusses a numerical approach, based on beam-to-solid modelling, for the simulation of the nonlinear structural behaviour of timber-to-concrete composite beams made with screws. The present contribution is an alternative to the detailed 3D modelling of the screws using solid elements and simplified approaches which use spring elements at each screw location. The screws were modelled using one-dimensional beam element, while the timber and concrete members were modelled, in detail, using 3D solid elements. To deal with the coupling between the common nodes, the 4-node beam element with only translational degrees of freedom (d.o.f.) per node, recently developed by the authors [1,2], has been extended to nonlinear analysis and employed to model the screws, since the existing 2-node beam element is obviously not fulfilled for screws in timber [2]. The effectiveness of the numerical model developed was verified experimentally showing several advantages by comparison to the existing models in the literature