Locking-free two-layer Timoshenko beam element with interlayer slip

A new locking-free strain-based finite element formulation for the numerical treatment of linear static analysis of two-layer planar composite beams with interlayer slip is proposed. In this formulation, the modified principle of virtual work is introduced as a basis for the finite element discretization. The linear kinematic equations are included into the principle by the procedure, similar to that of Lagrangian multipliers. A strain field vector remains the only unknown function to be interpolated in the finite element implementation of the principle. In contrast with some of the displacement-based and mixed finite element formulations of the composite beams with interlayer slip, the present formulation is completely locking-free. Hence, there are no shear and slip locking, poor convergence and stress oscillations in these finite elements. The generalization of the composite beam theory with the consideration of the Timoshenko beam theory for the individual component of a composite beam represents a substantial contribution in the field of analysis of non-slender composite beams with an interlayer slip. An extension of the present formulation to the non-linear material problems is straightforward. As only a few finite elements are needed to describe a composite beam with great precision, the new finite element formulations is perfectly suited for practical calculations. (c) 2007 Elsevier B.V. All rights reserved

Bending modes, elastic constants and mechanical stability of graphitic systems

The thermodynamic and mechanical properties of graphitic systems are strongly dependent on the shear elastic constant C44. Using state-of-the-art density functional calculations, we provide the first complete determination of their elastic constants and exfoliation energies. We show that stacking misorientations lead to a severe lowering of C44 of at least one order of magnitude. The lower exfoliation energy and the lower C44 (more bending modes) suggest that flakes with random stacking should be easier to exfoliate than the ones with perfect or rhombohedral stacking. We also predict ultralow friction behaviour in turbostratic graphitic systems.Comment: 7 pages, 6 figure

Analytical solution of two-layer beam taking into account interlayer slip and shear deformation

A mathematical model is proposed and its analytical solution derived for the analysis of the geometrically and materially linear two-layer beams with different material and geometric characteristics of an individual layer. The model takes into account the effect of the transverse shear deformation on displacements in each layer. The analytical study is carried out to evaluate the influence of the transverse shear deformation on the static and kinematic quantities. We study a simply supported two-layer planar beam subjected to the uniformly distributed load. Parametric studies have been performed to investigate the influence of shear by varying material and geometric parameters, such as interlayer slip modulus (K), flexural-to-shear moduli ratios (E/G) and span-to-depth ratios (L/h). The comparison of the results for vertical deflections shows that shear deformations are more important for high slip modulus, for ``short'' beams with small L/h ratios, and beams with high E/G ratios. In these cases, the effect of the shear deformations becomes significant and has to be addressed in design. It also becomes apparent that models, which consider the partial interaction between the layers, should be employed if beams have very flexible connections

Influence of temperature on post-breakage behaviour of laminated glass beams: experimental approach

The assessment of the post-breakage performances of laminated glass elements used in construction need to take into account the sensitivity to the temperature of the mechanical behaviour and properties of the product, in particular of the interlayer material. A general problem statement and an overview of different experimental approaches are firstly presented. Then results of specific orientation tests on pre-cracked laminated glass beams with a stiff interlayer of DuPont carried at three different temperatures (23, 45 and 60°C) are presented and commented. A comparison of the mechanical behaviour at the different temperatures is done, aiming to give a comprehensive order of magnitude of the sensitivity to temperature of the post-breakage behaviour observed during the tests

Fire analysis of timber composite beams with interlayer slip

The purpose of this paper is to model the behaviour of timber composite beams with interlayer slip, when simultaneously exposed to static loading and fire. A transient moisture-thermal state of a timber beam is analysed by the Luikov equations, and mechanical behaviour of timber composite beam is modelled by Reissner's kinematic equations. The model can handle layers of different materials. Material properties are functions of temperature. The thermal model is validated against the experimental data presented in the literature. Generally, the model provides excellent agreement with the experimental data. It is shown that the material properties of timber play an important role in the fire resistance analysis of timber structures when exposed to fire

Effects of intra- and inter-laminar resin content on the mechanical properties of toughened composite materials

Composite materials having multiphase toughened matrix systems and laminate architectures characterized by resin-rich interlaminar layers (RIL) have been the subject of much recent attention. Such materials are likely to find applications in thick compressively loaded structures such as the keel area of commercial aircraft fuselages. The effects of resin content and its interlaminar and intralaminar distribution on mechanical properties were investigated with test and analysis of two carbon-epoxy systems. The RIL was found to reduce the in situ strengthening effect for matrix cracking in laminates. Mode 2 fracture toughness was found to increase with increasing RIL thickness over the range investigated, and Mode 1 interlaminar toughness was negligibly affected. Compressive failure strains were found to increase with increasing resin content for specimens having no damage, holes, and impact damage. Analytical tools for predicting matrix cracking of off-axis plies and damage tolerance in compression after impact (CAI) were successfully applied to materials with RIL