Study on the effect of functionally graded coating layers on elastic deformation of thick circular plates: A closed-form elasticity solution

In this paper, a closed-form solution is presented for displacements and stresses in a thick homogeneous circular plate coated by functionally grade (FG) layers subjected to transverse loading. The solution procedure is in the framework of infinitesimal theory of elasticity. The elasticity modulus of the FG coating layers is assumed to vary exponentially through the thickness, whereas Poisson\u27s ratio remains constant. The solution procedure is on the basis of a Plevako\u27s representation, which reformulates the elasticity equations into some uncoupled fourth-order partial differential equations with respect to some potential functions. We explicitly obtain the analytical solution by writing the potential functions as Fourier-Bessel series expansions with respect to the radial coordinate. The solution is validated by comparing the numerical results with their counterparts reported in literature for the conventional system of thick plates coated by homogeneous layers, as well as the 3-D finite element analysis. A comparative study is presented between a thick circular plate coated by functionally graded layers and the one with homogeneous coating layers

Stability analysis of three-layer shear deformable partial composite columns

International audienceThis paper is focused on the effect of imperfect bonding and partial composite interaction between the sub-elements of a box-type column on the critical buckling loads. The box column is modelled as a symmetric three-layer composite structure with interlayer slips at the interfaces, based on the Engesser-Timoshenko theory with uniform shear deformation assumptions. Linear shear springs or slip modulus is considered at the interfaces to model the partial interaction between the sub-elements of the structure. The minimum total potential energy principle is utilized to obtain governing equations and boundary conditions. A direct analytical solution of the original governing equations is presented for obtaining exact buckling characteristic equation of the three-layer partial composite column with different end conditions including clamped-pinned end conditions. Also, the coupled equations are recast into an efficient uncoupled form and shown that there is a strong similarity with those for the two layer element. It is shown that the obtained formulae are converted to the known Euler column formulae when the slip modulus approaches infinity (i.e. perfect bonding) and no shear deformations in the sub-elements are considered. A differential shear Engesser-Timoshenko partial composite model is also employed and critical buckling loads, obtained from an inverse solution method, are compared to examine the validity and accuracy level of the uniform shear model. Comprehensive dimensionless numerical results are presented and discussed. (C) 2016 Elsevier Ltd. All rights reserved

A weak shear web model for deflection analysis of deep composite box-type beams

International audienceDeep box-type beams, consisting of framing members and sheathings, are sensitive to shear deformations and hence appropriate refined theories or complicated magnification factors are needed to be used to obtain accurate results. For sheathings or webs between the framing members that are weak in shear, additional shear deformations occur corresponding to the relative axial displacement between the framing members. These sandwich -type or partial interaction-type of in-plane shear behaviour between the framing members, needs to be taken into account, especially when the web shear stiffness is very low. The composite box-type beam treated here is composed of three framing members with sheathings on both sides. To incorporate effects of the sheathings shear deformations between the framing members on the deflection, the sheathings, here called web interlayers, are modelled as shear media with equivalent slip moduli corresponding to a partially interacting composite beam model. Governing equilibrium equations of the model are obtained using the minimum total potential energy principle and solved explicitly. The obtained results are compared with those based on different conventional beam theories and 3-D finite element (FE) simulations. It is shown that the model is capable of predicting accurately the deflection for a wide range of geometry and property parameters. It is demonstrated that the deflection of such deep box-type beams can be expressed as the summation of three different effects, namely bending deformations, conventional shear deformations in the framing members and sheathings, and additional in-plane shear deformations or shear slips of the weak web causing relative axial displacements between the framing members