Search results for "Plate theory"
showing 10 items of 18 documents
A Multilayered Plate Theory with Transverse Shear and Normal Warping Functions
2016
A multilayered plate theory which takes into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear behaviour, the fifth is related to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho-Parmerter and (a modified version of) Beakou-Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal s…
A class of shear deformable isotropic elastic plates with parametrically variable warping shapes
2017
A homogeneous shear deformable isotropic elastic plate model is addressed in which the normal transverse fibers are allowed to rotate and to warp in a physically consistent manner specified by a fixed value of a real non-negative warping parameter ω. On letting ω vary continuously (at fixed load and boundary conditions), a continuous family of shear deformable plates Pω is generated, which spans from the Kirchhoff plate at the lower limit ω=0, to the Mindlin plate at the upper limit ω=∞; for ω=2, Pω identifies with the third-order Reddy plate. The boundary-value problem for the generic plate Pω is addressed in the case of quasi-static loads, for which a principle of minimum total potential …
A bending theory of thermoelastic diffusion plates based on Green-Naghdi theory
2017
Abstract This article is concerned with bending plate theory for thermoelastic diffusion materials under Green-Naghdi theory. First, we present the basic equations which characterize the bending of thin thermoelastic diffusion plates for type II and III models. The theory allows for the effect of transverse shear deformation without any shear correction factor, and permits the propagation of waves at a finite speed without energy dissipation for type II model and with energy dissipation for type III model. By the semigroup theory of linear operators, we prove the well-posedness of the both models and the asymptotic behavior of the solutions of type III model. For unbounded plate of type III…
The polar method as a tool for solving inverse problems of the classical laminated plate theory
2000
Publisher Summary Fiber reinforced laminates are widely used in modem applications. For these kinds of structures, the Classical Laminated Plate Theory and its various extensions provide efficient methods for theoretical analysis, that is, when the stacking sequence, the orientations, and the properties of the individual laminas are known. For design of laminates, a very limited number of rules are available. For stiffriess design, two are currently known and used in practical applications: the Werren and Norris rule to get membrane isotropy, and the symmetrical sequence rule to suppress stretching/bending coupling. This chapter deals with the resolution of inverse problems of the Classical…
Orthotropic plate dynamics by a novel meshfree method
2003
Publisher Summary This chapter deals with a novel meshfree method for the dynamic analysis of orthotropic plates under the Kirchhoff small deflection theory. The approach starts from a modified function whose stationarity conditions lead to the meshfree plate dynamic model through a discretization process—based on the use of orthotropic plate static fundamental solutions. The resolving system obtained is characterized by—frequency independent stiffness and mass matrices, which preserve the symmetry and definiteness properties of the continuum. Moreover, these operators are computed by boundary integrals of regular kernels. The method allows the application of standard numerical routines ava…
Advanced models for smart multilayered plates based on Reissner Mixed Variational Theorem
2017
In the present work, families of equivalent singe layer and layer-wise models for the static and free vibrations analysis of magneto-electro-elastic multilayered plates are developed. The models are defined in the framework of a unified formulation, which offers a systematic approach for generating refined plate theories through suitable expansions of the through-the-thickness components of the relevant fields, considering the expansion order as a free parameter. The key features of the developed formulation are: a) the condensation of the electric and magnetic description into the mechanical representation, based on the quasi-static electric-magnetic approximation, which allows to reduce t…
Assessment of the cortical bone thickness using ultrasonic guided waves: Modelling and in vitro study
2007
Determination of cortical bone thickness is warranted, e.g., for assessing the level of endosteal resorption in osteoporosis or other bone pathologies. We have shown previously that the velocity of the fundamental antisymmetric (or flexural) guided wave, measured for bone phantoms and bones in vitro, correlates with the cortical thickness significantly better than those by other axial ultrasound methods. In addition, we have introduced an inversion scheme based on guided wave theory, group velocity filtering and 2-D fast Fourier transform, for determination of cortical thickness from the measured velocity of guided waves. In this study, the method was validated for tubular structures by usi…
Nonlocal model for a magneto-electro-elastic nanoplate
2013
A mathematical model based on nonlocal third-order shear deformation plate theory has been developed to evaluate the mechanical and electromagnetic behavior of magneto-electro-elastic nanoplates. Two types of magneto-electro-elastic composites have been considered, all of them combination of Barium Titanate sheets, that represents the piezoelectric phase, and Cobalt Ferrite, that is the piezomagnetic component. Setting magneto-electric boundary conditions on each laminate, it has been possible to extrapolate and to analyze free vibrations frequencies for all considered plates, allowing to do objective assessments on what factors influence laminate modes and, especially, how these vary in th…
Large deflection of magneto-electro-elastic laminated plates
2014
Abstract A model for the large deflection analysis of magneto-electro-elastic laminated plates is derived. The first order shear deformation theory and the von Karman stress function approach are employed. A set of resolving partial differential equations involving kinematical variables and the stress function is obtained as a consequence of the preliminary condensation of the electro-magnetic state to the plate kinematics. A closed form solution for simply-supported plates is presented. Numerical results are carried out for plates consisting of piezoelectric BaTiO 3 and piezomagnetic CoFe 2 O 4 layers. These results show the influence of large deflections on the plate response and could be…
Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations
2014
Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functio…