Search results for "Bending of plates"
showing 10 items of 12 documents
Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid
2010
The out-of-plane instability of a moving plate, travelling between two rollers with constant velocity, is studied, taking into account the mutual interaction between the buckled plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the buckled plate (assumed cylindrical) is described by an integro-differential equation that includes the centrifugal force, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, and the bending force. The aerodynamic reaction is found analytically as a functional of the displacement. To find the critical divergence velocity of the moving plate and its corresponding buckling mode, an eigenvalue…
Dynamic Behaviour of an Axially Moving Plate Undergoing Small Cylindrical Deformation Submerged in Axially Flowing Ideal Fluid
2011
Abstract The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindri…
A symmetric Galerkin BEM for plate bending analysis
2009
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…
A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time
2004
The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency doma…
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 …
Analytical Refinement of Sandwich Plate Bending Problem Considering Local Effects-I
1999
Analytic expressions for local flexural characteristics and stresses of sandwich panels under loading by point forces have been found. A discrete-layer model for bending of a three-layer panel with a soft filler is proposed. Contractility of a normal in the model is deduced in terms of a difference between deflections of face layers. The accountability of transverse shear in the filler and the sheets is deduced on piecewise rotation of the normal. Equations of the model having four degrees of displacement freedom are of twelfth order. The specific features of the stress from point forces in cylindrical bending are considered using the operational Laplace method with the generalized Dirac f…
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…
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…
Variational approach to the mechanics of metal V-belt systems
2005
The mechanical behaviour of metal V-belt drives is strongly dependent on the elastic properties of both the belt and the pulley, which influence the belt penetration into the groove and the sliding on the pulley wall. The distribution of tension and penetration is quite different from the rubber belts, which may be dealt with in the assumption of perfectly rigid pulleys. The restoring effect of the centrifugal forces of the plate elements has also to be taken into account. The present analysis considers the combination of all those effects, choosing a three parameter deformation function to describe the plate bending and applying the principle of virtual work for the calculation of the unkn…
A NEW SYMMETRIC AND POSITIVE DEFINITE BOUNDARY ELEMENT FORMULATION FOR LATERAL VIBRATIONS OF PLATES
1997
Abstract A new symmetric and positive definite boundary element method in the time domain is presented for the dynamic analysis of thin elastic plates. The governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed. The functional is expressed in terms of the domain and boundary basic variables in plate bending, assumed to be independent of each other. In the discretized model the boundary variables are expressed by nodal values, whereas the internal displacement field is modelled by a superposition of static fundamental solutions. The equations of motion are deduced from the functional stationarity conditions and they cons…