Unbonded contact between a circular plate and an elastic half-space

The paper concerns the unbonded contact between a thin circular plate of finite radius, governed by Kirchhof or Reissner theory, pressed by means of rotationally symmetric distributed load and its own weight against the surface of an elastic half-space. The contact is assumed frictionless and unbonded. A Hankel transform solution is used for the half-space and the plate deflection is found by inverting the plate equation. The coefficients in a power expansion are obtained by equating plate and half-space deflections at a number of points in the contact region. The variation of contact radius with plate radius, the radius of the uniformly applied load, and the relative stiffness of plate and foundation, is displayed in a series of figures.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

Bending of a cantilever rectangular plate loaded discontinuously

The cantilever rectangular plates discussed previously are all loaded continuously. For example, the load may be either a uniform or a concentrated load at the free ledge of the plate. Now we go a step further to deal with the case of a discontinuously loaded rectangular cantilever plate. The problem to be solved will involve a concentrated load at the center of the plate, as shown in Fig. 1. The method of solution used is the same as before.     

Axisymmetric contact problem for an elastic half-space and a circular cover plate

The contact interaction problem for a thin circular rigid cover plate and an elastic half-space loaded at infinity by a tensile force directed in parallel to the boundary of the half-space is considered. It is assumed that the cover plate is not resistant to bending deformations. The problem can be reduced to an integral equation of the first kind whose kernel has a logarithmic singularity. The equation is solved approximately by the Multhopp-Kalandia method. The resulting approximate solution is compared with the previously obtained asymptotic solution.     

Bending of a highly stretched plate containing an eccentrically plate-reinforced circular hole

In this paper, we consider the problem of finding the stress distribution in a highly stretched plate containing a circular hole that is eccentrically reinforced by thickening the plate, on one side only, in an annular region concentric with the hole. A solution of the nonlinear Kármán plate equations is obtained that is asymptotically valid for large membrane stresses. We show that, except for a narrow bending boundary layer in the neighbourhood of the boundary between the reinforced area and the rest of the plate, a state of plane stress prevails and the reinforced area undergoes a transverse deflection that brings its middle surface into the plane of the middle surface of the plate.     

Bending of a circular plate on a nonuniform elastic foundation in partial contact with the plate

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 162–169, January–February, 1989.     

Unbonded contact of a Mindlin plate on an elastic half-space

Summary In this paper a penalty formulation of the frictionless unilateral contact problem between an elastic rectangular plate and an elastic half-space is presented. In order to take into account the effects of the shear stress, the Mindlin plate model is analyzed. Some numerical results, obtained via finite elements, are given.

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Sommario In questo lavoro viene presentata una formulazione penalty del problema di contatto unilaterale senza attrito tra una piastra rettangolare elastica ed un semispazio elastico. Per la piastra si utilizza il modello di Mindlin, che consente di tener conto dell'effetto delle tensioni da taglio. Si forniscono alcuni risultati numerici ottenuti mediante discretizzazione agli elementi finiti.

     

Bending problems of non-homogeneous cylindrical orthotropic circular plate

ＢＥＮＤＩＮＧＰＲＯＢＬＥＭＳＯＦＮＯＮ－ＨＯＭＯＧＥＮＥＯＵＳＣＹＬＩＮＤＲＩＣＡＬＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＱｉｎＳｈｅｎｇ－ｌｉ（秦圣立）（ＱｕｆｕＮｏｒｍａｌＵｎｉｃｅｒｓｉｔｙ,Ｑｕｆｕ,Ｓｈａｎｄｏｎｇ）（Ｒｅｃｅｉ...     

The non-linear,dynamic response of an impulsively loaded circular plate with a central hole

A numerical method, called Direct Analysis, is described and applied to solve the problem of a plate undergoing a large impulsive load. For generality, an expanded, non-linear form of the equations of motion is used and shear correction and rotatory inertia are considered. The wave speeds are calculated from the non-linear equations and appropriate boundary conditions are applied so that reflected waves are included. The results for two types of step loading pulses are presented and compared with previously presented solutions. The response of the plate is discussed and conclusions as to the effects of the non-linearities are given.     

Forced axisymmetric vibrations of a thick circular rigidly fixed piezoceramic plate

A new closed-form solution of the axisymmetric nonstationary problem of elasticity is constructed for a circular thick piezoceramic plate whose outer cylindrical surface is rigidly fixed. The use of mixed boundary conditions for a curvilinear plane allows one to obtain sufficiently simple computational relations. The closed-form solution is constructed by the method of expansion in the vector eigenfunctions in the form of a structure algorithm of finite transformations. The obtained solutions are used to determine the natural vibration frequency, the stress-strain state of the considered element, and all characteristics of the induced electric field.