DIFFERENTIAL QUADRATURE FOR AXISYMMETRIC GEOMETRICALLY NONLINEAR ANALYSIS OF CIRCULAR PLATES

New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.

A FURTHER STUDY OF THE THEORY OF ELASTIC CIRCULAR PLATES WITH NON－KIRCHHOFF－LOVE ASSUMPTIONS

Based on the general theory of elastic plates which abandons Kirchhoff-Loveassunption in the classical theory. this paper establishes a first order approximationtheory of elastic circular plates with non-Kirchhoff-Love assumption, and presents ananalytic solution to the axisymmetric problem of elastic circular plates with clampedboundary under uniformly distributed load. By comparing with the classical solution ofthe thin circular plates, it is verified that the new solution is closer to the experimentresults than the classical solution. By virtue of the new theory. the influence of thediameter-to=thickness ratio upon the precision of the classical theory is examined.

LARGE DEFLECTION PROBLEM OF CIRCULAR PLATES WITH VARIABLE THICKNESS UNDER THE ACTION OF COMBINED LOADS

By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF A PRIMARY RESONANCE OF A THREE CIRCULAR PLATES TORSION VIBRATION SYSTEM

The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurcation equation of the steady state response is obtained and its singularity analysis is given. The results of theoretical analysis are shown to be in good agreement with experimental ones.

VIBRATION PROBLEMS OF FLEXIBLE CIRCULAR PLATES WITH INITIAL DEFLECTION

In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for circular plates with initial deflection are obtained by use of Galerkin method and Lindstedt-Poincare perturbation method. The effect of initial deflection on the dynamic behavior of the flexible plates are also discussed.

A NEW TECHNIQUE FOR SOLVING NON-AXIALLY SYMMETRICALLARGE DEFLECTION OF ELASTIC AND THIN CIRCULAR PLATES

A new technique for solving large deflection problem of circular plates flexural non-axisymmetrically is proposed in this paper. The large deflection problem of a circular plate with built-in edge under non-axisymmetrical load is taken as an example to clarify the principle and procedure of the technique mentioned here. The technique given here can also be used to solve large deflection problem of circular plates under other non-axisymmetrical loads and boundary conditions.

Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.

EXACT SOLUTIONS FOR FREE VIBRATIONS OF TRANSVERSELY ISOTROPIC CIRCULAR PLATES

By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made.

EXACT SOLUTIONS FOR FREE VIBRATION OF TRANSVERSELY ISOTROPIC PIEZOELECTRIC CIRCULAR PLATES

By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.

On asymmetric bending of functionally graded solid circular plates

Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England＇s method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.

Free axisymmetric vibration of FGM circular plates

Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the Corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.

ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP

Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform transverse pressure and in-plane tensile force in the radial direction was analyzed. And an analytical solution is presented by using the perturbation method. The relation of surface adhesive energies with critical load to detach the contacted surfaces is obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigid bump size and contact radius on the critical load are discussed, and the relation of critical contact radius with the gap between the central rigid bump and the substrate for different adhesive energies is investigated.

Dynamic Plastic Response of Circular Plates Resting on Fluid with Finite Deformation

This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible and inviscous, and the plate is made of rigid-plastic material and simply supported along its edge. By using the method of the Hankel integral transformation, the nonuniform fluid resistance is derived as the plate and the fluid is coupled. Finally, an analytic solution for a circular plate under a medium load is obtained according to the equations of motion of the plate with finite deformation.

SHEAR EFFECTS ON LARGE AMPLITUDE FORCED VIBRATIONOF SYMMETRICALLY LAMINATED RECTILINEARLYORTHOTROPIC CIRCULAR PLATES

In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.

Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman＇s plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material （FGM） circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.

AN INVESTIGATION ON METERIAL PROPERTIESOF NON-HOMOGENEOUS CYLINDRICALLYORTHOTROPIC CIRCULAR PLATES

It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this paper is to verify the effect of radius on the materal properties According to the flat stress-strain relation the values of material properties E E andwhich are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.

THE GENERAL SOLUTION FOR AXIAL SYMMETRICAL BENDING OF NONHOMOGENEOUS CIRCULAR PLATES RESTING ON AN ELASTIC FOUNDATION

In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting, on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions. The uniform convergence of the solution is proved. This general solution can also he applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

FREE AXISYMMETRIC VIBRATION OF TRANSVERSELY ISOTROPIC LAMINATED CIRCULAR PLATES

Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact solutions are derived for two boundaryconditions, i.e. the rigid-slipping boundary and elastic simplysupported boundary. Finally, numerical results are presented and com-pared with those of FEM.

Free Vibration Analysis of Functionally Graded Plates with Multiple Circular and Non-circular Cutouts

Cutouts are inevitable in structures due to practical consideration.In order to investigate the free vibration of functionally graded plates with multiple circular and non-circular cutouts,finite element method is used.The volume fraction of the material constituents is assumed to follow a simple power law distribution.The parameters considered in this paper are as follows：cutout size,cutout location,number of cutouts and different boundary conditions.It should be mentioned that free vibration for FG plates（such as rectangular？skew？trapezoidal？circular plates） with multiple cutouts has not been studied yet and hence the results out coming from this paper may be used as bench marks for future works.