LARGE DEFLECTION PROBLEM OF THIN ORTHOTROPIC CIRCULAR PLATE WITH VARIABLE THICKNESS UNDER UNIFORM PRESSURE

Basic equations for large deflection theory of thin orthotropic circular plate withvariable thickness are derived in this paper.The modified iteration method is adopted tosolve the large deflection problem of thin orthotropic circular plate with variable thicknessunder uniform pressure.Ifε=0 ,then the solution derived from the result in this papercoincides completely with the result given by J.Nowinski(using perturbation method)forsolving large deflection problem of thin orthotropic circular plate with constant thicknessunder uniform pressure.     

THE LARGE DEFLECTION PROBLEM OF CIRCULAR THIN PLATE WITH VARIABLE THICKNESS UNDER UNIFORMLY DISTRIBUTED LOADS

In this paper,to begin with,the large deflection equationof variable thickness circular plates is given.By using smallparameter method and revised iteration jointly a cubic approxi-mate solution is obtained.A characteristic is also given forcomparison with linear theory.     

A DISCUSSION ON“THE LARGE DEFLECTION PROBLEM OF CIRCULAR THIN PLATE WITH VARIABLE THICKNESS UNDER UNIFORMLY DISTRIBUTED LOADS”

“The large deflection problem of circular thin plate with variable thickness under uniformlydistributed loads”has been solved by using the small parameter method and modified iterationmethod jointly in the ref.[1].The solution of ref.[1]and its special results are correct.But,theprocedure in the ref.[1]is almost same as those of perturbation method in essence[2].The loadwas assumed to be     

A DISCUSSION ON“THE LARGE DEFLECTION PROBLEM OF CIRCULAR THIN PLATE WITH VARIABLE THICKNESS UNDER UNIFORMLY DISTRIBUTED LOADS”

"The large deflection problem of circular thin plate with variable thickness under uniformly distributed loads" has been solved by using the small parameter method and modified iteration method jointly in the ref.[1].The solution of the ref. [1] and its special results are procedure in the ref.     

THE LARGE DEFLECTION ON PROBLEM OF CIRCULAR PLATE ON ELASTIC FOUNDATION AND IN CONJUNCTION WITH LINEAR ELASTIC STRUCTURE

This paper deals with the axisymmetrical deformation of the circular plate in largedeflection,which is on elastic foundation and in conjunction with a certain linear elasticstructure.The governing integral equations are established by the method of mixedboundary condition I and the simplified form is given.The pertrubation method is used toobtain the solutions and an example of the composite structure made up of a circular plateand a cylindrical shell is presented.     

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 withvariable thickness,we solve the problem of circular plates with variable thicknesssubjected to combined loads under the boundary conditions of the clamped edges and getcomparatively more accurate second-order approximate analytical solution.If the resultsof 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 somecomparisons are made.The results of this paper are satisfactory.     

LARGE DEFLECTION OF CIRCULAR PLATE UNDER COMPOUND LOAD

By means of the perturbation method,this paperpresents an approximate solution for large deflec-tion of clamped circular plate under uniform pres-sure together with a concentrated load at the center.The special case of vanishing central deflection isalso discussed.In this paper,a load distributionfunction is introduced so as to make the compound.loads depend on a single load parameter,and averageangular deflection is used as the single displace-ment perturbation parameter.     

ON THE JUMPING PROBLEMS OF A CIRCULAR THIN PLATE WITH INITIAL DEFLECTION

In this paper,the jumping problems of a circular thin plate with initial defletion arestudied by using the method of two variables proposed by Jiang Fu-ru and the methodof the normal perturbation(in this paper (1.1), (1.2)).We obtain Nth-order uniformly validasymptotic expansion of the solution of this problem ((1.66), (1.67)).When the initialdeflection vanishes the solution of a circular thinplate with initial deflection is reduced tothe solution of the problems of the nonlinear bending of a circular thin plate.If the initialdeflection is largish and the signs of the initial deflection with the intensity of the transverseload are opposite,when the intensity of the transverse load reaches a certain value,thecircular thin plate with initial deflection should produce the jumping phenomenon.     

THE SOLUTION OF LARGE DEFLECTION PROBLEM OF THIN CIRCULAR PLATE BY THE METHOD OF COMPOSITE EXPANSION

In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky's membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.     

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ     

Large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure

Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure.     

Unsymmetrical nonlinear bending problem of circular thin plate with variable thickness

Introduction Manystructuralelements(pole,plate,shell)withunevenandvariablethicknessarewidely usedinallkindsofengineeringfields.Engineerscansavematerialswhentheydesignbecause theseelementshavebetteroptimizedshapeofstructuralfeature,butthisaddsdifficultytotheanalysisoftheirmechanicalcapability.Manypreviouspapers[1-4]havesolvedtheproblemof symmetricalaxis,butnobodyhassolvedtheunsymmetricalnonlineardeformationproblemof circularthinplatewithvariablethicknessandunsymmetricalaxisuptonow,afewworkonly …     

The problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness

I-Intr0ducti0nThebendingproblemofcircularthinplateisimriartantbothintheoryandinengineeringpractice,butbecausethebasicequationsoftheproblemsofnon-linearunsymmetricalbendingf0rcircularthinplate'arenonlineardifferentialequations,itisquitedifficulttoobtainana…     

Large deflection problem of a clamped elliptical plate subjected to uniform pressure

In this paper, the perturbation solution of large deflection problem of clamped elliptical plate subjected to uniform pressure is given on the basis of the perturbation solution of large deflection problem of similar clamped circular plate (1948), (1954). The analytical solution of this problem was obtained in 1957. However, due to social difficulties, these results have never been published. Nash and Cooley (1959) published a brief note of similar nature, in which only the case λ=a/b=2 is given. In this paper, the analytical solution is given in detail up to the 2nd approximation. The numerical solutions are given for various Poisson ratios v=0.25, 0.30, 0.35 and for various eccentricities λ=1, 2, 3, 4, 5, which can be used in the calculation of engineering designs.     

用能量法研究双模量大挠度圆板的轴对称弯曲

双模量圆板在外载荷作用下发生轴对称弯曲变形时,会形成各向同性的拉伸区和压缩区.此种情况下,可把双模量圆板看成两种各向同性材料组成的层合板,采用弹性理论建立了双模量圆板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量圆板的中性面位置.在此基础上,采用能量法研究了双模量大挠度圆板轴对称弯曲变形问题,将该方法计算结...     

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 properties 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 expressions of four analytic functions. Expanding the transverse load 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.     

Application of the modified method of multiple scales to solving the problem of a thin clamped circular plate of a very large deflection

In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.     

Basic equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness

Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction ( z-direction ), the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given; then introducing the dimensionless variables and three small parameters, the dimensionaless governing equations of the deflection function and stress function are given.     

Navier solution for the elastic equilibrium problems of anisotropic skew thin plate wite variable thickness in nonlinear theories

This paper discusses the elastic equilibrium problems of anisotropic skew thin plate ofvariable thickness simply supported on all four sides in nonlinear theories,and uses theNavier method to seek an approach to the problem,and to illustrate the solution with theexamples.In conclusion,the mention is made of the scope of application and theconvergency of the solution.     

Uniformly valid asymptotic solutions of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate of four clamped edges with variable thickness

By using “the method of modified two-variable”,“the method of mixing perturbation ”and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth- order for ε1 and Mth- order for ε2 of the deflection functions and stress function are obtained.