THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULA RPLATE（I）

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P-FEMOL ANALYSIS OF PLATE BENDING PROBLEMS

In this paper,the p-version of the finite element method of lines(FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presentedand a class of p-FEMOL elements with polynomial degrees as high as nine isdeveloped.Numerical examples given in this paper show tremendous performance ofthe present method;namely,rapid convergence rate,high accuracy for bothdisplacements and stress resultants,removal of shear-locking trouble,capability ofdealing with difficult problems such as the boundary layer behavior near a free edgeand stress concentration around a hole.     

PERTURBATION METHOD FOR THIN PLATE BENDING PROBLEMS

In this paper.problems of bending of a thin plateunder the action of in-plane forces are studied by us-ing the method of multiple scales.     

UNSYMMETRICAL BENDING PROBLEMS FOR THE ANNULAR AND CIRCULAR THIN PLATES UNDER VARIOUS SUPPORTING CONDITIONS(Ⅰ)

In this paper we consider the nonlinear and unsymmetricalbendings of annular and circular thin plates under varioussupports.The uniformly valid asymptotic solutions havebeen derived by means of the perturbation method presentedin[7].     

KANTOROVICH SOLUTION FOR THE PROBLEM OF BENDING OF A LADDER PLATE

ctangular plate in bending, this paper deals with the solutions for the ladder plate with various boundary conditions. The deflection of the plate is expressed in a first-order displacement function ω(x,y)=μ(x,y)υ(y) where the μ(x,y) in x direction is the generalized beam function. By making use of the principle of least potential energy, the variable coefficients differential equations for v(y) may be established. By solvingis, these differential euqations and making use of the boundary conditions, the accurate solutions of v(y) in y direction may be obtained. Then the displacement function w(x,y) is the solution for the problem of the bending of the ladder plate with a better degree of approximation.     

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION AND THE ASYMPTOTICS OF SOLUTIONS(Ⅱ)

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APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION ANDTHE ASYMPTOTICS OF SOLUTIONS (Ⅰ)

I.IntroductionThestudyorbendingproblemsforcircularthinplatewithlargedeflectionhasalonghistoryandalotofresearchhasbeendoned~41.Especially,aftertheappearanceoftheChienWeizangmethodthatusestheratioofthecenterdeflectiontothethicknessofP-l'Llteasperturbationparameter,theapplicationofperturbationmethodstothestudyofthebendingproblemsofplatesandshellsbecomesmoreandmorepopular,owingtothet'actthatonlybyusingregularperturbationmethodonecanfinditssufficientlycorrectsolution.OneweaknessinChienWeizangmet…     

THE SYMMETRICAL BENDING OF AN ELASTIC CIRCULAR PLATE SUPPORTED AT KINTERNAL POINTS

This paper treats the symmetrical bending of a uniformly loaded circular plate supported at k internal points.The boundary displacement and slope are expanded in Fourier seriesr.The method proposed by[6]is applied.As both the governing differential equation and boundary conditions are satisfied exactly,we therefore obtain the analytic expression of the transverse deflectional equation of the circular plate.This is an easy and effective methed.     

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION AND THE ASYMPTOTICS OF SOLUTIONS(Ⅱ)

This paper is a continuation of part (Ⅰ), on the asymptotics behaviors of the series solutions investigated in (Ⅰ). The remainder terms of the series solutions are estimated by the maximum norm.     

THE UNSYMMETRICAL BENDING OF CANTILEVER RECTANGULAR PLATES

This paper discusses the problems of the unsymmetrical bending of cantileverrectangular plates under various loads by the energy method.We illustrate numerouscalculating examples such as the plates which are subjected by the concentrated forces orconcentrated couples unsymmetrically on free sides and corner points and by a uniformly ornonuniformly distributed loads unsymmetrically on free edges and so forth.     

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

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

Bending problems of non-homogeneous cylindrical orthotropic circular plate

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The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

（黄家寅）（秦圣立）ＴＨＥＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＢＥＮＤＩＮＧＦＯＲＯＲＴＨＯＴＲＯＰＩＣＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳ￥ＨｕａｎｇＪｉａｙｉｎ;ＱｉｎＳｈｅｎｇｌｉ（ＱｕｆｕＮｏｒｍａｌＵｎ...     

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.     

An investigation of meterial properties of non-homogeneous cylindrically orthotropic 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_r E_a and v_θr which are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.     

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.     

Axisymmetric bending for thick laminated circular plate under a concentrated load

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New solution system for circular sector plate bending and its application

Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solutions for the circular sector plate. The results show that the new method is effective. Project supported by National Natural Science Foundation (No. 19732020) and the Doctoral Research Foundation of China.     

An exact solution for the bending of point-supported orthotropic rectangular thin plates

A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse load are arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.