THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARYUNDER UNIFORM SURFACE LOADING (Ⅱ)

VI.SimplifiedAssumptionsforFirstorderSimplifiedApproximateTheory,TheirSystemofEquationsandRelatedBoundaryConditionsInthepreviouspaper['l,theassumptionsinfirstorderapproximationtheoryaree.=A, Alz,e,:=(h'/4-z')(S, S1z S:z:)(6.la,b)inwhich,theKirchhoffLoveas…     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅰ)

Based on the approximation theory adopting non-kirchhoff-Love assumption for three dimensional elastic plates with arbitrary shapes^[1],[2], the author derives a functional of generalized variation for three dimensional elastic circular plates, thereby obtains a set of differential equations and the relate boundary conditions to establish a first order approximation theory for elastic circular plate with fixed boundary and under uniform loading on one of its surface. The analytical solution of this problem will present in another paper.     

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARYUNDER UNIFORM SURFACE LOADING (Ⅱ)

Based upon the differential equations and their related boundary conditions given in the previous paper, this paper finds the analytical solution of non-Kirchhoff-Love theory for elastic circular plate with fixed boundary conditions under uniform surface loading. However, for the sake of saving computational work, the first order approximation theory can be further simplified in more rational bases.     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDERUNIFORM SURFACE LOADING (Ⅰ)

I.1ntroductionTheaxisymmetricproblemofthreedimensionalelasticcircularplatecanbetreatedasthreedimensionalaxisymmetricproblemofelasticity.Weconsideracircularplatewithauniformthicknessh,andsetupacircumferentialcoordinates(r,o)onitsmidd1esurfacewithabscissazp…     

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

ＬＡＲＧＥＤＥＦＬＥＣＴＩＯＮＰＲＯＢＬＥＭＯＦＴＨＩＮＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＯＮＥＬＡＳＴＩＣＦＯＵＮＤＡＴＩＯＮＷＩＴＨＶＡＲＩＡＢＬＥＴＨＩＣＫＮＥＳＳＵＮＤＥＲＵＮＩＦＯＲＭＰＲＥＳＳＵＲＥ（王嘉新）（刘杰）ＬＡＲＧ...     

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.     

THE ELASTO-PLASTIC STRAIN ANALYSIS OF NOTCHED PLATE UNDER CYCLIC LOADING—AN APPLICATION OF PLASTIC ANISOTROPIC HARDENING THEORY

In order to predict the life of engineering structures,it is necessary to investigate thestrain distribution in notched members.In general,the Bauschinger Effect of materialsunder cyclic loading is not negligible,and so the anisotropic hardening model has beensuggested.From the comparison between the calculated and experimental results in thispaper,we can see that even the linear kinematic hardening model is quite suitable for strainanalysis under cyclic loading.     

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.     

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

ＡＦＵＲＴＨＥＲＳＴＵＤＹＯＦＴＨＥＴＨＥＯＲＹＯＦＥＬＡＳＴＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＳＷＩＴＨＮＯＮ－ＫＩＲＣＨＨＯＦＦ－ＬＯＶＥＡＳＳＵＭＰＴＩＯＮＳＣｈｉｅｎＷｅｉ－ｚａｎｇ（钱伟长）ＲｕＸｕｅ－ｐｉｎｇ（茹学萍）（ＳｈａｎｇｈａｉＵｎｉ...     

THE ELASTO-PLASTIC STRAIN ANALYSIS OF NOTCHED PLATE UNDER CYCLIC LOADING—AN APPLICATION OF PLASTIC ANISOTROPIC HARDENING THEORY

In order to predict the life of engineering structures, it is necessary to investigate the strain distribution in notched members. In general, the Bauschinger Effect of materials under cyclic loading is not negligible, and so the anisotropic hardening model has been suggested. From the comparison between the calculated and experimental results in this paper, we can see that even the linear kinematic hardening model is quite suitable for strain analysis under cyclic loading.     

A BOUNDARY LAYER THEORY FOR THE BUCKLING OF THIN CYLINDRICAL SHELLS UNDER EXTERNAL PRESSURE

Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref [14]. the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical rcsuhs, for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.     

AN ACCURATE SOLUTION FOR THE SURFACE OF ELASTIC LAYER UNDER NORMAL CONCENTRATED LOAD ACTING ON A RIGID HORIZONTAL BASE

On the basis of ref.,this paper deduces an accurate solution for the surface ofelastic layer under normal concentrated load acting on a rigidhorizontal base,andgives numerical results, which suit civil engineers for reference.     

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     

BOUNDARY ELEMENT METHOD FOR SOLVING DYNAMICALRESPONSE OF VISCOELASTIC THIN PLATE(II)──-THEORETICAL ANALYSIS

I.IntroductionInpaper[l],thedynamicresponseoftheviscoelasticthinplate-onrectangledomainisdiscussedbytheusingofthetwokindsofapproximatefundamentalsolutionsandthecorrespondingboundaryelementmethod(BEM)inLaplacespace.Theanalysisofthenumericalexamplesshowsthatonlywhenthetruncatednumberkintheapproximatefundamentalsolutionandthemaximummeshsizehsatisfycertainrelation,itcouldbeguaranteedthattheapproximatesolutionhaveenoughaccuracy.Inpresentpaper,theerrorestimationfortheapproximateboundaryelemelltmet…     

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 METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)—CANTILEVER RECTANGULAR PLATES

In this paper,applying the method of the reciprocal theorem,we give the stationarysolutions of the forced vibration of cantilever rectangular plates under uniformly distributedharmonic load and concentrated harmonic load acting at any point of the plates,the figuresand tables of number value of bending moment and the deflection amplitudes as well.     

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)

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］，ｔｈｅｓｅｒｉｅｓｓｏｌｕｔｉｏｎｓｏｆｔｈｅｃｉｒｃｕｌａｒｐｌａｔｅｗｉｔｈｈｉｎｇｅｄｅｄｇｅａｎｄｗｉｔｈｔｈｅｓｉｍｐｌｙｓｕｐｐｏｒｔｅｄｅｄｇｅｈａｓｙｅｔｂｅｎｃｏｎｓｔｒｕｃｔｅｄ，ｗｈｉｃｈａ...     

BOUNDARY ELEMENT METHOD FOR SOLVING DYNAMICAL RESPONSE OF VISCOELASTIC THIN PLATE(Ⅱ)──THEORETICAL ANALYSIS

In this paper, the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is discussed. The theorem of existence and uniqueness of the approximate solution and the error estimation are also obtained. Based on these conclusions, the principle for choosing the mesh size and the number of truncated terms in the fundamental solution are given. It is shown that the theoretical analysis in this paper are consistent with the numerical results in [1]. Project supported by the National Natural Science Fundation of China     

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.