FREE VIBRATION OF PIEZOELECTRIC CYLINDRICAL SHELLS

Three displacement functions are introduced to represent each mechanical displacementaccording to the 3-D theory in this paper,By expanding the displacement functions and the electric po-tential in orthogonal series,the free vibration equation of piezoelectric cylindrical shells satisfying SS3boundary conditions can be obtained.The equation was solved by utilizing Bessel functions with com-plex arguments.Results are presented graphically as well as in table,and compared with those of otherreferences.Some frequencies that were missing in Ref.[9]are discovered.     

THE RING SHELLS UNDER GRAVITATIVE LOADS

This paper gives Novozlov’s equation (ref.[1]) in a simple style of ring shells withequal thickness under the actions of gravitative loads.By means of Fourier series,thespecial solution of the equation is established. Using the results of the homogeneous solutionin ref.[2],we find out the general solution of the problrm, and derive the expressions ofstress and displacement.Two examples are given as the application of the above results.     

BUCKLING OF COOLING TOWER SHELLS WITH RING-STIFFENERS

With the stability analysis of hyperbolic cooling tower shells with ring-stiffeners,ourpaper proposes the linear pre-buckling consistent theory.The numerical result shows thatthis linear analysis method is very effective and practical in engineering,for its precision ofcomputation is up to the level of the nonlinear analysis when it is used for the study of criticalloads of the hyperbolic cooling tower which is mainly governed by wind pressure and for thestudy of the effect of some other factors concerned in design on the buckling of shells.Basedon that.we have obtained a series of conclusions which will greatly benefits the engineeringdesign when discussing the effect on the critical wind loading of the shell which is caused bythe following factors such as the position of rings,the number of rings and the dead weight.     

TORSIONAL RIGIDITY OF SHELLS OF REVOLUTION

In this paper,the general equations of equilibrium for axisymmetrical deformationincluding the torsional deformation of revolutional shells are derived.It is shown that theshearing stress distribution due to torsion is independent of other stress componentsincluding those of membrane stress and bending stress.In this paper,the torsional deformation is considered to be represented by membraneaction only,and also by the combined action of bending membrane deformation.It is shownthat the main contribution of torsional rigidity is that related to membrane action.     

STUDIES OF NONLINEAR THEORIES FOR THIN SHELLS

In order to formulate the equations for the study here,the Fourier expansions upon the system of orthonormal polynomials are used.It may be considerably convenient to obtain the expressions of dis-placements as well as stresses directly from the solutions.Based on the principle of virtual work the equilibrium equations of va-rious orders are formulated.In particular,the system of third-order is given in detail,thus providing the reference for accur-acy analysis of lower-order equations.A theorem about the differentiation of Legendre series term by term is proved as the basis of mathematical analysis.Therefore the functions used are specified and the analysis rendered is no longer a formal one.The analysis will show that the Kirchhoff-Love’s theory is merely of the first-order and the theory which includes the transverse de-formation but keeps the normal straight is essentially of the first order,too.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITSAPPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

InPartl,anonlineartheoryformultilayersand`"ichshellsundergoingsmallstrainsandmoderaterotatiol1sisgiven-inwhichtranst'ersesheardeformationisconsidered.Thesimplifiedtheoryfortheshellsundergoingmoderateormoderate/smallrotationsisalsoPresented.Theexpressionsi…     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(III)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

Exactsolutionsoflargedeflectionandpostbucklingofrectangularplatesaredifficultproblems.Usually,appropriateseriesofsolutionsbasedonspecificboundaryareassumedtosolvetheproblems['].LiuandChengl'lsolvedthenonlinearbendingproblemofsimplysuPPortedrectangularsand…     

STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS

Based on Donnell's shallow shell equation, a new method is given in this paper to ana-lyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With themethod of complex variable function, a series of conformal mapping functions are obtained from dif-ferent cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And,the general expressions for the equations of a cylindrical shell, including the solutions of stress concen-trations meeting the boundary conditions of the large openings' edges, are given in the mapping plane.Furthermore, by applying the orthogonal function expansion technique, the problem can be summa-rized into the solution of infinite algebraic equation series. Finally, numerical results are obtained forstress concentration factors at the cutout's edge with various opening's ratios and different loadingconditions. This new method, at the same time, gives a possibility to the research of cylindrical shellswith large non-circular openings or with nozzles.     

THE CREEP EFFECTS ON THE BUCKLING OF SHALLOW SHELLS

An analysis of the creep effects on the buckling of concreteshallow shells is presented in this paper.Based on the non-linear theory of thin elastic shells.it is found that forthose of the elliptical paraboloidal type.the upper cri-tical load of the load-deflection curve will decrease whilethe lower limit Will increase with time.As to the problemof local buckling of the shell.the critical load is de-pendent only upon the modulus of elasticity at the instantit occurs.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(Ⅲ)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

In this paper, exact solutions of large deflection of multilayer sandwich shallow shells under transverse forces and different boundary conditions are presented. Exact results of postbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlinear deflection of general shallow shells such as spherical shells under inplane edge forces are also obtained by the same procedure.     

STRESS AND DISPLACEMENT OF RING SHELLS UNDER CENTRIFUGAL FORCE

Using the results of refs. [1]and[2]about the general axial symmetrical problem. thispaper calculates the stress and displacement of ring shells under centrifugal force. Thesolution is given in Fourier series form.In the paper the examples of open ring shells and close ring shells are givenrespectively.     

METHOD OF GREEN’S FUNCTION OF CORRUGATED SHELLS

Introduction Corrugateddiaphragmiswidelyusedaselasticmeasurementelementinprecision instruments.Sometimes,corrugateddiaphragmismanufacturedwithconicorsphericaltaper toadjustthecharacteristicofdiaphragm.Forexample,theshapetaperisoftenusedtoincreasesensitivityofdiaphragmindesignofvacuumdiaphragmforheightmeter.Inmanyengineeringpracticalproblems,controlequationscanbedescribedbyeither differentialequationsorintegralequations.Usually,differentialincreaseserrorandintegral decreaseserrorinnumericalana…     

METHOD OF GREEN＇S FUNCTION OF CORRUGATED SHELLS

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.     

THE FINITE DEFLECTION EQUATIONS OF ANISOTROPIC LAMINATED SHALLOW SHELLS

In this paper,basing on ref.[1]we improved andextended that Which is concerned with a view of inves-tigating the finite deflection equations of anisotro-pic laminated shallow shells subjected to static loads,dynamic loads and thermal loads.We have consideredthe most general bending-stretching couplings and theshear deformations in the thickness direction.and de-rived the equilibrium equations,boundary conditionsand initial conditions.The differential equationsexpressed in terms of generalized displacements u_o,υ_o,φ_x, φ_y and w are obtained.From them,we could solvethe problems of stress analysis,deformation,stabilityand vibration.For some commonly encountered cases,we derived the simplified equations and methods.     

AXISYMMETRY PROBLEMS OF RING SHELLS UNDER ARBITRARY DISTRIBUTED LOADS

Extending Novozhilov’s transformation,this paper simplifies successfully theaxisymmetry problems of ring shells under arbitrary distributed loads, and the equation ofthe problems in complex form which is similar to Novozhilov’s is obtained The particularsolution is obtained.Combining with Chien’s general solution of homogeneous equation,this paper gives the general solution for the general symmetry problems of ring shells.Various examples of useful loads and closed ring shells are discussed respectively.     

AXISYMMETRIC PROBLEMS OF CYLINDRICAL SHELLS WITH VARIABLE WALL THICKNESS

The purpose of this paper is to give the general solutions for axisymmetric cylindricalshells with parabolically varying wall thickness.     

A NEW HIGHER-ORDER THEORY TO LAMINATED PLATES AND SHELLS

In this paper a new ltigher-order theory to laminated plates and shells is presented and tIII,I,vhcIlv t1v I)r‘..v(,III‘,lI(IIIIIthen symmetric and antisymmetric cross-ply lammated plates.cylmdric bending andbending of spherical shells are also studied.In order to examine the accuracy of the theory.!(‘IhI‘‘It.l‘uI.at:1‘(!l‘Ih(‘Ih(‘l)I:1..several particular examples have been calculated The numerical results are in goodagreement with the exdct solution.which shows the theory is possessed of higher accuracyand is easy to solve a problem with few unknowns.     

GENERALIZED EXPRESSIONS FOR BOUNDARY CONDITIONS OF SHELLS OF REVOLUTION

For the boundary conditions of shells of revolution,tra-ditionally,four out of the eight quantities which are thefour displacements on the middle surface u,v.w and (?) to-gether with the four correspondinq forces,are given.Whenthe generalized displacements on the nodal circles are usedas basic unknowns.the number of unknowns on a nodal cir-cle is more than four.In this case,how todeal with the boundary conditions is still a problem thathas not been solved satisfactorily yet.In this paper,therelations between the generalized and nongenerlized quan-tities of a shell’s edge are derived according to the prin-ciple of virtual work.Seven types of common edges arestudied and their expressions of boundary conditions in theform of generalized displacements or forces are given.Thenumber of expressions for each type of edge may correspondwith the number of unknowns used on a nodal circle.withthese expressions,boundary conditions can be put directlyinto equations of motion of generalized displacement methodso as t     

ELASTIC PULSE BUCKLING OF CYLINDRICAL SHELLS UNDER RADIAL IMPULSIVE LOADING

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