ON SOME PROBLEMS OF PLASTIC BUCKLING OF PLATES AND SHELLS

This paper gives the stress-strain relations of the variational types on the basis of an assumption concerning the small deformation in the theory of el-asto-plasticity.The compact form of fundamental equations of plastic buckling of the plates and shells is obtained in terms of secant modulus.     

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

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

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.     

EQUILIBRIUM AND BUCKLING OF COMBINED SHELLS UNDER UNIFORM EXTERNAL PRESSURE

Nonlinear strain is used to formulate the energy functional of combined structure withseveral kind of shells.The nonlinear finite element method (N.F.E.M.) is proposed forcalculating bending and buckling of the structure subjected to external hydrostaticpressure.The numerical results are found to be in good agreement with experimental ones.     

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to bt, cubic polynomials and to satLyfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical.shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.     

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.     

PROGRESSING STEP BY STEP AND INTEGRATING CALCULATION OF OVERCRITICAL DEFORMATION OF SPHERICAL SHALLOW SHELLS

In this paper,the problem of second buckling of the spherical shallow shell is calculatedby use of the method of progressing step by step and in integating.The result is more exactthan that of first approximate analyis for over-critical deformation of spherical shallowshell It has been solved that the solution of second appoximate analysis in this problemcan’t befound.The calculating example in this paper shows that the solution of progressingstep by step and integrating converges to second approximate solution.     

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

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

SOME APPLICATIONS OF THE SINGULAR PERTURBATION METHOD TO THE BENDING PROBLEMS OF THIN PLATES AND SHELLS

This paper presents a review which tackles some nonlinear bending problems of plates and shells in a unified way by means of the technique of undetermined small parameters.     

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

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

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.     

DETERMINATION OF THE PERTURBATION PARAMETER IN LARGE DEFLECTION OF PLATES AND SHALLOW SHELLS BY MEANS OF THE LEAST SQUARE METHOD

In this paper the least square method of determination of the perturbation parameteris presented when the perturbation technique is used in the solution of large deflection ofaxisymmetrical plates and shallow shells.The examples of circular plates are calculatedand compared with the exact solution and other perturbation solutions. The results show thebest agreement with the exact solution among those perturbation solutions.     

THE SCHR(?)DINGER EQUATION IN THEORY OF PLATES AND SHELLS WITH ORTHORHOMBIC ANISOTROPY

This work is the continuation of the discussion of Refs.[1-5].In this paper:[A] The Love-Kirchhoff equations of vibration problem with small deflection fororthorhombic anisotropic thin shells or orthorhombic anisotropic thin plates on Winkler’sbase are classified as several of the same solutions of Schr?dinger equation.and we canobtain the general solutions for the two above-mentioned problems by the method in Refs.[1]and[3-5].[B]The von Kármán-Vlasov equations of large deflection problem for shallow shellswith orthorhombic anisotropy(their special cases are the von Kármán equations of largedeflection problem for thin plates with orthorhombic anisotropy)are classified as thesolutions of AKNS equation or Dirac equation,and we can obtain the exact solutions forthe two abovementioned problems by the inverse scattering method in Refs.[4-5].The general solution of small deflection problem or the exact solution of largedeflection problem for the corrugated or rib-reinforced plates and shells as special c     

ON THE PROBLEM OF AXISYMMETRICALLY LOADED SHELLS OF REVOLUTION WITH SMALL ELASTIC STRAINS AND ARBITRARILY LARGE AXIAL DEFLECTIONS

For the problem of axisymmetrically loaded shells of revolution with small elasticstrains and arbitrarily large axial deflections, this paper suggests a group of state variables:radial displacement u, axial displacement W,angular deflection of tangent in the meridianX,radial stress resultant H and meridional bending moment M_q, and derives aSystem of First-order Nonlinear Differential Equations under global coordinate systemwith these variables. The Principle of Minimum Potential Energy for the Problem isobtained by means of weighted residual method, and its Generalized Variational Principleby means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionizationwith a scale of load parameter, which may efficiently raise the probability of success fornonlinearity calculation. The obtained Nondimenensional System of Differential Equationsand Nondimensional Principle of Minimum Potential Energy could be taken as thetheoretical basis for the numerica     

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.     

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     

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.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅰ)──GENERAL THEORY

1.Intr0ductionInrecentyears,multilayersandwichshells,duetotheirhighrigidityandlightweight,havefoundwideapplicationinaeronautical,astronauticalandnavalengineerings.Withpropermaterialsforfacingsandcores,theshellsmaypossessshock-mitigating,thermal-insulating…     

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.