Application of subregion function method for solving beam-board structure

In this paper,the solution to the structure consisting of a bead and a board is given as aresult of the application of the subregion function method which was suggested in ref.[1].The same problem is also computed with finite element method.The comparison betweenthe two results shows that the application of the subregion function in the method of weightedresiduals is practical and effective,especially for solving compound structures.     

ONE-DIMENSIONAL NONUNIFORM TEMPERATURE FLOW WITH HEAT TRANSFER BY CONVECTION

In ref.[1],V.E.Najenov studied the conditions that when the viscosity of the liquid isan exponential function of temperature,the pipe flow,having steady heat transfer,is one-dimensional and with nonuniform temperature.For plane canal circular pipe he stillstudied the velocity and the temperture fields.In this paper,the author presents two new methods for solving the same problem.Themethod as in ref.[1]may be regarded as the natural branch of the methods of this paper.One of our new methods only can solve the same problem as in ref.[1]and the complexdegree of its computing process is nearly the same as that in ref.[1].But the other can gobeyond the studying scope of ref.[1],namely,for the case that the curvatures ofcircumference of the cross section of the pipe are not equivalent everywhere,the problemmay also be solved.     

APPLICATIONS OF THE EXTRAPOLATION METHOD TO THE NUMERICAL SOLUTION OF SINGULAR PERTURBATION PROBLEMS

In this paper we consider applications of extrapolation method to the numericalsolution of singular perturbation problem for elliptic—parabolic equation in order tomanifesting accuracy of approximations and estimate the order of accuracy,Concerningthe uniform convergence in ref.[1].its proof is given in the appendix.     

An approximate analytical solution of the cylindrical detonation wave generated by the linear explosion

The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref.[1].In this paper,when the ratio of specific heatγ》1 by using the enlargement coordinate method,the first-order analytical solutions are obtained.The perturbation parameter isε=1/γ~2 .The correction of these solutions is checked at the end of this paper.     

BUCKLING AND POSTBUCKLING OF MODERATELY THICK PLATES

This paper gives the basic differential equations for finite deflections of elastic platesaccording to Reissner’s approximate stress distributions.The buckling and postbucklingproblems of elastic rectangular plates.including the effect of transverse shear deformation.are solved and discussed by using perturbation method suggested in ref.[8].Thepostbuckling equilibrium paths of perfect and imperfect moderately thick rectangularplates are presented and compared with the results based on thin plate theory.     

SEVERAL CRITERIONS OF ABSOLUTE STABILITY FOR THE SECOND CANONICAL FORM OF CONTROL SYSTEM

In this paper,several explicit criterions of absolute stability for the real secondcanonical form of control systemare given,which generalize and include the known result in ref.[2].By applying thesecriterions to the well known equations of the longitudinal motion of aircraft,a result thatgeneralizes and includes the known results in refs.[3,4,2]is obtained.     

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 A CLASS OF METHOD FOR SOLVING PROBLEMS WITH RANDOM BOUNDARY NOTCHES AND/OR CRACKS—(Ⅲ) COMPUTATIONS FOR BOUNDARY CRACKS

This paper continues the discussions to a class of method for solving problems withrandom boundary notches and for cracks in refs.[1] and [2].Using the method developed in[1].[2]with important modifications about inclusion of singularities in the formulation. wearrive at a very effective computational process for problems with random boundarycracks. Actual computations for boundary cracks with or without apptied tractions in theirsurfaces. Show that the present method is quite workable for the problems consideredwithin proper range of characteristic parameters. The results obtained here extend thecontents of “Handbook of Stress Intensity Factors” given by G. C. Sih.     

EXACT SOLUTION OF NAVIER-STOKES EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRACPAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅱ)

This work is the continuation of the discussion of ref.[1].In ref.[1] we applied thetheory of functions of a complex variable under Dirac-Pauli representation,introduced theKaluza“Ghost”coordinate, and turned Navier-Stokes equations of viscofluid dynamics ofhomogeneous and incompressible fluid into nonlinear equation with only a pair of complexunknown functions.In this paper we again combine the complex independent variableexcept time,and cause it to decrease in a pair to the number of complex independentvariables.Lastly,we turn Navier-Stokes equations into classical Burgers equation.TheCole-Hopf transformation join up with Burgers equation and the diffusion equation isB(?)cklund transformation in fact,and the diffusion equation has the general solution aseveryone knows.Thus,we obtain the exact solution of Navier-Stokes equations byB(?)cklund transformation.     

THE APPLICATION OF GENERALIZED VARIATIONAL PRINCIPLE IN FINITE ELEMENT-SEMIANALYTICAL METHOD

The method developed in this paper is inspired by the siewpoint in ref. [1] that sufficient attention has not been paid to the value of the generalized variational principle in dealing with the houndary conditions in the finite element method. This method applies the generalized variational principle and chooses the series constituted by spline function multiplied by sinusoidal function and added by polynomial as the approximate deflection of plates and shells. By taking the deflection problem of thin plate, it shows that this method can solve the coupling problem in the finite element-semianalytical method. compared with the finite element method and finite stripe method, this method has much fewer unknown variables and higher precision. Hence, it proposer an effective way to solve this kind of engineering problems by minicomputer.     

CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅱ)

The present paper uses the mathematics model for consolidation of unsaturatedsoil developed in ref.[1]to solve boundary value problems.The analytical solutionsfor one-dimensional consolidation problem are gained by making use of Laplacetransform and finite Fourier transform.The displacement and the pore water pressureas well as the pore gas pressure are found from governing equations simultaneously.The theoretical formulae of coefficient and degree of consolidation are also given inthe paper.With the help of the method of Galerkin Weighted Residuals,the finiteelement equations for two-dimensional consolidation problem are derived.A FORTRANprogram named CSU8 using8-node isoparameter element is designed.A plane strainconsolidation problem is solved using the program,and some distinguishing features onconsolidation of unsaturated soil and certain peculiarities on numerical analysis arerevealed.These achievements make it convenient to apply the theory proposed by theauthor in engineering practice.     

A new approximate solution of nonlinear diffusion equation

In this paper,the same problem in ref.[1] is studied.The author’s solutionapproximately satisfies the whole fundamental equations (1.1)and(1.2)and the wholebound values conditions (1.3-1.5).But the Liu’s solution does not satisfy theequation of continuity(1.2).     

Buckling and postbuckling of moderately thick plates

This paper gives the basic differential equations for finite deflections of elastic plates according to Reissner’s approximate stress distributions. The buckling and postbuckling problems of elastic rectangular plates, including the effect of transverse shear deformation, are solved and discussed, by using perturbation method suggested in ref. [8]. The postbuckling equilibrium paths of perfect and imperfect moderately thick rectangular plates are presented and compared with the results based on thin plate theory.     

The more general displacement solutions for the plane elasticity problems

In this paper,the author obtains the more general displacement solutions for theisotropic plane elasticity problems.The general solution obtained in ref.[1 ]is merelythe particular case of this paper,In comparison with ref.[1],the general solutions ofthis paper contain more arbitrary constants.Thus they may satisfy more boundaryconditions.     

THE SCHRDINGER EQUATION OF THIN SHELL THEORIES

This work is the continuation of the discussions of[50]and[51].In this paper:(A)The Love-Kirchhoff equation of small deflection problem for elastic thin shellwith constant curvature are classified as the same several solutions of Schr(?)dingerequation,and we show clearly that its form in axisymmetric problem;(B)For example for the small deflection problem,we extract the general solution ofthe vibration problem of thin spherical shell with equal thickness by the force in centralsurface and axisymmetric external field,that this is distinct from ref.[50]in variable.Today the variable is a space-place,and is not time;(C)The von Kármán-Vlasov equation of large deflection problem for shallow shellare classified as the solutions of AKNS equations and in it the one-dimensional problem isclassified as the solution of simple Schr(?)dinger equation for eigenvalues problem,and wetransform the large deflection of shallow shell from nonlinear problem into soluble linearproblem.     

THE ANTIPLANE PROBLEM OF DOUBLE PERIOD NON-UNIFORM DISTRIBUTION CRACK FIELD

Originating from Robert Hooke’s law and equilibrious equations,and using the theoryof the complex variable function,this paper transfers the rectaugle region in which thecracks emerge into upper-half part of ξplane by means of conformal mapping.Thenaccording to the theory of ref.[1].We find the solution in closed form,thereby the stressintensity factors are derived.     

ON UNILATERAL CONTACT LARGE DEFORMATION PROBLEM WITH FRICTION(Ⅱ)—NONLINEAR FINITE ELEMENT TECHNIQUE AND ITS APPLICATION

Based on the variational equation derived in ref.[1]a nonlinear incremental F.E.equation is formulated for unilateral contact elastic and plastie large deformationproblems.A new technique-co-moving coordinate finite element method is introduced,and a practical mathematical model for large deformation contact problem is described.To show the effectiveness of the method,problems of contact large deformation ofcantilever beam.cireular plate,as well as metal ring are computed.Compared withexperiments.the results show good agreements.     

The antiplane problem of double period non-uniform distribution crack field

Originating from Robert Hooke’s law and equilibrious equations. and using the theory of the complex variable function, this paper transfers the rectaugle region in which the cracks emerge into upper-half part of ζplane by means of conformal mapping. Then according to the theory of ref.[1]. We find the solution in closed form. there by the stress intensity factors are derived.     

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.     

Supplementary study on anisotropic plastic stress fields at a stationary plane-stress crack-tip

The results in Ref.[1]are not suitable for the cases of a≥2 .For this reason,we use the method in Ref.[1]to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of a=2 and a>2 .As an example,we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of modeⅠand modeⅡplane-stress cracks for the case of a=2.