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 NEW ELEMENT FOR THIN PLATE OF BENDING WITH CURVILINEAR BOUNDARY—CURVILINEAR BOUNDARY QUADRILATERAL ELEMENT

This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.     

A NEW ELEMENT FOR THIN PLATE OF BENDING WITH CURVILINEAR BOUNDARY—CURVILINEAR BOUNDARY QUADRILATERAL ELEMENT

This paper presents a curvilinear boundary quadrilateral element for the problem ofthin plate of bending with curvilinear boundary.A coordinate transformation of twodimensions is performed in the calculation of FEM.The introduction of an additionalstiffness matrix based on the generalized variational principles results in high accuracy andless computation time.The numerical results agree with the analytical solution very well.     

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

I. INTRODUCTION The composite material and the composite structure are liable to generate damage during manufactureand under load, which will lead to a decrease of the material and structure’s mechanical properties.It is accepted that there exist four…     

A TIME DOMAIN BOUNDARY ELEMENT METHOD FOR WATER-SOLID IMPACT ANALYSIS

A reciprocal theorem of dynamics for potential flow problems is first derived by meansof the Laplace transform in which the compressibility of water is taken into account.Based on this the-orem,the corresponding time-space boundary integral equation is obtained.Then,a set of time do-main boundary element equations with recurrence form is immediately formulated through discretiza-tion in both time and boundary.After having carried out the numerical calculation two solutions arefound in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impacton the surface of a half-space fluid.The results show that the present method is more efficient than theprevious ones.     

ANALYSIS OF NONLINEAR LARGE DEFORMATION PROBLEMS BY BOUNDARY ELEMENT METHOD

In this paper, the author deduces an approximate solution of nonlinear influence function in rate form for two-dimensional elastic problems on current configuration by the method of comoving coordinate system. Here BEM formulation of large deformation based on Chen's theory is given. The computational processes of nonlinear boundary integral equation is discussed. The author also compiles a nonlinear computing program NBEM. Numerical examples show that the results presented here is available to the solution of engineering problems.     

BOUNDARY ELEMENT METHOD FOR BUCKLING EIGENVALUE PROBLEM AND ITS CONVERGENCE ANALYSIS

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

This work is a continuation of the discussion of [1], On a class of method for solving problems with random boundary notches and/or cracks, (I) by C. Ouyang (Appl. Math. & Mech., vol. 1, No. 2, 1980). Here computations for boundary notches are made by using the theory and formulas presented in [1]. In the computation modification is also made for the boundary conditions in parametric plane in [1]. Numerical results for examples show that within ranges of parameter considered in the paper, for example L, the present method in quite workable in practical computations.     

FIXED STREAM-TUBE METHOD FOR SOLVING TWO-PHASE PLANE FLOW PROBLEMS AND ITS THEORETICAL ANALYSIS

The fixed stream-tube method widely adopted in engineering field for giving anapproximate solution to the two-dimensional problems of two-phase flow through porousmedia is summarized and an improvement has been made in this paper.Its core part,i.e.,thefluid displacement within a one-dimensional stream tube with variable cross-sectional areaunder a given pressure difference across the tube is thoroughly studied.The existence anduniqueness of solution are proved the exact solution,numerical solution and itsconvergence.stability analyses are given in this paper.     

THE APPLICATION OF BOUNDARY ELEMENT METHOD IN STRESS ANALYSIS OF AUTOFRETTED TUBE WITH NOTCH

In this paper.the boundary element method is anplied to investigate the internal state ofstress of autofretted tube with notch and the calculated results are important in the practicaldesign.     

NEW BOUNDARY ELEMENT METHOD FOR TORSION PROBLEMS OF CYLINDER WITH CURVILINEAR CRACKS

The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.     

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ     

AN EXACT ELEMENT METHOD FOR THE BENDING OF NONHOMOGENEOUS REISSNER’S PLATE

In this paper,based on the step reduction method and exact analytic method,a new method,the exact element method for constructing finite element,is presented.Since the new method doesn’t need variational principle,it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficients.By this method,a triangle noncompatible element with15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner’s plate.Because the displacement parameters at the nodal point only contain deflection and rotation angle.it is convenient to deal with arbitrary boundary conditions.In this paper,the convergence of displacement and stress resultants is proved.The element obtained by the present method can be used for thin and thick plates as well,Four numerical examples are given at the end of this paper,which indicates that we can obtain satisfactory results and have higher numerical precision.     

ELASTIC ANALYSIS OF ORTHOTROPIC PLANE PROBLEMS BY THE SPLINE FICTITIOUS BOUNDARY ELEMENT METHOD

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｃｏｎｖｅｎｔｉｏｎａｌｂｏｕｎｄａｒｙｅｌｅｍｅｎｔｍｅｔｈｏｄ (ＢＥＭ) ,ｓｉｎｇｕｌａｒｐｏｉｎｔｓａｒｅｄｉｓｔｒｉｂｕｔｅｄａｌｏｎｇｔｈｅｂｏｕｎｄａｒｙｏｆｔｈｅｄｏｍａｉｎｕｎｄｅｒｓｔｕｄｙ ,ｗｈｉｃｈｌｅａｄｓｔｏｓｉｎｇｕｌａｒｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓｄｕｅｔｏｔｈｅｓｉｎｇｕｌａｒｉｔｙｏｆｆｕｎｄａｍｅｎｔａｌｓｏｌｕｔｉｏｎｓ .Ｔｈｅｒｅｆｏｒｅ ,ｓｉｎｇｕｌａｒｉｎｔｅｇｒａｔｉｏｎｍｕｓｔｂｅｈａｎｄｌｅｄｗｈｅｎｓｏｌ…     

A SEKIES BOUNDARY INTEGRATION METHOD FOR THE BENDING ANALYSIS OF ANISOTROPIC PLATES

A series boundary integration method is given which exactly satisfies the fundamentalequation of bending analysis of general anisotropic plates or laminated plates in Kirchhoffssense.With a unified deflection series,the method may be applied to the plates havingdifferent planforms and support conditions.Several groups of representative examples arecalculated.The examples include circular,square and triangular plates,and theirboundaries include clamped edges.simply supported edges,free edges and free corner.Numerical results indicate rapid convergency for both deflection and stress resultants anddemonstrate wide applicability of the method.     

A NEW METHOD FOR THE UNCERTAIN RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

A computing method for estimating the upper and lower bounds of the response ofstructures with uncertainties is presented.The uncertain parameters are described by the convexmodel.A numerical example of the frame structure is given to illustrate the effectiveness of thismethod.     

THE PERTURBATION FINITE ELEMENT METHOD FOR SOLVING THE PLANE PROBLEM IN CONSIDERATION OF LINEAR CREEP

In this paper, amethod (PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, prestressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on. In the presented method, the assumption made in the general increment method that variables remain constant in a divtded time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased. Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.     

A WEIGHTED PENALTY FINITE ELEMENT METHOD FOR THE ANALYSIS OF POWER-LAW FLUID FLOW PROBLEMS

In this paper,a new finite element method for the flow analysis of the viscousincompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finiteelement formulation and by the introduction of an alternative perturbation,which isweighted by viscosity,of the continuity equation.A numerical example is presented toexhibit the efficiency of the method.     

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…