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.     

ON LARGE DEFORMATION UNILATERAL CONTACT PROBLEM WITH FRICTION(Ⅰ)—INCREMENTAL VARIATIONAL EQUATIONS

Based on the theory and technique of nonlinear geometric field theory of continuum,a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper.An expression for two and three-dimensicnal continua is derived,and the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form are obtained,which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.     

ON LARGE DEFORMATION UNILATERAL CONTACT PROBLEM WITH FRICTION (I)—INCREMENTAL VARIATIONAL EQUATIONS

Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper. An expression for two and three-dimensional continua is derived, and the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form are obtained, which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.     

CONTACT PROBLEM OF RUBBER RINGS WITH LARGE DEFORMATION

A contact problem with friction between a rubber ring with large deformation and alinear elastic thin plate is solved by means of the substructuring technique in this paper. Astudy of the influence of frictional contact,of the influence of plate thickness onrubber ring’deformation is presented.     

MIXED HYBRID PENALTY FINITE ELEMENT METHOD AND ITS APPLICATION

The penalty and hybrid methods are being much used in dealing with the general incompatible element. With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower; and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element isextremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together.And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element.That is to say, they are optimal to each other. Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degrees of freedom are given on each corner——one displacement and two rotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle     

QUASI－FLOW CORNER THEORY ON LARGE PLASTIC DEFORMATION OF DUCTILE METALS AND ITS APPLICATIONS

ＱＵＡＳＩ－ＦＬＯＷＣＯＲＮＥＲＴＨＥＯＲＹＯＮＬＡＲＧＥＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＤＵＣＴＩＬＥＭＥＴＡＬＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＨｕＰｉｎｇ（胡平）ＬｉｕＹｕｑｉ（柳玉启）ＧｕｏＷｅｉ（郭威）ＴａｉＦｅｎｇ（台风）（Ｒ...     

LUBRICATION THEORY FOR MICROPOLAR FLUIDS AND ITS APPLICATION TO A JOURNAL BEARING WITH FINITE LENGTH

In this paper,the field equation of micropolar fluid with general lubrication theoryassumptions is simplified into two systems of coupled ordinary differential equation.Theanalytical solutions of velocity and microrotation velocity are obtained.Micropolar fluidlubrication Reynolds equation is deduced.By means of numerical method,thecharacteristic of a finitely long journal bearing under various dynamic parameters,geometrical parameters and micropolar parameters are shown in curve form.Thesecharacteristics are pressure distribution,load capacity,coefficient of flow flux andcoefficient of friction.Practical value of micropolar effects is shown,so micropolar fluidtheory further close to engineering application.     

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.     

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established(see,Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell—I),the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell.The numerical modeling composes of finite element equations for three sub-systems of magnetic,thermal and deformation fields,as well as iterative methods for n...     

ON PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORMATION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅱ)——COUNTING VARIATION OF THICKNESS DISTRIBUTION

On the basis of paper[1],assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry,perturbation solutions of the corresponding problems of large axisymmetrical deflection are given.The effects of thickness distribution variation,which result from technology factors,on stiffness of bellows are discussed.     

ON PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORMATION OF LARGE AXISYMMETRICAL DEFLECTION (Ⅱ)——COUNTING VARIATION OF THICKNESS DISTRIBUTION

On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions of the corresponding problems of large axisymmetrical deflection are given. The effects of thickness distribution variation, which result from technology factors, on stiffness of bellows are discussed.     

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

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

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.     

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     

HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS

A new direct method for solving unsymmetrical sparse linear systems(USLS) arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin (MLPG) method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｑｕａｔｉｏｎｓａｎｄｔｈｅｓｏｌｕｔｉｏｎｐｒｏｃｅｄｕｒｅｓｏｆｔｈｅｆｉｎｉｔｅ＿ｅｌｅｍｅｎｔ＿ｄｉｓｐｌａｃｅｍｅｎｔ＿ｐｅｒｔｕｒｂａｔｉｏｎｍｅｔｈｏｄ (ＦＥＤＰＭ)ｆｏｒｔｈｅｇｅｏｍｅｔｒｉｃｎｏｎｌｉｎｅａｒｂｅｈａｖｉｏｒｓｏｆｓｈｅｌｌｓｏｆｒｅｖｏｌｕｔｉｏｎｓｕｂｊｅｃｔｅｄｔｏｐｕｒｅｂｅｎｄｉｎｇｍｏｍｅｎｔｓｏｒｌａｔｅｒａｌｆｏｒｃｅｓｉｎｏｎｅｏｆｔｈｅｉｒｍｅｒｉｄｉｏｎａｌｐｌａｎｅｓｗｅｒｅｐｒｅｓｅｎｔｅｄｉｎ (Ⅰ ) .…     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.     

ON SINGULAR PERTURBATION FOR A NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM (Ⅱ)

In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary. When certain assumptions are satisfied and e is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solutioh exists. The layer exists in the neighborhood of t=0. This paper is the development of references.     

ON SINGULAR PERTURBATION FOR A NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM (Ⅱ)

In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references [3–5]. The Project supported by the National Natural Science Foundation of China.     

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.