Block pivot methods for solving frictional contact problems

Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is “relative small”. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables. The project supported by the National Natural Science Foundation of China     

Periodic solutions of a class of higher order neutral type equations

In this paper, by ssing the theory of Fourier series, some necessary and sufficient conditions of existence and uniqueness of periodic solutions of a class of higher order neutral type equations are obtained. The main results by Shi Jianguo in “Discussion on the periodic solutions for linear equation of neutral type with constant coefficients” are improved, i. e., the condition |b₀|≠1 instead of the condtion |b₀|<1/2 of Theorem 1 by Shi Jianguo is given. Other theorems by Shi are rebuilt and improved according to the new assumption. Foundation item: the Natural Science Foundation of Yunnan Province, China (97A012G)     

A Simple Fast Method in Finding Particular Solutions of Some Nonlinear PDE

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MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.     

Mineral bridges of nacre and its effects

Nacre, or mother-of-pearl, is a kind of composites of aragonite platelets sandwiched between organic materials. Its excellent mechanical properties are thought to stem from the microarchitecture that is traditionally described as a “brick and mortar” arrangement. In this paper, a new microstructure, referred to as mineral bridge in the biomineralization, is directly observed in the organic matrix layers (mortar) of nacre. This is an indication that the organic matrix layer of nacre should be treated as a three-dimensional interface and the microarchitecture of nacre ought to be considered as a “brick-bridge-mortar” structure rather than the traditional one. Experiments and analyses show that the mineral bridges not only improve the mechanical properties of the organic matrix layers but also play an important role in the pattern of the crack extension in nacre. The project supported by the Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-201) and the National Natural Science Foundation of China (19891180 and 10072067)     

Numerical study of vortex reconnection for two anti-parallel vortex tubes

By direct numerical simulation of the Navier-Stokes equations we investigate the reconnection of two antiparallel vortex tubes. A new type of perturbation of the initial vorticity field is given which is different from that presented in Refs. [8] and [9]. The formation and the evolution of the “curved vortex belts”, their mutual action with the “bridges” are found. These are important phenomena not studied by others. The project supported by the LNM of Institute of Mechanics, Academia Sinica and The National Natural Science Foundation of China     

Computation of super-convergent nodal stresses of timoshenko beam elements by EEP method

The newly proposed element energy projection (EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements. Generalformul as based on element projection theorem were derived and illustrative numerical examples using two typical elements were given. Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions. The EEP method gives super-convergent nodal stresses, which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude. And in addition, it can overcome the “ shear locking“ difficulty for stresses even when the displacements are badly affected. This research paves the way for application of the EEP method to general onedimensional systems of ordinary differential equations.     

Formation Mechanism of Cracks in Saturated Sand

The formation mechanism of “water film” (or crack) in saturated sand is analyzed theoretically and numerically. The theoretical analysis shows that there will be no stable “water film” in the saturated sand if the strength of the skeleton is zero and no positions are choked. It is shown by numerical simulation that stable water films initiate and grow if the choking state keeps unchanged once the fluid velocities decrease to zero in the liquefied sand column. The developments of “water film” based on the model presented in this paper are compared with experimental results.The project supported by the National Natural Science Foundation of China (40025103 and 10202024) and Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences. The English text was polished by Keren Wang.     

Uniformly valid asymptotic solutions of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate of four clamped edges with variable thickness

By using “the method of modified two-variable”,“the method of mixing perturbation ”and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth- order for ε1 and Mth- order for ε2 of the deflection functions and stress function are obtained.     

Reduced augmented Lagrangian bi-conjugate gradient method for impact-contact problems

To avoid the numerical oscillation of the penalty method and non-compatibility with explicit operators of conventional Lagrange multiplier methods used in transient contact problems to enforce surface contact conditions, a new approach to enforcing surface contact constraints for the transient nonlinear finite element problems, referred to as “the reduced augmented Lagrangian bi-conjugate gradient method (ALCG)”, is developed in this paper. Based on the nonlinear constrained optimization theory and is compatible with the explicit time integration scheme, this approach can also be used in implicit scheme naturally. The new surface contact constraint method presented has significant advantages over the widely adopted penalty function methods and the conventional Lagrangian multiplier methods. The surface contact constraints are satisfied more accurately for each step by the algorithm, so the oscillation of numerical solution for the explicit scheme is depressed. Through the development of new iteration strategy for solving nonlinear equations, ALCG method improves the computational efficiency greatly. Project supported by State Education Commission Doctoral Foundation and Natural Science Foundation of Liaoning Province.     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences Biography: Mo Jia-qi (1937−)     

Secondary buckled states of rectangular sandwich plates

In this paper, for a rectangular sandwich plate with edges simply supported and subjected to a constant compressive thrust λ along two opposite edges; the secondary bifurcation points and the secondary buckled states that bifurcate from the primary buckled states are determined by a perturbation method. These results are useful for their numerical calculation and can be used to explain the phenomenon of “mode-jumping”. Project Supported by National Natural Science Foundation of China.     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION （Ⅰ）——THE CONTINUOUS-TIME CASE

An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.     

Comprehensive mathematical model of microcirculatory dynamics (II)—Calculation and the results

The mathematical model described in Part I was solved using “influence line method” combining analytical method and finite element method. Many important aspects of microcirculatory dynamics were analyzed and discussed. It show that interstitial fluid pressure changes its sign twice within one arteriolar vasomotion period and it is therefore not important that interstitial fluid pressure is a little higher or lower than atmospheric pressure; arteriolar vasomotion can periodically result in lymph formation and interstitial total pressure plays an important role in this procedure; local regulation of microcirculation can meet metabolic need some extent in the form of dynamic equilibrium. The property of arteriole as a “resistant vessel” and the efficiency of microvascular network as heat exchanger are also shown. These results show that the comprehensive mathematical model developed in Part I is physiologically resonable. Foundation item: the Natural Science Foundation of Sichuan Province, P R China Biography: Guo Zhongsan (1947-)     

IMPACT MODEL RESOLUTION ON PAINLEVE’S PARADOX

Painlev&#233;‘s paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlev&#233;‘s example. The results confirm ““““impact without collision““““ in the inconsistent states of the system. A ““““critical normal force““““ which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical results, a rule of the velocity‘s jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough.     

THE MULTI-SYMPLECTIC ALGORITHM FOR “GOOD” BOUSSINESQ EQUATION

The multi-symplectic formulations of the “Good” Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical experiments show that the multi-symplectic scheme have excellent long-time numerical behavior. Foundation items: the Foundation for Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences; the Natural Science Foundation of Huaqiao University. Biography: ZENG Wen-ping (1940-), Professor (E-mail: qmz@1sec.cc.ac.cn)     

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Studies on nonlinear stability of three-dimensional H-type disturbance

The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE). The key initial conditions for sub-harmonic disturbances are obtained by means of the secondaryinstability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region, increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the “H-type“ evolution are studied in detail. The results of the three-dimensional nonlinear “H-type“ evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.     

Microgravity experiments of two-phase flow patterns aboard MIR space station

A first experimental study on two-phase flow patterns at a long-term, steady microgravity condition was conducted on board the Russian Space Station “MIR” in August 1999. Carbogal and air are used as the liquid and the gas phase, respectively. Bubble, slug, slug-annular transitional, and annular flows are observed. A new region of annular flow with lower liquid superficial velocity is discovered, and the region of the slug-annular transitional flow is wider than that observed by experiments on board the parabolic aircraft. The main patterns are bubble, slug-annular transitional and annular flows based on the experiments on board MIR space station. Some influences on the two-phase flow patterns in the present experiments are discussed. The project supported by the National Natural Science Foundation of China (19789201), the Ministry of Science and Technology of China (95-Yu-34), and the Post-doctoral Science Foundation of China     

ANALYTICAL SOLUTIONS FOR ELASTOSTATIC PROBLEMS OF PARTICLE-AND FIBER-REINFORCED COMPOSITES WITH INHOMOGENEOUS INTERPHASES

IntroductionRecently ,theinterphaseincompositeshasattractedtheattentionofmanyresearchers[1- 7].Someinterphasesareproducedbydesignandothersbychemicalreactionsinfabricatingcomposites.Fromtheviewpointofmechanicsofcompositematerials,oneofthefundamentalproblemsofcompositeswithinterphasesistopredicttheeffectivemoduli.Therearemanymethodsforpredictingeffectivemoduliofcomposites,suchasgeneralizedself_consistentmethod(GSCM) ,compositesphereandcompositecylindermodels (CCAandCSA)andIDDestimate ,etc …