An adaptive algorithm of precise integration for transient analysis

This paper presents an improved precise integration algorithm for transient analysis of heat transfer and some other problems. The original precise integration method is improved by means of the inverse accuracy analysis so that the parameterN, which has been taken as a constant and an independent parameter without consideration of the problems in the original method, can be generated automatically by the algorithm itself. Thus, the improved algorithm is adaptive and the accuracy of the algorithm is not dependent on the length of the time step in the integration process. It is shown that the numerical results obtained by the method proposed are more accurate than those obtained by the conventional time integration methods such as the difference method and others. Four examples are given to demonstrate the validity, accuracy and efficiency of the new method. Project supported by the National Natural Science Foundation of China (No. 19872016, 19872017), the National Key Basic Research Special Foundation (G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China.     

A combined parametric quadratic programming and precise integration method based dynamic analysis of elastic-plastic hardening/softening problems

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (19872016, 50178016, 19832010) and the Foundation for University Key Teacher by the Ministry of Education of China     

Mixed energy method for solution of quadratic programming problems and elastic-plastic analysis of truss structures

A new algorithm for the solution of quadratic programming problems is put forward in terms of the mixed energy theory and is further used for the incremental solution of elastic-plastic truss structures. The method proposed is different from the traditional one, for which the unknown variables are selected just in one class such as displacements or stresses. The present method selects the variables in the mixed form with both displacement and stress. As the method is established in the hybrid space, the information found in the previous incremental step can be used for the solution of the present step, making the algorithm highly efficient in the numerical solution process of quadratic programming problems. The results obained in the examples of the elastic-plastic solution of the truss structures verify what has been predicted in the theoretical analysis. Project supported by the National Natural Science Foundation of China (No. 50178916, No. 19732020 and No. 19872016), the National Key Basic Research Special Foundation (No. G1999032805), the Special Funds for Major State Basic Research Projects and the Foundation for University Key Teachers by the Ministry of Education of China.     

A novel incompressible finite-difference lattice Boltzmann equation for particle-laden flow

In this paper, we propose a novel incompressible finite-difference lattice Boltzmann Equation (FDLBE). Because source terms that reflect the interaction between phases can be accurately described, the new model is suitable for simulating two-way coupling incompressible multiphase flow. The 2-D particle-laden flow over a backward-facing step is chosen as a test case to validate the present method. Favorable results are obtained and the present scheme is shown to have good prospects in practical applications. The project supported by the National Natural Science Foundation of China (60073044), and the State Key Development Programme for Basic Research of China (G1999022207). The English text was polished by Guowei Yang and Yunming Chen.     

Study on the Prediction Method of Low-Dimension Time Series that Arise from the Intrinsic Nonlinear Dynamics

The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low-dimension are discussed mainly. Based on the work of the foreign researchers, the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed. At first, the model parameters were estimated by using the improved least square method. Then as the precision was satisfied, the optimization method was used to estimate these parameters. At the end by using the obtained chaotic model, the future data of the chaotic time series in the phase space was predicted. Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper. The results show that if the algorithms developed here are adopted, the parameters of the corresponding chaotic model will be easily calculated well and true. Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations. And if the optimal model rank is chosen, the prediction precision will increase notably. Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable. Paper from Chen Yu-shu, Member of Editorial of Committee, AMM Foundation item: the National Natural Science Foundation of China (19990510); the National Key Basic Research Special Fund(G1998020316) Biography: Ma Jun-hai(1965-), Professor, Doctor     

1:2 Internal Resonance of Coupled Dynamic System with Quadratic and Cubic Nonlinearities

The1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in1:2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the4-dimension bifurcation equations were reduced to3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on4-dimension center manifolds. Paper from Chen Yu-shu, Member of Editorial Commuttee, AMM Foundation item: the National Natural Science Foundation of China (1990510); the National Key Basic Research Special Fund (G1998020316); the Doctoral Point Fund of Education Committee of China (D09901) Biography: Chen Yu-shu (1931-)     

Comments on <Emphasis Type="Italic">Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD</Emphasis>

The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.     

A finite element model for numerical simulation of thermo-mechanical frictional contact problems

Two kinds of variational principles for numerical simulation of heat transfer and contact analysis are respectively presented. A finite element model for numerical simulation of the thermal contact problems is developed with a pressure dependent heat transfer constitutive model across the contact surface. The numerical algorithm for the finite element analysis of the thermomechanical contact problems is thus developed. Numerical examples are computed and the results demonstrate the validity of the model and algorithm developed. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (50178016, 10225212) and the Foundation for University Key Teacher by the Ministry of Education of China     

Solving frictional contact problems by two aggregate-function-based algorithms

Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-function-based algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms. The project supported by the National Natural Science Foundation of China(10225212, 50178016, 10302007), the National Key Basic Research Special Foundation and the Ministry of Education of China The English text was polished by Ron Marshall.     

Recent progress in nonlinear eddy-viscosity turbulence modeling

This article presents recent progresses in turbulence modeling in the Unit for Turbulence Simulation in the Department of Engineering Mechanics at Tsinghua University. The main contents include: compact Non-Linear Eddy-Viscosity Model (NLEVM) based on the second-moment closure, near-wall low-Re non-linear eddy-viscosity model and curvature sensitive turbulence model. The models have been validated in a wide range of complex flow test cases and the calculated results show that the present models exhibited overall good performance. The project supported by the National Natural Science Foundation of China (10232020), the National Key Basic Research Special Fund of China (2001CB409600) and the National High-Tech Development Program (2002AA311240)     

An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

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Time discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed. As compared with the existing discontinuous Galerkin finite element methods, the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured, whereas the discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously reduced, particularly, for material non-linear problems. Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed. Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain. The project supported by the National Natural Science Foundation of China (19832010, 50278012, 10272027) and the National Key Basic Research and Development Program (973 Program, 2002CB412709)     

Scattering of love waves by an interface crack between a piezoelectric layer and an elastic substrate

The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration. Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China.     

A note for analysis of thermo-mechanical contact problems

A discussion about the bifurcation and non-uniqueness of solutions in the analysis of thermo-mechanical contact problems with initial gap is given. Without loss of generality, a mechanical contact problem coupled with steady heat transfer is studied and an example of non-uniqueness of solutions caused by the thermo-mechanical mechanism is presented. The important work is that the non-uniqueness of solutions, which is different from that found in the analysis of the traditional frictional contact problems, is studied in detail. The possible oscillation and non-convergence problems in the iteraction process of the numerical computation are discussed, and an enhanced algorithm is put forward to overcome the difficulties. Project sypported by the National Natural Science Foundation of China (Nos. 50178016, 10225212 and 19872016), the National Key Basic Research Special Foundation (No. G1999032805) and the Foundation for University Key Teacher by the Ministry of Education.     

A mixed finite element scheme for viscoelastic flows with XPP model

A mixed finite element formulation for viscoelastic flows is derived in this paper, in which the FIC （finite incremental calculus） pressure stabilization process and the DEVSS （discrete elastic viscous stress splitting） method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU （streamline-upwind） method is particularly chosen to tackle the convective terms in constitutive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP （extended Pom-Pom） constitutive model for describing viscoelastic behaviors is particularly integrated into the proposed scheme. The numerical results for the 4：1 sudden contraction flow problem demonstrate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the ＂die swell＂ phenomenon observed in the polymer injection molding process.     

Progress in the study of retrospective numerical scheme and the climate prediction

The retrospective numerical scheme (RNS) is a numerical computation scheme designed for multiple past value problems of the initial value in mathematics and considering the self-memory property of the system in physics. This paper briefly presents the historical background of RNS, elaborates the relation of the scheme with other difference, schemes and other meteorological prediction methods, and introduces the application of RNS to the regional climatic self-memory model, simplified climate model, barotropic model, spectral model, and mesoscale model. At last, the paper sums up and points out the application perspective of the scheme and the direction for the future study. The project supported by the Research Program of the Climatic System Model of China, the National Natural Science Foundation of China (40275031 and 40231006) and the National Key Program for Developing Basic Sciences (1999043408)     

A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Time delays in the feedback control often dete- riorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly time-varying input delay based on a transformation, which sire-plifies the time-delay system the relation is discussed for into a delay-free one. Firstly, two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.     

An improved level-set re-initialization solver

Re-initialization procedure in level-set interface capturing method were investigated. The algorithm accomplishes the re-initialization step through locking the interface positions. Better accuracy was obtained both on the interface positions and the total fluid volume keeping. Though one mare step of the interpolations is added in the procedure, there is no significant increase in total machine time spent.     

THE ROBUST CONTROL SCHEME FOR FREEFLOATING SPACE MANIPULATOR TO TRACK *THE DESIRED TRAJECTORY IN JOINTSPACE

The control of a free-floating space manipulator system is discussed. With the augmentation approach, the nonlinear parameterization problem of the dynamic equations of the space manipulator system is overcome. Based on the results, the robust control scheme for free-floating space manipulator with uncertain payload parameters to track the desired trajectory in jointspace is proposed, and the global convergence of the tracking is verified by using the Lyapunov method. The proposed control scheme is computationally simple, because we choose to make the controller robust to the uncertain inertial parameters rather than explicitly estimate them online. In particular, it needn't control the position and attitude of the floating base. A two-link planar space manipulator system is simulated to verify the control scheme proposed. Project supported by the National Natural Science Foundation of China (No. 19872032), Aeronautical Science Foundation, and Science Foundation of Fuzhou University.     

Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak. The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education