Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval

A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed in this paper. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to be ill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, we can see that the new algorithm is not limited to be only efficient for the data measured in the near-field of the Fresnel region and thus it has a broader validity range.     

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables , was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.     

Lift force on rotating sphere at low Reynolds numbers and high rotational speeds

The lift force on an isolated rotating sphere in a uniform flow was investigated by means of a three-dimensional numerical simulation for low Reynolds numbers (based on the sphere diameter) (Re<68.4) and high dimensionless rotational speeds (Г5). The Navier-Stokes equations in Cartesian coordinate system were solved using a finite volume formulation based on SIMPLE procedure. The accuracy of the numerical simulation was tested through a comparison with available theoretical, numerical and experimental results at low Reynolds numbers, and it was found that they were in close agreement under the above mentioned ranges of the Reynolds number and rotational speed. From a detailed computation of the flow field around a rotational sphere in extended ranges of the Reynolds number and rotational speed, the results show that, with increasing the rotational speed or decreasing the Reynolds number, the lift coefficient increases. An empirical equation more accurate than those obtained by previous studies was obtained to describe both effects of the rotational speed and Reynolds number on the lift force on a sphere. It was found in calcttlations that the drag coefficient is not significantly affected by the rotation of the sphere. The ratio of the lift force to the drag force, both of which act on a sphere in a uniform flow at the same time, was investigated. For a small spherical particle such as one of about 100μm in diameter, even if the rotational speed reaches about 10^6 revolutions per minute, the lift force can be neglected as compared with the drag force.     

SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FOUNDATION

A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb's solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.     

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.     

A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING

A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method (FEM) and the boundary element method (BEM). The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element (FE-BE) coupling method.     

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional three-dimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.     

Bending analysis of five-layer curved functionally graded sandwich panel in magnetic field: closed-form solution

In this paper,an exact closed-form solution for a curved sandwich panel with two piezoelectric layers as actuator and sensor that are inserted in the top and bottom facings is presented.The core is made from functionally graded(FG)material that has heterogeneous power-law distribution through the radial coordinate.It is assumed that the core is subjected to a magnetic field whereas the core is covered by two insulated composite layers.To determine the exact solution,first characteristic equations are derived for different material types in a polar coordinate system,namely,magneto-elastic,elastic,and electro-elastic for the FG,orthotropic,and piezoelectric materials,respectively.The displacement-based method is used instead of the stress-based method to derive a set of closed-form real-valued solutions for both real and complex roots.Based on the elasticity theory,exact solutions for the governing equations are determined layer-by-layer that are considerably more accurate than typical simplified theories.The accuracy of the presented method is compared and validated with the available literature and the finite element simulation.The effects of geometrical and material parameters such as FG index,angular span along with external conditions such as magnetic field,mechanical pressure,and electrical difference are investigated in detail through numerical examples.     

EFFICIENT NUMERICAL INTEGRATORS FOR HIGHLY OSCILLATORY DYNAMIC SYSTEMS BASED ON MODIFIED MAGNUS INTEGRATOR METHOD

Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method was proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the second-order dynamic system was reformulated as the first-order system and the frame of reference was transfered by introducing new variables so that highly oscillatory behaviour inherits from the entries in the meantime. Then the modified Magnus integrator method based on local linearization was appropriately designed for solving the above new form and some improved also were presented. Finally, numerical examples show that the proposed methods appear to be quite adequate for integration for highly oscillatory dynamic systems including Hamiltonian systems problem with long time and effectiveness     

LOCAL DISCONTINUOUS GALERKIN METHOD FOR RADIAL POROUS FLOW WITH DISPERSION AND ADSORPTION

Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu, according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption, a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed, a high order accurary new scheme for radial porous flow is obtained. The presented method was applied to the numerical tests of two cases of radial porous, i. e. , the convection-dispersion flow and the convection-dispersion-adsorption flow, the corresponding parts of the numerical results are in good agreement with the published solutions, so the presented method is reliable. Reckoning of the computational cost also shows that the method is practicable.     

INVESTIGATION ON GRADIENT-DEPENDENT NONLOCAL CONSTITUTIVE MODELS FOR ELASTO-PLASTICITY COUPLED WITH DAMAGE

IntroductionIntheframeworkofconventionalplasticity ,materialinstabilityisoneoftheprincipalfactorsthatresultinginthestrainlocalizationphenomenon .Byusingtheterminology‘homogenized’ ,itisreferredtothefactthatinitialflawsandboundaryconditionsnecessarilyinduceanon_homogeneousstressstateinaspecimenduringtesting .Inparticularintheprocessofprogressivefailure ,theflawsandlocalstressconcentrationwillcausestronglyinhomogeneousdeformationofthespecimen[1,2 ].Asthedeformation_inducedfracture/damagephenom…     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｙｎａｍｉｃｅｑｕａｔｉｏｎｓｏｆｍｏｔｉｏｎｏｆｍｕｌｔｉｂｏｄｙｓｙｓｔｅｍｓｗｉｔｈｃｏｎｓｔｒａｉｎｔｓａｒｅｔｈｅｆｏｌｌｏｗｉｎｇｄｉｆｆｅｒｅｎｔｉａｌ／ａｌｇｅｂｒａｉｃｅｑｕａｔｉｏｎｓ,ｉ．ｅ．,Ｅ...     

Interval Arithmetic and Static Interval Finite Element Method

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅａｎａｌｙｓｉｓａｎｄｄｅｓｉｇｎｏｆｓｔｒｕｃｔｕｒｅｓ,ｓｏｍｅｕｎａｖｏｉｄａｂｌｅｕｎｃｅｒｔａｉｎｔｉｅｓ ,ｓｕｃｈａｓｔｈａｔｏｆｍａｔｅｒｉａｌａｎｄｇｅｏｍｅｔｒｉｃａｌｐｒｏｐｅｒｔｉｅｓ,ｌｏａｄｓ ,ａｎｄｓｏｏｎ ,ｓｈｏｕｌｄｂｅｒｅａｓｏｎａｂｌｙｔａｋｅｎｉｎｔｏａｃｃｏｕｎｔ.Ｉｎｔｈｅｐａｓｔｄｅｃａｄｅｓ,ｔｈｅｓｅｕｎｃｅｒｔａｉｎｔｉｅｓｗｅｒｅｍｏｓｔｌｙｔｒｅａｔｅｄｗｉｔｈｐｒｏｂａｂｉｌｉｔｙｔｈｅｏｒｙｏｒｒａｎｄｏｍｐ…     

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.     

A mixture differential quadrature method for solving two-dimensional incompressible Navier-Stokes equations

Ｔｈｅｄｉｆｆｅｒｅｎｔｉａｌｑｕａｄｒａｔｕｒｅｍｅｔｈｏｄ（ＤＱＭ）ｐｒｏｐｏｓｅｄｂｙＲ．Ｂｅｌｌｍａｎ［１,２］ｈａｓｂｅｅｎｓｕｃｃｅｓｓｆｕｌｌｙｅｍｐｌｏｙｅｄｉｎｎｕｍｅｒｉｃａｌｃｏｍｐｕｔａｔｉｏｎｓｏｆｐｒｏｂｌｅｍｓｉｎｅｎｇｉｎｅｅｒｉｎｇａｎｄｐｈｙｓｉｃａｌｓｃｉｅｎｃｅ．ＢｅｃａｕｓｅｔｈｅｉｎｆｏｒｍａｔｉｏｎｏｎａｌｌｇｒｉｄｐｏｉｎｔｓｉｓｕｓｅｄｔｏｆｉｔｔｈｅｄｅｒｉｖａｔｉｖｅｓａｔｇｒｉｄｐｏｉｎｔｓｉｎｔｈｅＤＱＭ,ｉｔｉｓｅｎｏｕｇｈｔｏｏｂｔａ…     

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.     

Lie symmetries and conserved quantities of nonconservative nonholonomic systems in phase space

The invariance and conserved quantities of the nonconservative nonholonomic systems are studied by introducing the infinitesimal transformations in phase space.The Lie’s symmetrical determining equations are establish ed.The Lie’s symmetrical structure equation is obtained.An example to illustrate the application of the result is given.     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

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)     

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.