GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

Science Letters：On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems

A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.

NEW TYPE OF VIBRATION STRUCTURE OF VERTICAL DYNAMIC BALANCING MACHINE

A new type of vibration structure of vertical dynamic balancing machine isdesigned, which is based on the analysis for swing frame of a traditional vertical dynamic balancingmachine. The static unbalance and couple unbalance can be separated effectively by using the newmachine with the new swing frame. By building the dynamics model, the advantages of the newstructure are discussed in detail. The modal and harmonic response are analyzed by using theANSYS7.0. By comparing the finite element modal analysis with the experimental modal analysis, thenatural frequencies and vibration modes are found out. There are many spring boards in the new swingframe. Their stiffness is different and assort with each other. Furthermore, there are threesensors on the measurement points. Therefore, the new dynamic balancing machine can measure thestatic unbalance and couple unbalance directly, and the influence between them is faint. The newstructure has the function of belt-strain compensation to improve the measurement precision. Thepractical result indicates that the new vertical dynamic balancing machine is suitable for inertialmeasurement of flying objects, and can overcome the shortcomings of traditional double-planevertical dynamic balancing machines. The vertical dynamic balancing machine with the new vibrationstructure can be widely used in the future applications. The modeling and analysis of the newvibration structure provide theoretic instruction and practical experience for designing new type ofvertical dynamic balancing machines. Based on the design principles such as stiffness-matching,frequency-adjacence and strain-compensation and so on, various new type of vibration structures canbe designed.

A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

Numerical simulation of the sedimentation of cylindrical pollutant particles in fluid

The sedimentation of cylindrical pollutant particles which fall through a fluid is investigated. Differing from previous research work, particle oscillation and effect of particle on the fluid are considered, and the torque exerted on a particle when viscous fluid flow around a particle is got through experiment and included in the numerical simulation. The computational results showed that the sedimentation velocities of particle increase slowly with the increase of particle aspect ratio . For disk like particle, when the motion direction of particle is parallel to axis of particle, particle falls more slowly than the case of perpendicular to axis of particle; while for rod like particle, it is inverse. For sedimentation of a crowd of high frequency oscillating cylindrical particles with arbitrary initial orientation, both vertical velocity and horizontal velocity oscillate dramatically, the degree of oscillation of the former is stronger than the later. A crowd of particles fall more quickly than an isolated particle. Particles tend to strongly align in the direction of gravity. The computational results agreed well with the experimental ones and helpful for controlling of pollutant particles.

On the structural features of fiber suspensions in converging channel flow

The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in converging channel flow were calculated, and the evolutions of the fiber alignment and the bulk effective vis-cosity were analyzed. The results showed that the bulk stress and the effective viscosity were functions of therate-of-strain tensor and the fiber orientation state ; and that the fiber suspensions evolved to steady alignment and tended to concentrate to some preferred directions close to but not same as the directions of local stream-lines. The bulk effective viscosity depended on the product of Reynolds number and time. The decrease of ef-fective viscosity near the boundary benefited the increase of the rate of flow. Finally when the fiber alignment went into steady state, the structural features of fiber suspensions were not dependent on the Reynolds numberbut on the converging channel angle.

Research on the orientation distribution of fibers immersed in a pipe flow

The computed orientation distribution of fibers immersed in laminar pipe flows showed that the longitudinal distributions are wide for small Reynolds numbers and become narrower with increasing Re.For low Re number.the axial orientation distributions are broad with almost no preferred orientations.For high Re numer,the axial distribution becomes narrow.with sharp maxima..The mean values of the longitudinal orientation depend strongly on the Re number.The computed results are in qualitative agreemernt with relevant experimental results.

ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity.The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure.The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage, which is related to the piezoelectric properties.

Sedimentation of a single particle between two parallel walls

The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result.

A NEW STOCHASTIC OPTIMAL CONTROL STRATEGY FOR HYSTERETIC MR DAMPERS

A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic be- havior of an MR damper is characterized by the Bouc-Wen hysteretic model. The control force produced by the MR damper is separated into a passive part incorporated in the uncontrolled system and a semi-active part to be determined. The system combining the Bouc-Wen hysteretic force is converted into an equivalent non-hysteretic nonlinear stochastic control system. Then It?o stochastic di?erential equations are derived from the equivalent system by using the stochastic averaging method. A dynamical programming equation for the controlled di?usion processes is established based on the stochastic dynamical programming principle. The non-clipping nonlin- ear optimal control law is obtained for a certain performance index by minimizing the dynamical programming equation. Finally, an example is given to illustrate the application and e?ectiveness of the proposed control strategy.

Cavitation for Incompressible Anisotropic Hyper-Elastic Materials

The cavitation problem in a solid sphere composed of an incompressible anisotropic hyper elastic material under a uniform radial tensile dead load was examined. A new analytical solution was obtained. The stress contributions were given and the jumping and concentration of stresses were discussed. The stability of solutions and the effect of the degree of anisotropy of the material were analyzed.

ROBUST OPTIMUM DESIGN OF LAMINATED COMPOSITE PLATES

A last-ply failure (LPF) analysis method for laminated composite plates is incorpo- rated into the ?nite element code-ANSYS, and a robust optimum design method is presented. The composite structure is analyzed by considering both in-plane and out-of-plane loads. For a lamina, two major failure modes are considered: matrix failure and ?ber breakage that are characterized by the proper strength criteria in the literature. When a lamina has failed, the laminate sti?ness is modi?ed to re?ect the damage, and stresses in the structure are re-analyzed. This procedure is repeatedly performed until the whole structure fails and thus the ultimate strength is determined. A structural optimization problem is solved with the ?ber orientation and the lamina thickness as the design variables and the LPF load as the objective. Finally, the robust optimum design method for laminates is presented and discussed.

COMBINED DAMAGE FRACTURE CRITERIA FOR PIEZOELECTRIC CERAMICS

Mechanical and electrical damages are introduced to study the fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are established using the method of least squares combined with a damage analysis of the well-known piezoelectric fracture experiments of Park and Sun’s. One is based on a linear combination of the mechanical and electrical damages and the other on their nonlinear combination. When the combined damage D is up to its critical value Dc, piezoelectric fracture occurs. It is found from the qualitative comparison of the numerical results with the experimental data that the nonlinearly combined damage fracture criterion can give a better prediction of piezoelectric fracture. And it is concluded from the nonlinearly combined damage fracture criterion that a negative electric feld impedes fracture whereas the efect of a positive electric feld on fracture depends on its magnitude.

NONLINEAR DYNAMIC SIMULATION OF AN AXIALLY SLIDE-SPIN ROCKET FLEXIBLE SYSTEM WITH CLEARANCE

A hybrid approach is presented to investigate the dynamic behavior of anaxially slide-spin flexible rocket with nonlinear clearance. The equations of motion of the flexiblerocket are derived based upon Euler-Bernoulli beam theory and Hamilton principle and the finiteelement method. The characteristics of clearance between the spinning rocket and launcher areconsidered to be piecewise linear. Numerical solution is developed by direct integration method anddemonstrates the validity of the method. The coupled dynamic behavior of axial motion and transversevibrations of rocket are analyzed, and the influences of axially moving acceleration, spin speed,linking stiffness of elastic 'shoes', and the nonlinearity of clearance on the motion attitude ofrocket are studied.

The stress-microstructure relationship in an evolving mixing layer of fiber suspensions

The equations for fiber suspensions in an evolving mixing layer were solved by the spectral method, and the trajectory and orientation of fibers were calculated based on the slender body theory. The calculated spatial and orientation distributions of fibers are consistent with the experimental ones that were performed in this paper. The relationship between the microstructure of fibers and additional stress was examined. The results show that the spatial and orientation distributions of fibers are heterogeneous because of the influence of coherent vortices in the flow, which leads to the heterogeneity of the additional stress. The degree of heterogeneity increases with the increasing of St number and fiber aspect ratio. The fibers in the flow make the momentum loss thickness of the mixing layer thicker and accelerate the vorticity dispersion.

THE INFLUENCE OF SHRINKAGE AND MOISTURE DIFFUSION ON IDEALIZED TOOTH STRUCTURE INVOLVING DEBONDING DAMAGE

This study highlights the joint effect of early polymerization shrinkage and long-term moisture diffusion on the behavior of the restoration-tooth structure. The interphase debonding between particle and polymer resin in dental composite is taken into account by introducing the damage variable. The idealized model is designed and constructed for representing the restorationtooth structure, which consists of enamel, dentin, composite and interphase, each considered as homogenous material. The simulation is carried out using the general-purpose finite element software package, ABAQUS incorporated with a user subroutine for definition of damaged material behavior. The influence of Young's moduli of composite and interphase on stress and displacement is discussed. The compensating effect of water sorption on the polymerization shrinkage is examined with and without involving damage evolution. A comparison is made between the influence of hyper-, equi- and hypo-water sorption. Interfacial failure in the specific regions as well as cuspal movement has been predicated. The damage evolving in dental composite reduces the rigidity of composite, thus in turn reducing consequent stress and increasing consequent displacement. The development of stresses at the restoration-tooth interface can have a detrimental effect on the longevity of a restoration.

GENERALIZED VARIATIONAL PRINCIPLES FOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.

STRESS ANALYSIS AND GEOMETRICAL CONFIGURATION SELECTION FOR MULTILAYER PIEZOELECTRIC DISPLACEMENT ACTUATOR

Multilayer piezoelectric ceramic displacement actuators are susceptible to cracking in the region near the edge of the internal electrode, which may cause system damage or failure. In this paper, the stress distribution of a multilayer piezoelectric composite is investigated in a working environment and the optimized geometrical con?guration of the piezoelectric layer is obtained. The stress distribution in the structure and the stress concentration near the edge of the internal electrode, induced by non-uniform electric ?eld distribution, are analyzed by moir′e interferometry experiment and ?nite element numerical simulation. Based on the above analysis, two optimized geometrical models are presented for the purpose of geometrical con?guration selection, with which stress concentration can be reduced signi?cantly while the feasibility of the machining process and the basic structural functions occurring in the conventional model are retained. The numerical results indicate that the maximum stress in the optimized models is e?ectively diminished compared to the conventional model. For instance, the peak value of the principal stress in the optimized model II is 93.1% smaller than that in the conventional model. It is proved that stress concentration can be e?ectively relaxed in the latter of the two optimized models and thus the probability of fracture damage can be decreased.

A micro-mechanical model of knitted fabric and its application to the analysis of buckling under tension in wale direction:buckling analysis

With the aid of the micro-mechanical model of knitted fabric proposed in Part 1 we analyze the buckling of a knitted fabric sheet when it is subjected to a tension along the wale direction. The large deformation of the fabric sheet in the critical configuration is considered and, to avoid possible deviation due to the approximation of the theory of thin plate, the three-dimensional theory of instability is used. The fabric sheet is considered as a three-dimensional body and all boundary conditions are satisfied. It is shown that the buckling of the fabric sheet is possible, two buckling modes and the corresponding buckling conditions are obtained, but only the flexural mode is physically possible as observed in experiments.

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface,in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell,by means of expanding field quantities as Legendre series,a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate,which has a satisfactory computational effectiveness and precision for an arbitrary frequency range.It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed.It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell,and give the coupling system a very rich resonance frequency spectrum.Moreover,the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.