Elastic Model of Flexure-Based Linkage under Motion Constrains and External Load

For a flexible mechanism with several-stage flexible linkage, the flexible linkage is equivalent to work under the actions of an external load and motion constrains. This paper aims to deal with a simplified elastic model on the kinematic characteristics of a flexure-based linkage under these conditions. The elastic modeling method was developed based on motion constrains and the elastic beam theorem(EBT). Effects of a constant force, an elastic force with a constant stiffness, and the materials were taken into account. The proposed modeling method was verified by comparing with the finite element method(FEM). Further, the developed modeling method was used to optimize a flexure-based mechanism based on a two-stage flexible linkage to realize a maximum displacement amplification ratio of 6.56. The flexure-based mechanism was employed to drive a miniature sucker, which performed with a negative pressure of 2.45 kPa at a frequency of 13.2 kHz.

Trajectory compensation for multi-robot coordinated lifting system considering elastic catenary of the rope

The multi-robot coordinated lifting system is an unconstrained system with a rigid and flexible coupling.The deformation of the flexible rope causes errors in the movement trajectory of the lifting system.Based on the kinematic and dynamic analysis of the lifting system,the elastic catenary mod-el considering the elasticity and mass of the flexible rope is established,and the effect of the deform-ation of the flexible rope on the position and posture of the suspended object is analyzed.According to the deformation of flexible rope,a real-time trajectory compensation method is proposed based on the compensation principle of position and posture.Under the lifting task of the low-speed move-ment,this is compared with that of the system which neglects the deformation of the flexible rope.The trajectoy of the lifting system considering the deformation of flexible rope.The results show that the mass and elasticity of the flexible rope can not be neglected.Meanwhile,the proposed trajectory compensation method can improve the movement accuracy of the lifting system,which verifies the ef-fectiveness of this compensation method.The research results provide the basis for trajectory plan-ning and coordinated control of the lifting system。

The Time-Consistent Optimal Reinsurance Strategy of Insurance Group under the CEV Model

The article introduces proportional reinsurance contracts under the mean-variance criterion,studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsurance companies.The insurance claims process follows a jump-diffusion model,assuming that the risk asset prices of insurance companies and reinsurance companies follow CEV models different from each other.In the framework of game theory,the time-consistent equilibrium reinsurance strategy is obtained by solving the extended HJB equation analytically.Finally,numerical examples are used to illustrate the impact of model parameters on equilibrium strategies and provide economic explanations.The results indicate that the decision weights of insurance companies and reinsurance companies do have a significant impact on both the reinsurance ratio and the equilibrium reinsurance strategy.

On the Elastic Vibration Model for High Length-Diameter Ratio Rocket with Attitude Control System

An elastic vibration model for high length diameter ratio spinning rocket with attitude control system which can be used for trajectory simulation is established. The basic theory of elastic dynamics and vibration dynamics were both used to set up the elastic vibration model of rocket body. In order to study the problem more conveniently, the rocket's body was simplified to be an even beam with two free ends. The model was validated by simulation results and the test data.

Study of elastic wave propagation in two phase anisotropic media by numerical modeling of pseudospectral method

When there exists anisotropy in underground media elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed.

PERFORMANCE MODELING AND ANALYSIS OF BLOOD FLOW IN ELASTIC ARTERIES

Two different non_Newtonian models for blood flow are considered,first a simple power law model displaying shear thinning viscosity,and second a generalized Maxwell model displaying both shear thinning viscosity and oscillating flow viscous_elasticity.These models are used along with a Newtonian model to study sinusoidal flow of blood in rigid and elastic straight arteries in the presence of magnetic field.The elasticity of blood does not appear to influence its flow behavior under physiological conditions in the large arteries,purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions.On using the power law model with high shear rate for sinusoidal flow simulation in elastic arteries,the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to Newtonian fluid for the same pressure gradient.The governing equations have been solved by Crank_Niclson scheme.The results are interpreted in the context of blood in the elastic arteries keeping the magnetic effects in view.For physiological flow simulation in the aorta,an increase in mean wall shear stress,but a reduction in peak wall shear stress were observed for power law model compared to a Newtonian fluid model for matched flow rate wave form.Blood flow in the presence of transverse magnetic field in an elastic artery is investigated and the influence of factors such as morphology and surface irregularity is evaluated.

Ferroelectricity in a diatomic Ising chain as investigated by the elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca3CoMnO6, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca3Co2-xMnxO6 （x ≈ 0.96） （Phys. Rev. Lett. 100 047601 （2008））, although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.

Prediction Model of Abutment Pressure Affected by Far-Field Hard Stratum Based on Elastic Foundation Theory

In view of the three-dimensional dynamic abutment pressure,the influence of the far-field hard stratum(FHS)in deep,thick coal seams is indeterminant.Based on elastic foundation theory,a three-dimensional dynamic prediction model of the abutment pressure was established.Using this model,the dynamic change in the coal seam abutment pressure caused by the movement of the FHS was studied,and a method for determining the dynamic change range of the abutment pressure was developed.The results of the new prediction model of the abutment pressure are slightly higher than the measured values,with an error of 0.51%,which avoids the shortcomings of the results because the Winkler foundation model results are lower than the measured values and have an error of 9.98%.As time progresses,the abutment pressure and its distribution range are affected by the FHS movement,which has the characteristics of gradually increasing dynamic change until the FHS fractures.The peak value of the abutment pressure increases linearly with time,and the influence range increases with time following a power function with an exponent of less than 1.The influence range of the FHS movement on the abutment pressure ahead of the working face,behind the working face,and along the working face is 10 times,25 times,and 17 times the mining thickness,respectively.According to the actual geological parameters,the dynamic change range of the coal seam abutment pressure was determined by drawing an additional stress curve and by determining the threshold value.These research results are of great significance to the partition optimization of the roadway support design of deep,thick coal seams.

A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model

In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （no-shorting）. First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman （HJB） equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem （i.e., the efficientstrategies and efficient frontier） are derived explicitly.

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal（MPFC） model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.

Multi-scale Simulation Method with Coupled Finite/Discrete Element Model and Its Application

The existing research on continuous structure is usually analyzed with finite element method (FEM) and granular medium with discrete element method (DEM), but there are few researches on the coupling interaction between continuous structure and discrete medium. To the issue of this coupling interaction, a multi-scale simulation method with coupled finite/discrete element model is put forward, in their respective domains of discrete and finite elements, the nodes follow force law and motion law of their own method, and on the their interaction interface, the touch type between discrete and finite elements is distinguished as two types: full touch and partial touch, the interaction force between them is calculated with linear elastic model. For full touch, the contact force is proportional to the overlap distance between discrete element and finite element patch. For partial touch, first the finite element patch is extended on all sides indefinitely to be a complete plane, the full contact force can be obtained with the touch type between discrete element and plane being viewed as full touch, then the full overlap area between them and the actual overlap area between discrete element and finite element patch are computed, the actual contact force is obtained by scaling the full contact force with a factor which is determined by the ratio of the actual overlap area to the full overlap area. The contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the ideal simulation results can be got. This method has been used to simulate the cutter disk of the earth pressure balance shield machine (EPBSM) made in North Heavy Industry (NHI) with its excavation diameter of 6.28 m cutting and digging the sandy clay layer. The simulation results show that as the gradual increase of excavating depth of the cutter head, the maximum stress occurs at the roots of cutters on the cutter head, while for the soil, the largest stress is distributed at the region which directly contacted with the cutters. The proposed research can provide good solutions for correct design and installation of cutters, and it is necessary to design mounting bracket to fix cutters on cutter head.

Investigation of Coulomb stress changes in south Tibet(central Himalayas) due to the 25th April 2015 M_W 7.8 Nepal earthquake using a Coulomb stress transfer model

After Mw 7.8 Nepal earthquake occurred, the rearrangement of stresses in the crust commonly leads to subsequent damaging earthquakes. We present the calculations of the coseismic stress changes that resulted from the 25th April event using models of regional faults designed according to south Tibet-Nepal structure, and show that some indicative significant stress increases. We calculate static stress changes caused by the displacement of a fault on which dislocations happen and an earthquake occurs. A Mw 7.3 earthquake broke on 12 May at a distance of - 130 km SEE of the Mw 7.8 earthquake, whose focus roughly located on high Coulomb stress change （CSC） site. Aftershocks （first 15 days after the mainshock） are associated with stress increase zone caused by the main rupture. We set receiver faults with specified strikes, dips, and rakes, on which the stresses imparted by the source fault are resolved. Four group normal faults to the north of the Nepal earthquake seismogenic fault were set as receiver faults and variant results followed. We provide a discussion on Coulomb stress transfer for the seismogenic fault, which is useful to identify potential future rupture zones.

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.

Influence of random shrinkage porosity on equivalent elastic modulus of casting： A statistical and numerical approach

Shrinkage porosity is a type of random distribution defects and exists in most large castings. Different from the periodic symmetry defects or certain distribution defects, shrinkage porosity presents a random "cloud-like" configuration, which brings difficulties in quantifying the effective performance of defected casting. In this paper, the influences of random shrinkage porosity on the equivalent elastic modulus of QT400-18 casting were studied by a numerical statistics approach. An improved random algorithm was applied into the lattice model to simulate the "cloud-like" morphology of shrinkage porosity. Then, a large number of numerical samples containing random levels of shrinkage were generated by the proposed algorithm. The stress concentration factor and equivalent elastic modulus of these numerical samples were calculated. Based on a statistical approach, the effects of shrinkage porosity's distribution characteristics, such as area fraction, shape, and relative location on the casting's equivalent mechanical properties were discussed respectively. It is shown that the approach with randomly distributed defects has better predictive capabilities than traditional methods. The following conclusions can be drawn from the statistical simulations:(1) the effective modulus decreases remarkably if the shrinkage porosity percent is greater than 1.5%;(2) the average Stress Concentration Factor(SCF) produced by shrinkage porosity is about 2.0;(3) the defect's length across the loading direction plays a more important role in the effective modulus than the length along the loading direction;(4) the surface defect perpendicular to loading direction reduces the mean modulus about 1.5% more than a defect of other position.

Selection of regression models for predicting strength and deformability properties of rocks using GA

Recently,many regression models have been presented for prediction of mechanical parameters of rocks regarding to rock index properties.Although statistical analysis is a common method for developing regression models,but still selection of suitable transformation of the independent variables in a regression model is diffcult.In this paper,a genetic algorithm(GA)has been employed as a heuristic search method for selection of best transformation of the independent variables(some index properties of rocks)in regression models for prediction of uniaxial compressive strength(UCS)and modulus of elasticity(E).Firstly,multiple linear regression(MLR)analysis was performed on a data set to establish predictive models.Then,two GA models were developed in which root mean squared error(RMSE)was defned as ftness function.Results have shown that GA models are more precise than MLR models and are able to explain the relation between the intrinsic strength/elasticity properties and index properties of rocks by simple formulation and accepted accuracy.

Elastic Modulus Limit of Support Layer in Twin-Block Ballastless Track Based on Train Load Effect

The support layer is an important component of twin-block ballastless track. The modulus of the support layer is an important design parameter and must be carefully solved. We studied the bending stress and deformation of track slab and support layer due to train load using the beam-plate finite element model on elastic foundation. The results show that support layer type has great impact on both support layer deformation and the stress on subgrade, but has little impact on the bending stress of either track slab or support layer. The continuous support layer type, and articulated support layer type with shear transfer device at their ends, are recommended. In order to keep the stress in the support layer less than that in track slab, the modulus of the continuous, unit, and articulated types of support layer （ in unit twin-block ballastless track）, and the support layer in continuous twin-block ballastless track, should not be larger than 15, 22, 20.5 and 5 GPa, respectively. In addition, the modulus of the unit-type support layer should not be more than 20 GPa, to ensure the step in support layer remains less than 1 mm.

Motion estimation of elastic articulated objects from image contours

A new method of elastic articulated objects (human bodies) modeling was presented based on a new conic curve. The model includes 3D object deformable curves which can represent the deformation of human occluding contours. The deformation of human occluding contour can be represented by adjusting only four deformation parameters for each limb. Then, the 3D deformation parameters are determined by corresponding 2D contours from a sequence of stereo images. The algorithm presented in this paper includes deformable conic curve parameters determination and the plane, 3D conic curve lying on, parameter determination.

Enhanced elastic beam model with BADS integrated for settlement assessment of immersed tunnels

Excessive settlement may induce structural damage and water leakage in immersed tunnels,seriously threatening the tunnels’safety.However,making accurate assessment of the settlement in immersed tunnels is difficult due to the incomplete knowledge of the geotechnical parameters and the inadequacy of the model itself.This paper proposes an effective method to accurately assess the settlement in immersed tunnels.An enhanced beam on elastic foundation model(E-BEFM)is developed for the settlement assessment,with the Bayesian adaptive direct search algorithm adopted to estimate unknown model parameters based on previous observations.The proposed method is applied to a field case of the Hong Kong–Zhuhai–Macao immersed tunnel.The original BEFM is used for comparison to highlight the better assessment performance of E-BEFM,particularly for joints’differential settlement.Results show that the proposed method can provide accurate predictions of the total settlement,angular distortion(a representation of tubes’relatively differential settlement),and joints’differential settlement,which consequently supports the associated maintenance decision-making and potential risk prevention for immersed tunnels in service.

On the role of piezoelectricity in phonon properties and thermal conductivity of GaN nanofilms

The effect of piezoelectricity on phonon properties and thermal conductivity of gallium nitride （GaN） nanofilms is theoretically investigated. The elasticity model is utilized to derive the phonon properties in spatially confined GaN nanofilms. The piezoelectric constitutive relation in GaN nanofilms is taken into account in calculating the phonon dispersion relation. The modified phonon group velocity and phonon density of state as well as the phonon thermal conductivity are also obtained due to the contribution of piezoelectricity. Theoretical results show that the piezoelectricity in GaN nanofilms can change significantly the phonon properties such as the phonon group velocity and density of states, resulting in the variation of the phonon thermal conductivity of GaN nanofilms remarkably. Moreover, the piezoelectricity of GaN can modify the dependence of thermal conductivity on the geometrical size and temperature. These results can be useful in modeling the thermal performance in the active region of GaN-based electronic devices.