Simulation Analysis of Torsion Beam Hydroforming Based on the Fluid-Solid Coupling Method

Hydroformed parts are widely used in industrial automotive parts because of their higher stiffness and fatigue strength and reduced weight relative to their corresponding cast and welded parts.This paper reports a hydraulicforming experimental platform for rectangular tube fittings that was constructed to conduct an experiment on the hydraulic forming of rectangular tube fittings.A finite element model was established on the basis of the fluid–solid coupling method and simulation analysis.The correctness of the simulation analysis and the feasibility of the fluid–solid coupling method for hydraulic forming simulation analysis were verified by comparing the experimental results with the simulation results.On the basis of the simulation analysis of the hydraulic process of the torsion beam using the fluid–solid coupling method,a sliding mold suitable for the hydroforming of torsion beams was designed for its structural characteristics.The effects of fluid characteristics,shaping pressure,axial feed rate,and friction coefficient on the wall thicknesses of torsions beams during formation were investigated.Fluid movement speed was related to tube deformation.Shaping pressure had a significant effect on rounded corners and straight edges.The axial feed speed was increased,and the uneven distribution of wall thicknesses was effectively improved.Although the friction coefficient had a nonsignificant effect on the wall thickness of the ladder-shaped region,it had a significant influence on a large deformation of wall thickness in the V-shaped area.In this paper,a method of fluid-solid coupling simulation analysis and sliding die is proposed to study the high pressure forming law in torsion beam.

Rigid block characteristics on subaerial landslide-tsunamis using a 3D coupled Eulerian-Lagrangian model

To quantitatively reveal how rock blocks falling into water affect the impulse waves,the influence of a rigid block on induced first wave and second wave is systematically investigated.The block characteristics include the initial velocity,density,volume,and incident angle,and the investigated wave behavior characteristics include the maximum kinetic energy of the water,the transformation ratio of the kinetic energy from the block to the waves,the duration of the waves,the maximum movement speed,and the maximum height and width of the waves.The coupled Eulerian-Lagrangian method(CEL)is introduced to establish the numerical models of the fluid-solid coupling,and a laboratory test of a rigid wedge sliding into water demonstrates that it can reasonably describe the dynamic behavior of a landslide-induced wave.A typical process of a block entering water and its energy variation are described and analyzed in detail.Further,the relationship between each characteristic parameter of the block and the waves is quantitatively investigated and fitted.The simulation results show that energy exchange between the block and the water is very rapid after the block collides with the water.The maximum kinetic energy,maximum velocity,duration,and side dimension of the waves mainly increase non-linearly with the above characteristic parameters of the block.The transformation ratio of the kinetic energy from the block to the water,the first wave,and the second wave are usually below 60%,45%,and 30%,respectively.The velocity of the block first decreases and then maintains a constant speed after entering the water.The displacement of the block increases linearly with the initial velocity and density of the block and exponentially increases with the block volume at different times.With the increase in the incident angle of the block,the kinetic energy and scale of the second wave increase correspondingly.

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics.The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given.The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given.The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail,and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron.

Fully coupled fluid-solid productivity numerical simulation of multistage fractured horizontal well in tight oil reservoirs

A mathematical model, fully coupling multiple porous media deformation and fluid flow, was established based on the elastic theory of porous media and fluid-solid coupling mechanism in tight oil reservoirs. The finite element method was used to determine the numerical solution and the accuracy of the model was verified. On this basis, the model was used to simulate productivity of multistage fractured horizontal wells in tight oil reservoirs. The results show that during the production of tight oil wells, the reservoir region close to artificial fractures deteriorated in physical properties significantly, e.g. the aperture and conductivity of artificial fractures dropped by 52.12% and 89.02% respectively. The simulations of 3000-day production of a horizontal well in tight oil reservoir showed that the predicted productivity by the uncoupled model had an error of 38.30% from that by the fully-coupled model. Apparently, ignoring the influence of fluid-solid interaction effect led to serious deviations of the productivity prediction results. The productivity of horizontal well in tight oil reservoir was most sensitive to the start-up pressure gradient, and second most sensitive to the opening of artificial fractures. Enhancing the initial conductivity of artificial fractures was helpful to improve the productivity of tight oil wells. The influence of conductivity, spacing, number and length of artificial fractures should be considered comprehensively in fracturing design. Increasing the number of artificial fractures unilaterally could not achieve the expected increase in production.

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated.A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils.The accuracy of the model is validated using a classic example in literature.The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils.The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model.The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy.The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model,which provides a weaker confining action to the underground structure.

FLUID-SOLID COUPLING MATHEMATICAL MODEL OF CONTAMINANT TRANSPORT IN UNSATURATED ZONE AND ITS ASYMPTOTICAL SOLUTION

The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid_solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure_saturation_permeability in laboratory.

Fluid-solid coupling model for studying wellbore instability in drilling of gas hydrate bearing sediments

As the oil or gas exploration and development activities in deep and ultra- deep waters become more and more, encountering gas hydrate bearing sediments （HBS） is almost inevitable. The variation in temperature and pressure can destabilize gas hydrate in nearby formation around the borehole, which may reduce the strength of the formation and result in wellbore instability. A non-isothermal, transient, two-phase, and fluid-solid coupling mathematical model is proposed to simulate the complex stability performance of a wellbore drilled in HBS. In the model, the phase transition of hydrate dissociation, the heat exchange between drilling fluid and formation, the change of mechanical and petrophysical properties, the gas-water two-phase seepage, and its interaction with rock deformation are considered. A finite element simulator is developed, and the impact of drilling mud on wellbore instability in HBS is simulated. Results indicate that the re- duction in pressure and the increase in temperature of the drilling fluid can accelerate hydrate decomposition and lead to mechanical properties getting worse tremendously. The cohesion decreases by 25% when the hydrate totally dissociates in HBS. This easily causes the wellbore instability accordingly. In the first two hours after the formation is drilled, the regions of hydrate dissociation and wellbore instability extend quickly. Then, with the soaking time of drilling fluid increasing, the regions enlarge little. Choosing the low temperature drilling fluid and increasing the drilling mud pressure appropriately can benefit the wellbore stability of HBS. The established model turns out to be an efficient tool in numerical studies of the hydrate dissociation behavior and wellbore stability of HBS.

Hlder continuity of two types of bidirectionally coupled generalised synchronisation manifold

This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation （GS）. Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.

Fluctuation theorem for entropy production at strong coupling

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium,which are helpful for understanding the thermodynamic state evolution.We investigate fluctuation theorems for strong coupling between a system and its reservoir,by path-dependent definition of work and heat satisfying the first law of thermodynamics.We present the fluctuation theorems for two kinds of entropy productions.One is the informational entropy production,which is always non-negative and can be employed in either strong or weak coupling systems.The other is the thermodynamic entropy production,which differs from the informational entropy production at strong coupling by the effects regarding the reservoir.We find that,it is the negative work on the reservoir,rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling.Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.

Positive Solutions for Singular Boundary Value Problems of Coupled Systems of Nonlinear Differential Equations

We establish the existence of positive solutions for singular boundary value problems of coupled systems? The proof relies on Schauder’s fixed point theorem. Some recent results in the literature are generalized and improved.

Existence and Uniqueness of Positive Solutions for a Coupled System of Nonlinear Fractional Differential Equations

In this paper, we research the existence and uniqueness of positive solutions for a coupled system of fractional differential equations. By means of some standard fixed point principles, some results on the existence and uniqueness of positive solutions for coupled systems are obtained.

Revised Virial Theorem for Hamiltonians with Coordinates-Momentum Coupling Terms

Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.

Positive Solutions of Boundary Value Problem for a Coupled System of Nonlinear Third-order Differential Equations

By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.

GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.

耦合拟线性扩散方程组Cauchy问题解的渐近行为

本文考虑一类含有对流项的耦合拟线性反应扩散方程组的Cauchy问题解的渐近行为,得到了临界Fujita指标并建立了Fujita型定理.该临界Fujita指标不仅与扩散项、反应项和空间维度有关,而且还和对流项有关.利用能量积分估计得到方程组解的爆破性;并利用构造方程组的自相似上解和比较原理得到方程组解的整体存在性.

具有积分边界条件的耦合φ-Hilfer分数阶微分系统解的存在性

为了拓展分数阶微分方程系统的相关理论,研究了一类具有积分边界条件的耦合φ-Hilfer分数阶微分系统。首先,将具有积分边界条件的耦合φ-Hilfer分数阶微分系统转化为积分系统;其次,定义合适的Banach乘积空间和范数,构造合适的积分算子,分别运用压缩映像原理和Kransnoselskii不动点定理得出耦合φ-Hilfer分数阶微分系统在积分边界条件下解的存在性结果;最后,通过列举实例说明所得结论的正确性。研究表明,积分边界条件下的耦合φ-Hilfer分数阶微分系统的解具有存在性。研究结论丰富了耦合分数阶微分系统理论可解性的相关理论,可为深入研究分数阶微分方程提供一定的理论参考。

距离空间中有限个等式约束下的Geraghty型耦合不动点问题

在距离空间中建立了一类有限个等式约束下的Geraghty型耦合不动点定理。作为推论,得到了对称等式约束下的不动点定理和公共耦合不动点定理。

Numerical Simulation of the Mass Movement Process of the 2018 Sedongpu Glacial Debris Flow by Using the Fluid-Solid Coupling Method

In the context of global warming and intensified human activities,glacier instability in plateau regions has increased,and glacier debris flows have become active,which poses a significant threat to the lives and property of people and socioeconomic development.The mass movement process of glacier debris flows is extremely complex,so this paper uses the 2018 Sedongpu glacier debris flow event on the Qinghai-Tibet Plateau as an example and applies a numerical simulation method to invert the whole process of mass movement.In view of the interaction between phases in the process of motion,we use the fluid-solid coupling method to describe the mass movement.The granular-flow model and drift-flux model are employed in FLOW3D software to study the mass movement process of glacier debris flows and explore their dynamic characteristics.The results indicate that the glacier debris flow lasted for 700 s,and the movement process was roughly divided into four stages,including initiation,scraping,surging and deposition;the depositional characteristics calculated by the fluid-solid coupling model are consistent with the actual survey results and have good reliability;strong erosion occurs during the mass movement,the clear volume amplification effect,and the first wave climbs 17.8 m across the slope.The fluid-solid coupling method can better simulate glacier debris flows in plateau regions,which is helpful for the study of the mechanism and dynamic characteristics of such disasters.

Transient Analysis of a Reactor Coolant Pump Rotor Seizure Nuclear Accident

The reactor coolant pump(RCP)rotor seizure accident is defined as a short-time seizure of the RCP rotor.This event typically leads to an abrupt flow decrease in the corresponding loop and an ensuing reactor and turbine trip.The significant reduction of core coolant flow while the reactor is being operated at full load can have very negative consequences.This potentially dangerous event is typically characterized by a complex transient behavior in terms of flow conditions and energy transformation,which need to be analyzed and understood.This study constructed transient flow and rotational speed mathematical models under various degrees of rotor seizure using the test data collected from a dedicated transient rotor seizure test system.Then,bidirectional fluid-solid coupling simulations were conducted to investigate the flow evolution mechanism.It is found that the influence of the impeller structure size and transient braking acceleration on the unsteady head(Hu)is dominant in rotor seizure accident events.Moreover,the present results also show that the rotational acceleration additional head(Hu1)is much higher than the instantaneous head(Hu2).