ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem

A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Reduced-order finite element method based on POD for fractional Tricomi-type equation

The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.

Finite Element Method for a Kind of Two-Dimensional Space-Fractional Diffusion Equation with Its Implementation

In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.

A COMPARATIVE STUDY OF THE OPENING AND CLOSING PROCESS OF TWO TYPES OF MECHANICAL HEART VALVES USING ALE FINITE ELEMENT METHOD

Using arbitrary Lagrangian-Eulerian(ALE)finite element method,this paper made a comparative study of the opening and closing behaviour of a downstream directional valve(DDM)and a St.Jude medical valve(SJM)through a two dimensional model of mechanical valve-blood interaction in which the valve is considered as a rigid body rotating around a fixed point,and the blood is simplified as viscous incompressible fluid It's concluded that:(1)Compared with SJM valve, DDM valve opens faster and closes the more gently.(2)The peak badk-flow-flow of DDM is smaller than that of SJM.The present investigation shows that being a better analogue of natural valve,DDM has a brighter potential on its durability than SJM.

Finite Element Methods Applied to the Tubular Linear Stepping Motor

In this paper proposes a Finite Element Methods analyzing applied to the linear tubular stepping actuator. The linear displacement is modeled by means of a layer of finite elements placed in the air gap. The design of the linear stepper motor for achieving a specific performance requires the choice of appropriate tooth geometry. The magnetic field of the actuator has been analyzed using the finite element method over a current-displacement variation. The magneto static field and electromagnetic force was introduced in order to predict before construction, the inductance values according to the displacement and the currents into the coils. The results were obtained for the magnetic flux density distribution and the electromagnetic force for different positions and current.

An Indirect Finite Element Method for Variable-Coefficient Space-Fractional Diffusion Equations and Its Optimal-Order Error Estimates

We study an indirect finite element approximation for two-sided space-fractional diffusion equations in one space dimension.By the representation formula of the solutions u(x)to the proposed variable coefficient models in terms of v(x),the solutions to the constant coefficient analogues,we apply finite element methods for the constant coefficient fractional diffusion equations to solve for the approximations vh(x)to v(x)and then obtain the approximations uh(x)of u(x)by plugging vh(x)into the representation of u(x).Optimal-order convergence estimates of u(x)−uh(x)are proved in both L2 and Hα∕2 norms.Several numerical experiments are presented to demonstrate the sharpness of the derived error estimates.

ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation

In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method.

ALE FINITE ELEMENT ANALYSIS OF NONLINEAR SLOSHING PROBLEMS BASED ON F LUID VELOCITY POTENTIAL

Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.

Strength reduction and step-loading finite element approaches in geotechnical engineering

The finite element limit analysis method has the advantages of both numerical and traditional limit equilibrium techniques and it is particularly useful to geotechnical engineering.This method has been developed in China,following well-accepted international procedures,to enhance understanding of stability issues in a number of geotechnical settings.Great advancements have been made in basic theory,the improvement of computational precision,and the broadening of practical applications.This paper presents the results of research on（1） the efficient design of embedded anti-slide piles,（2） the stability analysis of reservoir slopes with strength reduction theory,and（3） the determination of the ultimate bearing capacity of foundations using step-loading FEM（overloading）.These three applications are evidence of the design improvements and benefits made possible in geotechnical engineering by finite element modeling.

ALE FINITE ELEMENT ANALYSIS OF THE OPENING AND CLOSING PROCESS OF THE ARTIFICIAL MECHANICAL VALVE

Employing arbitrary Lagrangian-Eulerian (ALE) finite element method, this poper studies the opening and closing process of a St. Jude medical valve through a two-dimensional model of the mechanical valve-blood interaction in which the valve is regarded as a rigid body rotating around a fixed point, and foe blood is simplified as viscous incompressible Newtonian fluid. The numerical analysis of the opening and closing behaviour of as St. Jude valve suggested that: 1. The whole opening and closing process of an artificial mechanical valve is consisted of four phases: (1) Opening phase; (2) Opening maintenance phase; (3) Closing phase; (4) Closing maintenance phase. 2. The St. Jude medical valve closes with prominent regurgitat which results in water-hammer effect. 3. During the opening and closing process of the St. Jude valve,high shear stresses occur in the middle region of the two leaflets and on the valve ring. The present model has made a breakthrough on the coupling computational analysis considering the interactive movement of the valve and blood.

ELEMENT－BY－ELEMENT MATRIX DECOMPOSITION ANDSTEP－BY－STEP INTEGRATION METHOD FOR TRANSIENTDYNAMIC PROBLEMS

In this paper a general matrix decomposition scheme as well as an element-by-clement relaxation algorithm combined with step-by -step integration method is presented for transient dynamic problems thus the finite element method can be fromforming global stiffness matrix global mass matrix as well as solyin large scale sparse equations Theory analysis and numerical results show that the presented matrix decomposition scheme is the optimal one The presented algoithm has else physicalmeaning and can be busily applied to finite element codes

Finite Element Approach for the Solution of First-Order Differential Equations

The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.

冲旋步进钻井提速方法的井底裂纹拓展特性

针对深部地层井底岩石硬度高、强度大和应力集中现象导致的岩石可钻性差、破岩效率低和使用寿命短的问题,提出旋冲钻井和差压步进破岩方法相结合的冲旋步进钻井提速新理念。为了研究冲击作用下差压步进钻头破碎地层岩石的裂纹拓展规律,采用有限-离散元(FDEM)方法建立了球齿冲击三维薄板模型,开展了球齿在不同冲击能量、冲击位置及岩石种类等条件下的冲击破岩过程模拟,获得了阶梯型井底岩石在冲击作用下的裂纹扩展规律。研究结果表明:由于阶梯面的存在,球齿在冲击作用下对阶梯型井底造成的预损伤区域比常规井底更大,冲击位置靠近阶梯面的裂纹扩展效果更好;双球齿冲击阶梯井底容易形成较大范围的岩石破碎区,降低了破碎阶梯井底地层岩石的难度;球齿冲击过程中对青砂岩造成的预损伤区域比花岗岩大,在冲击能量相同的情况下球齿冲击破碎花岗岩更为困难。利用冲旋步进钻井方法理论上可以进一步提高难钻地层钻井速度,但具体效果需要经现场试验及优化。所得结论可为深部难钻地层钻井速度的提升提供新的思路。

Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation

New numerical techniques are presented for the solution of the twodimensional time fractional evolution equation in the unit square.In these methods,Galerkin finite element is used for the spatial discretization,and,for the time stepping,new alternating direction implicit(ADI)method based on the backward Euler method combined with the first order convolution quadrature approximating the integral term are considered.The ADI Galerkin finite element method is proved to be convergent in time and in the L2 norm in space.The convergence order is O(k|ln k|+h^(r)),where k is the temporal grid size and h is spatial grid size in the x and y directions,respectively.Numerical results are presented to support our theoretical analysis.

基于STEP的三维表面有限元网格生成技术的研究

研究了三维表面有限元网格自动生成的技术,利用映射法实现了模型表面的三角网格剖分。基于STEP文件格式的模型的导入和重建,将模型的每个表面映射至参数空间,利用推进波前法生成参数面网格,然后映射回三维表面。研制了一套网格剖分策略,运用该策略对多种类型表面进行了分析求解。

地震响应下时程单元的逐段自适应算法

有限元求解运动方程时,按最大模控制误差的自适应步长算法,大都要求荷载是连续可微的函数,但是对于离散形式的地震荷载,会出现单元跨时段而导致算法不适用的问题。针对这个问题,该文提出了一种基于二分法调整步长的逐段自适应步长算法,可有效避免单元跨段的问题。该文中给出相关算例,验证了本法的有效性和可靠性。

粘性流体大幅晃动的ALE迎风有限元方法

将任意的拉格朗日-欧拉(arbitraryLagrange-Euler,ALE)描述引入到速度修正格式中,利用迎风有限元法推导了数值离散方程,给出了ALE描述下的分步有限元计算格式,通过对不可压粘性流体大幅晃动问题进行数值模拟,证实了本文方法的有效性和可靠性.

Anybody仿真太极不同步法时股骨及下肢骨主要关节的应力特征

背景:Anybody骨肌建模系统,使用数学建模技术模拟人体骨骼、肌肉和环境的关系,可对人体的逆向动力学进行研究,得出下肢关节力等指标。目的:分析练习太极拳动作时下肢骨主要关节的应力分布规律,为其科学训练和锻炼价值提供依据。方法:在北京体育大学武术学院选取8名太极拳健将级运动员进行7组步法动作和右腿股骨CT的数据采集。使用BTS红外捕捉系统、Kistler三维测力台采集太极(八法五步)7组步法动作的运动和力学数据,利用Anybody 7.2骨肌模型的多体动力学仿真技术计算下肢关节动力学参数,结合Workbench 19.2对股骨进行应力计算分析。结果与结论:①利用Workbench软件分析得出了7组步法动作的股骨应力结果,7组动作的应力峰值由大至小顺序是:退步捋势(22.00 MPa)、退步採势(19.379 MPa)、左右移步挤按(9.35 MPa)、左右移步肘靠(6.30 MPa)、进步掤势(4.68 MPa)、进步挒势(2.57 MPa)、中定独立势(0.31 MPa)。②在7组步法动作中2种向后退步动作股骨应力最大(P<0.05),且在7组动作运动过程中的股骨最大应力位置均不同。③上述结果证实,在太极(八法五步)7种步法动作练习时,股骨应力阈值和最大应力位置会随着5种方向(7组动作)运动不同而变化,通过连续训练能够全面地刺激股骨体,进步动作对于股骨体正面和外侧上端影响较大,退步动作对股骨体后面和内侧影响较大,左右横向步法动作主要是股骨体两侧对称受力。④初学者要根据不同步法动作的受力特点来进行针对训练,进步动作和退步动作训练时要注重太极拳的旋转用力以及左右横移步法动作训练时的内侧对抗用力,根据自身薄弱问题,对太极拳训练步法有所侧重,进而达到更好的锻炼效果。

WAVE TRANSFORMATION AND BREAKING OVER A RECTANGULAR STEP

An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.