Finite elastic torsional instability of incompressible thermo-hyperelastic cylinder

Torsional instability of an incompressible thermo-hyperelastic cylindrical rod, subjected to axial stretching and large torsions, is examined within the framework of finite elasticity. When the cylinder is stretched and twisted by a sufficiently large degree, a knot may form suddenly at one point. This inherent elastic instability is analyzed with the minimum potential energy principle and the critical values of torsion are obtained. The distribution of stresses as well as the tensile force and the torque are studied. Effect of tem- perature change is specifically discussed.

Combined effects of axial load and temperature on finite deformation of incompressible thermo-hyperelastic cylinder

A finite deformation problem is examined for a cylinder composed of a class of incompressible thermo-hyperelastic Mooney-Rivlin materials under an equal axial load at its two fixed ends and a temperature field at its lateral boundary. Firstly, a thermomechanical coupling term is taken into account in the strain energy density function, and a governing equation of the problem is obtained. Secondly, an implicit analytical solution is derived by using the incompressibility and the boundary conditions. Significantly, numerical examples show that the middle portion of the cylinder undergoes almost a uniform radial deformation. However, the deformation near the two ends varies remarkably along the axial direction for relatively large axial loads. In addition, the rising temperature can increase the deformation of structures, and its influence is linear approximately. Specially,in the case of tensile load, the jump increase of the axial deformation may occur.

Experimental and Numerical Study of Three-Dimensional Unsteady Incompressible Flow Past Two Identical Circular Cylinders in Tandem Arrangements

The possible states in the flow past two identical cylinders in tandem arrangements are investigated. The effect of the gap （L/D = 1.5, 1.75 and 2） between the two cylinders at Reynolds number （Re = 52,639） is taken into consideration. The presence of three-dimensional flow structures was observed to include notable changes to the response of the flow as result of variation of cylinder separation. A number of planes （z/h = 0.02, 0.25, 0.5 and 0.98） were taken at 20 step times of interval 0.005 s. to cover the details of flow along the cylinders. CFD FLUENT program was used to detect the flow structure. It is observed that the gap between the two cylinders affects the flow regime, i.e., there is no distinct vortex shedding downstream of the first cylinder.

Least Square Finite Element Method for Viscous Splitting of Unsteady Incompressible Navier–Stokes Equations

In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.

不可压缩橡胶圆柱的空穴和分叉

利用Y.C.Gao给出的一类应变能函数,分析了不可压缩橡胶圆柱受静载荷作用时在等温条件下及有温度场分布时空穴产生的问题,给出了存在分叉解的条件,确定了外载荷与空穴半径的函数关系,研究了空穴形成时应力的分布,讨论了本构参数和温度对极限载荷和应力分布的影响.结果表明:当本构参数满足0<n<1时,橡胶圆柱体存在分叉解;由Neo-Hooken材料构成的圆柱体将会很稳定而不存在分叉解;本构参数n越大,材料越不容易发生孔洞化不稳定现象;温度越高,材料越不稳定.

圆柱面上微小后向台阶层流绕流场的数值研究

Results of numerical calcultions for viscous incompressible laminar flow over a rearwardfacing step on circular cylinder are presented. The domainsubdividing and matching method and the simplify SOLA solution are engaged in the simulation. The effects of the step’s height,installed position and the Reynolds number on the flow field are obtained and discussed.

弹性近不可压缩问题的精化元法

对于弹性问题,材料近不可压缩可引起有限元法的体积闭锁.为解决此问题,以精化元法为基础,将单元应变正交分解为常应变和高阶应变,其中常应变可以保证收敛,对于近不可压缩问题只需忽略高阶应变中的体应变,从而避免单元体积不可压缩闭锁.按照上述方法修改了平面八节点等参元(IQ 8),并用于平面应变厚壁筒计算,通过与ABAQUS系统软件的八节点等参元计算结果对比,表明IQ 8单元用于可压和近不可压缩问题都有效.

两种浸入式边界方法的比较

介绍两类不同的浸入式边界方法及其对它的改进.然后采用均匀矩形交错网格和压力校正投影法,对不可压流场中的二维圆柱绕流进行了数值求解并对比了两类方法的精度.计算分析表明,连续显力法具有构造简单,适用性强的优点.但离散隐力法在物面边界精度上要优于前者.改进后,在二阶精度的离散格式下物面边界精度较低的显示力源法的精度有一定提高,同时发现,加密网格以提高数值精度的方法对于连续显力法并不总是有效.而同样格式下,离散隐力法具有更高精度,其中预测-校正离散隐力法可以在此基础上获得更小的计算误差和更快的收敛速度.数值解与文献已有的数值和实验结果吻合得很好,表明边界算法及其程序是可靠和有效的.

求解非定常方柱绕流的可变周期时间谱方法

针对周期性非定常流动特点，采用时间谱方法求解了无限大区域内低雷诺数下二维不可压缩层流绕方柱流动问题．由于方柱绕流的非定常运动周期事先未知，在计算过程中加入了基于残差梯度的可变周期计算方法，使变量和周期可以同时迭代计算．研究了时间谱方法的计算精度和求解速度，分析了不同求解参数对最终结果的影响．计算结果表明，时间谱方法可以准确地模拟方柱后漩涡的非定常运动现象，而计算所需时间只是传统的基于有限差分的双时间推进方法的10％～25％，流体非定常运动的Strouhal数和方柱的阻力特性证实了这种方法的正确性．可变周期计算方法对求解参数的变化不敏感，可以准确地预测运动周期．

二阶ETG有限元方法在低雷诺数流动模拟中的应用

本文提出了二阶全展开Euler-Taylor-Galerkin(ETG)有限元方法,并应用于对低雷诺数二维不可压缩粘性流动的模拟。深入考虑粘性不可压缩流Navier-Stokes方程中每个子项的作用,利用二阶Taylor全展开完成时间项向空间项的转化,采用时间推进和张量分析的方法推导了N-S方程的有限元离散格式。对具有典型意义的低雷诺数方腔拖曳流、后台阶流及二维方柱受限绕流进行了模拟,得到与相关文献较为一致的结果。表明本文提出的二阶全展开ETG有限元方法是一种具有较好稳定性和较高精度的算法。

对粘弹性厚壁圆筒动态响应中不可压缩性的讨论

分析图1所示外表面受弹性套管约束的长粘弹性厚壁圆筒的动态响应，发现不能采用不可压缩模型，文[2]对这一问题的解法是不正确的。

复杂边界条件下管线受力的数值模拟

基于N-S方程,采用Galerkin方法加权的三步有限元方法.本文对不可压缩粘性流体的圆柱绕流问题作了分析。同时对于高雷诺数下的紊流,引入大涡模拟数值模型。程序比较成功地模拟了平底边界条件及有沟槽复杂边界条件下的海底管线的受力情况。在圆柱绕流力的过程线模拟计算中,对有一定缝隙比、平底裸置以及置于沟槽内的圆柱均进行了数值计算并和试验资料及已有文献作了对比,结果令人满意。

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation.The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity.The linear theory of the velocity potential is employed by assuming inviscid,incompressible fluid and irrotational flow.As the problem is set in 3-D space,the employment of the Wagner condition is essential.The set of equations we pose,is presented as a mixed boundary value problem for Laplace＇s equation in 3-D.Apart from the mixedtype of boundary conditions,the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface.We make some simple assumptions at the start but otherwise we proceed analytically.We find closed-form relations for the hydrodynamic variables,namely the time dependent potential,the pressure impulse,the shape of the wave front（from the contact point to beyond the cylinder） and the slamming force.

近平板圆柱绕流的边界元分析

应用边界元方法 ,对低雷诺数粘性不可压流体的半无界近平板圆柱绕流问题进行数值模拟 ,得到圆柱表面的压力、面力分布规律 ,给出数值模拟的圆柱绕流的流场 。

橡胶圆柱体的平面外剪切变形分析

利用Gao Y C给出的一类不可压缩的应变能函数,分析了不均匀橡胶圆柱体受平面外剪切变形问题。通过平面外剪切变形问题的变形模式,并结合应力和位移的边界条件以及界面连续条件得到了位移场和应力场在瞬时构型中的解析解,并讨论了材料的不均匀性对位移场及应力场分布的影响。结果表明:不均匀模型可以方便地退化成均匀模型;橡胶圆柱体的不均匀性对位移场和应力场的分布有着重要影响。

ADDED MASS MATRIX AND RADIATION RESISTANCE MATRIX OF AN OSCILLATING CYLINDER PARTIALLY SUBMERGED IN WATER

Suppose that the motion of the water is produced by the small amplitude periodic motion of a partially immersed cylinder and the water is incompressible, inviscid and irrotational. We denote by C the wetted curve of the cylinder cross section. Let the coordinate axis ox be along the undisturbed free surface and let oy lie in the C plane, be vertical and point downward to the water. Let the origin o be at the center of the x-axis within the cylinder cross section. We denote by a the distance between the origin and the intersection point of the curve C and the x-axis. We may use the velocity potential φ(x, y) exp (—iωt) to describe the motion of the water with angular frequency to in the half-plane y>0. Then, φ(x, y) satisfies the following

Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

A local domain-free discretization-immersed boundary method(DFDIBM)is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form.Like the conventional immersed boundary method(IBM),the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object.The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points.To be specific,the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity.As compared to the conventional IBM,the present approach accurately implements the non-slip boundary condition.As a result,there is no flow penetration,which is often appeared in the conventional IBM results.The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder.The obtained numerical results agree very well with the data in the literature.

Two-Dimensional Numerical Simulation of Flow Around Three-Stranded Rope

Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-ε model and Shear-Stress Transport κ-ω(SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3–1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

风雷软件LES开发设计与验证

基于国家数值风洞风雷软件开源框架,设计开发了LES(Large Eddy Simulation)湍流模型,主要包括Fourier谱/有限差分方法 LES求解器和有限体积/有限差分方法 LES求解器。简要介绍了采用的不可压缩流动求解的投影法、Fourier谱/有限差分混合方法、亚格子模型等理论方法,给出设计的软件框架和计算流程,尤其说明采用的松/紧2种耦合模式。通过数值模拟不可压缩槽道湍流、亚临界雷诺数圆柱绕流、NACA0012临界攻角的低频振荡算例,验证求解器的计算精度和复杂湍流模拟能力。基于风雷开源框架设计的开源LES模型,具备高精度数值格式、亚格子模型、湍流统计等通用模块,可为国内学者提供一个LES湍流模拟研究的开放平台。