弱耦合算法的实现及其应用

介绍了一种求解流固耦合问题更有效的方式即弱耦合技术,将计算结构动力学(CSD)和计算流体动力学(CFD)联合起来。CSD通过计算结构位移用来指定流体域的固体边界范围,而CFD计算用来定义作用在CSD上的荷载。荷载和位移的传递分别采用守恒和非守恒插值方法,详细介绍了其插值的实现过程。这种流固耦合算法是一种对整个问题进行离散化后,采用迭代求解方法的处理复杂的流固耦合问题的数值模拟方法。最后通过对一轻柔膜结构和风荷载的流固耦合问题的求解,表明了这种方法通过耦合CFD和CSD程序,提供了一种便利的、有效的耦合问题求解方法。     

横风下高速列车流固耦合动力学联合仿真

基于车辆-轨道耦合动力学和空气动力学建立了高速列车流固耦合动力学行为的联合仿真计算方法。通过将车辆-轨道耦合动力学计算程序嵌入流体力学程序中,避免了流体和固体两个求解器之间的数据交换通讯,并且采用耦合迭代步内流固边界条件气动力线性插值的办法,实现了流体和固体两个求解器时间迭代步长的独立选取,提高了计算速度。利用建立的流固耦合计算方法,研究了6级横风环境下列车以350km/h速度运行时的流固耦合动力学行为。比较了离线仿真和联合仿真两种方法下列车气动力与姿态、安全性和舒适性指标的差异。研究表明:列车-气流的流固耦合效应对头车气动力和姿态的影响显著,头车安全性指标有所恶化。     

楔形体匀速和自由落体水弹性砰击的半解析法求解EI北大核心CSCD

针对二维弹性楔形体入水过程的流固耦合问题,提出一种基于耦合Wagner理论和模态叠加法的半解析解方法。结构湿表面的速度势基于Wagner理论求解并考虑了结构弹性影响。砰击压力根据伯努利方程求解,为提高求解精度考虑了伯努利方程中速度平方项。通过平均弹性速度修正模型推导出附加质量和阻尼矩阵,将其代入固体动力学方程从而建立统一的流固耦合方程,耦合方程通过基于隐式的Newmark-β算法实现求解。通过计算楔形体垂直恒速和自由落体入水两种运动状态,并与基于半解析、数值和试验的文献结果进行了对比,验证了所提理论的可靠性。     

水下运动体的三维动力特性分析

在水下运行的物体,由于其与周围水之间的相互作用,从本质来说是一种典型的流固耦合问题。采用位移-压力格式(结构用位移来描述而流体用压力来描述)的流固耦合模型来描述运动体和水之间的相互作用。这种格式和有限元方法将水下运动体的三维动力特性问题,归结为一个大型非对称方程的特征值问题。采用Arnoldi方法进行此非对称特征值的求解。此外,对于刚体模态带来的零频问题,构造出一种特殊的迭代求解格式。最后,给出了一个水下圆柱体的实例计算分析,计算结果表明本文中的方法是切实有效的。     

基于改进涡方法的膜结构流固耦合研究

采用改进涡方法对膜结构的流固耦合进行模拟。将非协调边界元计算势流的方法引入到传统涡方法中,即为改进涡方法。该算法可以精确计算三维粘性、不可压缩流场。采用改进涡方法可以得到每个时间步膜结构的单元节点流场压力,通过与ansys有限元模型提取出的整体刚度矩阵联合求解得到单元节点位移,并可以由单元节点位移求解出下一时间步的流场分布。由于本文引入了高效的预处理循环型广义极小残余迭代算法(GMRES),使得边界元法的优势得到了充分发挥,大幅度节省了计算时间。完成了方形平屋盖膜结构气弹模型风洞试验。采用本文算法对膜结构流固耦合效应计算得到的位移均值大部分与风洞试验吻合,计算结果表明本文提出的方法是模拟膜结构流固耦合问题的有益尝试。     

采用快速动网格技术的时空同步流固耦合算法

为了减少流固耦合计算时间,发展了一种时空同步流固耦合算法。在每一次耦合迭代中,首先求解RANS(Reynolds Averaged Navier Stokes)方程,然后采用本课题组所提出的快速动网格技术计算结构及流场网格节点位移,并更新流场网格,实现流场与结构振动的空间同步求解。在每一时间步,通过多次耦合迭代,使流场计算收敛,同时保证结构振动计算的收敛,实现流场与结构振动的时间同步求解。采用该算法对弹性梁流固耦合振动及Wing 445.6颤振问题进行了研究,计算结果与文献中的结果一致。与已有文献的时间同步算法相比,此算法可以减少计算时间81.2%。     

流体固体动力耦合分析的有限元法

应用有限元法探讨了流体、固体接触界面由无限接触点对组成,并以接触点对的瞬态接触内力作为待定变量的流体固体动力耦合模型的数值求解方法。分析了流体、固体域插值函数的特点,用二维八节点等参元及流固接触面上的接触点对单元,对流固耦合系统进行了离散化处理;并采用变分原理推导了反映流体固体动力相互作用机理的接触约束矩阵(或称动力耦合矩阵),建立了有限元控制方程,给出了完整的数值计算方法,研编了动力耦合系统的分析程序。数值计算结果与经典理论解误差很小,验证了动力耦合模型和有限元求解方法的正确性及其较高的计算精度。     

基于流固耦合的重载飞艇副气囊形态分析与试验研究

为了研究非饱和副气囊在重载飞艇升降和巡航过程的形态变化,建立了缩尺比例氦气囊模型。基于向量式有限元(vector form of intrinsic finite element,VFIFE)对副气囊膜结构进行结构动力学分析,并考虑几何大变形和边界非线性;基于有限元法对氦气域和空气域进行流体动力学分析,分别采用自编MATLAB程序和ANSYS软件流体模块独立求解控制方程之后,通过映射网格在CSD(computational structural dynamics)/CFD(computational fluid dynamics)之间进行数据传递并迭代,以实现双向流固耦合。开展了氦气囊的缩尺比例模型试验,对囊体在泄气过程中得到的位移测量值与数值模拟结果进行对比。结果表明,氦气囊在不同充盈度下的形态变化与双向流固耦合数值分析结果一致,证明了该研究提出的数值模拟方法可有效用于副气囊随氦气充盈度变化导致的非稳定形态变化规律的研究。     

大跨柔性空间结构风压和耦合风效应分析

研究大跨柔性空间结构的表面风压和流固耦合风效应.引入流体运动控制方程和大涡模拟湍流模式,提出风与结构的流固耦合方程的迭代求解过程.提出张拉索膜结构的加载预应力态、稳定态和耦合态等三个受载状态概念和统一形式的动力方程表达.以某典型索穹顶结构为例,采用以风时程为荷载的动力响应时程方法、单向耦合算法和双向耦合算法,开展结构风效应的数值计算和比较.研究发现,动力响应时域方法和单向耦合算法的结构平均位移计算结果基本相同,但前者的结构风振系数较大.双向耦合算法的结构平均位移计算结果小于前两种方法,但风振系数在三种方法中最大.     

充液管道流固耦合的对称位移模型

本文以流固耦合４方程模型为基础，推出了以移为基本变量的，同时考虑泊松耦合与摩擦耦合以及和管道阻尼的，具有对称“刚度矩阵”的二阶微分方程组。     

A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation

This paper describes a new monolithic approach based on the fluid pressure Poisson equation (PPE) to solve an interaction problem of incompressible viscous fluid and an elastic body. The PPE is derived so as to be consistent with the coupled equation system for the fluid‐structure interaction (FSI). Based on this approach, we develop two kinds of efficient monolithic methods. In both methods, the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint, and all other unknown variables are derived fully explicitly or partially explicitly. The coefficient matrix of the PPE for the FSI becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties. The arbitrary Lagrangian–Eulerian (ALE) method is employed for the fluid part in order to take into account the deformable fluid‐structure interface. To demonstrate fundamental performances of the proposed approach, the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding. Copyright © 2005 John Wiley & Sons, Ltd.     

A computational approach for predicting the hydroelasticity of flexible structures based on the pressure Poisson equation

This work is concerned with the modeling of the interaction of fluid flow with flexible solid structures. The flow under consideration is governed by the Navier–Stokes equations for incompressible viscous fluids and modeled with low‐order velocity–pressure finite elements. The motion of the fluid domain is accounted for by the arbitrary Lagrangian–Eulerian formulation. The structure is represented by means of an appropriate standard finite element formulation. The spring smooth analogy is used to mesh control. The time integrating algorithm is based on the predictor–multi‐corrector algorithm. An important aspect of the present work is the introduction of a new monolithic approach based on the fluid pressure Poisson equation (PPE) to solve the hydroelasticity problem of an incompressible viscous fluid with an elastic body that is vibrating due to flow excitation. The PPE is derived to be consistent with the coupled system equation for the fluid–structure interaction (FSI). Based on this approach, an efficient monolithic method is adopted to simulate hydroelasticity between the flexible structure and the flow. The fluid pressure is implicitly derived to satisfy the incompressibility constraint, and the other unknown variables are explicitly derived. The coefficient matrix of the PPE for the FSI becomes symmetric and positive definite. To demonstrate the performance of the proposed approach, two working examples, a beam immersed in incompressible fluid and a guide vane of a Francis turbine passage, were used. The results show the validity of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Studies of the strong coupling and weak coupling methods in FSI analysis

The weak coupling methods in fluid–structure interaction analysis are newly classified into three types; the weak coupling method for solving structures with interfaces, the weak coupling method for solving fluids with interfaces, and the weak coupling method for solving both fluids and structures with interfaces. The consistent added matrices of these weak coupling methods are derived from the condensation of the strong coupling formulation. Some approximations for the consistent added matrices, which can avoid the matrix coupling, are proposed. The reasons for convergence difficulty in the weak coupling methods are clarified. A number of numerical results are presented to investigate the convergence properties and computational efficiency of these methods. Copyright © 2004 John Wiley & Sons, Ltd.     

The Timoshenko beam model of the differential quadrature element method

A new numerical approach for solving Timoshenko beam problems is proposed. The approach uses the differential quadrature method (DQM) to discretize the Timoshenko beam equations defined on all elements, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of Timoshenko beam structures. The resulting overall discrete equation can be solved by using a solver of the linear algebra. Numerical results of the DQEM Timoshenko beam model are presented. They demonstrate the DQEM numerical method.     

Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries

Blood flow in arteries is characterized by pulse pressure waves due to the interaction with the vessel walls. A 3D fluid-structure interaction (FSI) model in a compliant vessel is used to represent the pressure wave propagation. The 3D fluid is described through a shear-thinning generalized Newtonian model and the structure by a nonlinear hyperelastic model. In order to cope with the spurious reflections due to the truncation of the computational domain, several absorbing boundary conditions are analyzed. First, a 1D hyperbolic model that effectively captures the wave propagation nature of blood flow in arteries is coupled with the 3D FSI model. Extending previous results, an energy estimate is derived for the 3D FSI-1D coupling in the case of generalized Newtonian models. Secondly, absorbing boundary conditions obtained from the 1D model are imposed directly on the outflow sections of the 3D FSI model, and numerical results comparing the different absorbing conditions in an idealized vessel are presented. Results in a human carotid bifurcation reconstructed from medical images are also provided in order to show that the proposed methodology can be applied to anatomically realistic geometries.     

智能桁架结构最优振动控制与作动器优化配置

研究了智能桁架结构最优振动控制和作动器的优化配置问题。首先采用有限元方法,根据Hamilton原理推导了智能桁架结构的机电耦合动力学方程,根据线性二次型最优控制理论,推导了结构振动控制的数学模型,通过最小化性能泛函,求解黎卡提矩阵代数方程确定了最优控制输入。然后通过对最优控制性能指标函数的修正,得到了与初始状态无关的性能指标,以修正的性能指标为目标函数,应用模拟退火算法对作动器位置进行了优化配置。最后给出了空间智能桁架结构振动控制算例验证建模过程和算法。算例结果表明,通过最优振动控制可以使结构振动快速衰减,达到振动抑制的效果,而且通过模拟退火算法可以确定最佳的作动器布置方式。     

地震作用下水-轴对称柱体相互作用的子结构分析方法

针对水-轴对称柱体动力相互作用问题,提出了一种地震作用下水-结构相互作用的时域子结构分析方法。基于三维不可压缩水体的波动方程和边界条件,利用分离变量法将其转换为环向解析、竖向和径向数值的二维模型;基于比例边界有限元推导了截断边界处无限域水体的动力刚度方程,并将水体内域有限元方程和人工边界处的动水压力进行耦合,从而得到结构表面的动水压力方程;将轴对称柱体结构的有限元方程与动水压力方程耦合,从而得到水-轴对称柱体结构系统的时域有限元方程;数值算例验证该文提出的水-轴对称动力相互作用的子结构方法,结果表明:该文方法具有很高的精度和计算效率。通过对水中轴对称结构地震响应和自振频率的分析表明:地震动水压力对结构自振频率和动力响应的影响随水深的增加而增大。     

A thermodynamic framework for a gradient theory of continuum damage

In this paper, we present a formulation of state variable based gradient theory to model damage evolution and alleviate numerical instability associated within the post-bifurcation regime. This proposed theory is developed using basic microforce balance laws and appropriate state variables within a consistent thermodynamic framework. The proposed theory provides a strong coupling and consistent framework to prescribe energy storage and dissipation associated with internal damage. Moreover, the temporal evolution equation derived here naturally shows the effect of damage—nucleation, growth and coalescence. In addition, the theoretical framework presented here is easily extendable to the addition of other defects (not shown here), and can be generalized to the development of consistent coupled transport equations for species, such as hydrogen (Bammann et al. in JMPS, 2009, submitted), as well as providing a consistent structure for modeling events at diverse length scales.     

Investigation of fluid–structure interactions using a velocity‐linked P2/P1 finite element method and the generalized‐ α method

A velocity‐linked algorithm for solving unsteady fluid–structure interaction (FSI) problems in a fully coupled manner is developed using the arbitrary Lagrangian–Eulerian method. The P2/P1 finite element is used to spatially discretize the incompressible Navier–Stokes equations and structural equations, and the generalized‐ α method is adopted for temporal discretization. Common velocity variables are employed at the fluid–structure interface for the strong coupling of both equations. Because of the velocity‐linked formulation, kinematic compatibility is automatically satisfied and forcing terms do not need to be calculated explicitly. Both the numerical stability and the convergence characteristics of an iterative solver for the coupled algorithm are investigated by solving the FSI problem of flexible tube flows. It is noteworthy that the generalized‐ α method with small damping is free from unstable velocity fields. However, the convergence characteristics of the coupled system deteriorate greatly for certain Poisson's ratios so that direct solvers are essential for these cases. Furthermore, the proposed method is shown to clearly display the advantage of considering FSI in the simulation of flexible tube flows, while enabling much larger time‐steps than those adopted in some previous studies. This is possible through the strong coupling of the fluid and structural equations by employing common primitive variables. Copyright © 2012 John Wiley & Sons, Ltd.