A PARTICLE TRACKING TECHNIQUE FOR THE LAGRANGIAN–EULERIAN FINITE ELEMENT METHOD IN MULTI-DIMENSIONS

This paper presents a multi-dimensional particle tracking technique for applying the Lagrangian–Eulerian finite element method to solve transport equations in transient-state simulations. In the Lagrangian– Eulerian approach, the advection term is handled in the Lagrangian step so that the associated numerical errors can be considerably reduced. It is important to have an adequate particle tracking technique for computing advection accurately in the Lagrangian step. The particle tracking technique presented here is designed to trace fictitious particles in the real-world flow field where the flow velocity is either measured or computed at a limited number of locations. The technique, named ‘in-element’ particle tracking, traces fictitious particles on an element-by-element basis. Given a velocity field, a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed. For the tracking within an element, the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements. A fictitious particle, thus, is traced one subelement by one subelement within the element. The desired number of subelements can be determined based on the complexity of the flow field being considered. The more complicated the flow field is, the more subelements are needed to achieve accurate particle tracking results. A single-velocity approach can be used to efficiently perform particle tracking in a smooth flow field, while an average-velocity approach can be employed to increase the tracking accuracy for more complex flow fields.     

任意四边形平面问题的样条有限元法

用三次B样条有限元通过坐标变换和变分法求解任意四边形区域上的平面问题,利用分区势能原理推广到由四边形组成的任意平面区域,推导出了具体的计算公式,为平面问题求解提供了一种高效的计算方法。与普通有限单元相比,该方法计算量小,而且计算结果具有对网格畸变不敏感,精度高等显著特点。     

基于基面力概念的余能原理任意网格有限元方法

利用基面力概念,给出一种任意形状网格都可以使用的柔度矩阵表达式的具体形式,运用拉格朗日乘子法得到以基面力为基本未知量的余能原理有限元支配方程,提出计算节点位移的表达式,编制出相应的任意网格有限元计算程序。该文对不同形状的单元网格以及畸变网格进行了计算分析,并与理论解和传统的有限元进行了对比和讨论。结果表明:该方法可以适用于任意形状的有限元网格,对网格的畸变不敏感。     

DISPLACEMENT/PRESSURE BASED MIXED FINITE ELEMENT FORMULATIONS FOR ACOUSTIC FLUID–STRUCTURE INTERACTION PROBLEMS

We present reliable finite element discretizations based on displacement/pressure interpolations for the analysis of acoustic fluid–structure interaction problems. The finite element interpolations are selected using the inf-sup condition, and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation. We show that with our analysis procedure no spurious non-zero frequencies are encountered, as heretofore calculated with other displacement-based discretizations. © 1997 by John Wiley & Sons, Ltd.     

A DISTRIBUTED FINITE ELEMENT METHOD FOR SOLVING THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS

The potential for using a network of workstations for solving the incompressible Navier–Stokes equations using a finite element formulation is investigated. A programming paradigm suitable for a heterogeneous distributed workstation environment is developed and compared to the traditional paradigm employed for distributed memory parallel computers. In particular, the issues of load balancing and fault recovery are explored. Numerical results are presented for two computer configurations: (1) a homogeneous network of workstations and (2) a heterogeneous network of workstations. The superiority of the developed paradigm over the traditional paradigm employed for distributed memory parallel computers is shown in cases where a heterogeneous network of workstations is employed or when one of the workstations of the cluster is loaded by other users.     

A VELOCITY BASED APPROACH INCLUDING ACCELERATION TO THE FINITE ELEMENT COMPUTATION OF VISCOPLASTIC PROBLEMS

We present a velocity based approach including acceleration to the finite element computation of metal forming problems, based on the viscoplastic Norton–Hoff law. In order to reduce computational cost, we suggest substituting the classical solution procedure based on standard Newton–Raphson method for solving the set of non-linear equations, with a new one which needs only one computation inside a time step and which is based on the linearization of the non-linear equations over time. The new procedure was introduced as an option in the existing computer code FORGE2©. Some examples are used for comparison between the classical procedure and the new one. They show that the new procedure is stable and accurate, and in comparison to the classical one it reduces the total number of resolutions of linear systems. Therefore, significant computer time reduction can be expected for 3-D problems.     

FINITE ELEMENT SOLUTION OF INCOMPRESSIBLE FLUID–STRUCTURE VIBRATION PROBLEMS

In this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system, incompressible fluid – elastic structure, in absence of external forces. We use displacement variables for both the solid and the fluid but the fluid displacements are written as curls of a stream function. Classical linear triangular finite elements are used for the solid displacements and for the stream function in the fluid. The kinematic transmission conditions at the fluid–solid interface are taken into account in a weak sense by means of a Lagrange multiplier. The method does not present spurious or circulation modes for non-zero frequencies. Numerical results are given for some test cases. © 1997 by John Wiley & Sons, Ltd.     

摩擦接触裂纹问题的扩展有限元法

扩展有限元法(XFEM)是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法。扩展有限元法分析闭合型裂纹时,必须考虑裂纹面间的接触问题。已有文献均采用迭代法求解裂纹面的接触问题。该文建立了闭合型摩擦裂纹问题的扩展有限元线性互补模型,将裂纹面非线性摩擦接触转化为一个线性互补问题求解,不需要迭代求解。算例分析说明了该方法的正确性和有效性,同时表明扩展有限元法结合线性互补法求解接触问题具有较好的前景。     

基于Cosserat理论的应变梯度非协调数值研究

依据Cosserat连续介质理论下非协调离散体系的能量相容性,导出了非协调位移的一个合理约束条件。根据这个条件构造了一个应变梯度平面4节点非协调单元。计算结果表明,该单元对可压缩和不可压缩状态的Cosserat类型的应变梯度材料均给出合理的数值结果,再现了材料的应变梯度效应。     

弹性力学问题自适应有限元及其局部多重网格法

针对平面弹性力学问题,利用最新顶点二分法,设计了一种不需要标记振荡项和加密单元不需要满足“内节点”性质的自适应有限元法;利用自适应加密过程中每层网格上只有局部单元需要加密这一特性,设计了一种基于局部松弛的多重网格法.数值实验结果表明：该文设计的自适应有限元法具有一致收敛性和拟最优计算复杂度,基于局部松弛的多重网格法对求解弹性力学问题自适应网格下的有限元方程具有很好的计算效率和鲁棒性.     

中厚板问题的多变量小波有限元法

提出了一种基于二类变量广义变分原理的多变量小波有限元方法。首先构造了便于边界条件处理的插值小波基,应用乘积型二元插值小波基来构造中厚板的广义变量场函数,通过二类变量广义变分原理建立了多变量小波有限元模型。在计算各种变量时,不需要利用其物理关系,也不必求导,可直接计算其结果,因而各种变量均有足够的精度。     

An extended finite element formulation for contact in multi‐material arbitrary Lagrangian–Eulerian calculations

Multi‐material Eulerian and arbitrary Lagrangian–Eulerian methods were originally developed for solving hypervelocity impact problems, but they are attractive for solving a broad range of problems having large deformations, the evolution of new free surfaces, and chemical reactions. The contact, separation, and slip between two surfaces have traditionally been addressed by the mixture theory, however the accuracy of this approach is severely limited. To improve the accuracy, an extended finite element formulation is developed and example calculations are presented. As a side benefit, the mixture theory is eliminated from the multi‐material formulation, eliminating the issues associated with the equilibration time between adjacent materials. By design, the new formulation is relatively simple to implement in existing multi‐material codes, parallelizes without difficulty, and has a low memory burden. Copyright © 2006 John Wiley & Sons, Ltd.     

Updated Lagrangian/Arbitrary Lagrangian–Eulerian framework for interaction between a compressible neo‐Hookean structure and an incompressible fluid

We propose a numerical method for a fluid–structure interaction problem. The material of the structure is homogeneous, isotropic, and it can be described by the compressible neo‐Hookean constitutive equation, while the fluid is governed by the Navier–Stokes equations. Our study does not use turbulence model. Updated Lagrangian method is used for the structure and fluid equations are written in Arbitrary Lagrangian–Eulerian coordinates. One global moving mesh is employed for the fluid–structure domain, where the fluid–structure interface is an ‘interior boundary’ of the global mesh. At each time step, we solve a monolithic system of unknown velocity and pressure defined on the global mesh. The continuity of velocity at the interface is automatically satisfied, while the continuity of stress does not appear explicitly in the monolithic fluid–structure system. This method is very fast because at each time step, we solve only one linear system. This linear system was obtained by the linearization of the structure around the previous position in the updated Lagrangian formulation and by the employment of a linear convection term for the fluid. Numerical results are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

模拟三维裂纹问题的自适应多尺度扩展有限元法

为了在大型结构分析中考虑小裂纹或以小的代价提高裂纹附近求解精度,该文建立了分析三维裂纹问题的自适应多尺度扩展有限元法。基于恢复法评估三维扩展有限元后验误差,大于给定误差值的单元进行细化。所有尺度单元采用八结点六面体单元,采用六面体任意结点单元连接不同尺度单元。采用互作用积分法计算三维应力强度因子。三维I 型裂纹和I-II 复合型裂纹算例分析表明了该方法的正确性和有效性。     

具有任意形状单元离散模型的界面元法

文［１］推出了求解不连续介质体的界面应力元法，并在理论和实例验算两方面论证了该法具有精度好、效率高、适用范围广等优点。通过进一步研究，该法还可适应任意网络离散模型的计算。本文引用自然坐标，实施了任意形状单元的界面元算法，并给出了算例，成果表明，本文的算法可行，其精度也是令人满意的。     

Numerical simulation of flapping wings using a panel method and a high‐order Navier–Stokes solver

The design of efficient flapping wings for human engineered micro aerial vehicles (MAVs) has long been an elusive goal, in part because of the large size of the design space. One strategy for overcoming this difficulty is to use a multifidelity simulation strategy that appropriately balances computation time and accuracy. We compare two models with different geometric and physical fidelity. The low‐fidelity model is an inviscid doublet lattice method with infinitely thin lifting surfaces. The high‐fidelity model is a high‐order accurate discontinuous Galerkin Navier–Stokes solver, which uses an accurate representation of the flapping wing geometry. To compare the performance of the two methods, we consider a model flapping wing with an elliptical planform and an analytically prescribed spanwise wing twist, at size scales relevant to MAVs. Our results show that in many cases, including those with mild separation, low‐fidelity simulations can accurately predict integrated forces, provide insight into the flow structure, indicate regions of likely separation, and shed light on design–relevant quantities. But for problems with significant levels of separation, higher‐fidelity methods are required to capture the details of the flow field. Inevitably high‐fidelity simulations are needed to establish the limits of validity of the lower fidelity simulations.Copyright © 2012 John Wiley & Sons, Ltd.     

混合夹杂问题的边界元法

该文提出了一种求解含固体、流体和孔隙等多类型夹杂的混合夹杂问题的边界元法。混合夹杂问题实质也是多连通域问题,但内边界的位移和面力都是未知量,导致该问题因定解条件不足而无法直接求解。根据不同类型夹杂的本构关系建立了各夹杂与基体界面面力与位移之间的关联矩阵,从而形成除给定边界条件以外的补充定解条件,使问题得以解决。以平面问题为例,分别对只含固体夹杂、流体夹杂以及同时含有孔隙、固体和流体夹杂的情况进行了计算,模拟了含100个随机分布夹杂的板材的弹性模量,验证了该方法的有效性、程序的正确性和可靠性。     

BOUNDARY CONDITIONS FOR FINITE ELEMENT SIMULATIONS OF CONVECTIVE FLOWS WITH ARTIFICIAL BOUNDARIES

We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld-type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.     

用CAGD技术进行有限元前处理

本文介绍了用ＣＡＧＤ技术进行有限元前处理的设计要点。这种前处理包括用ＣＡＤ软件形成有限元单元图和用ＣＡＧＤ技术实现单元图的数值化处理。它避免了大量的有限元数据准备和输入工作，具有广泛的实用价值。     

组合材料加固砖砌体的有限元模拟方法

基于ABAQUS有限元软件,提出了组合材料加固砌体数值建模方法。该方法是在未加固砌体整体式模型的基础上,结合分离式思想建立组合材料加固砌体模型。通过对8片采用粘钢-聚合物砂浆组合材料加固的砖砌体墙体（其中,4片采用粘贴正交钢片,4片采用粘贴斜撑钢片）的拟静力试验结果进行了数值模拟对比分析,结果显示：模拟所得墙体滞回、骨架及刚度退化曲线与试验曲线基本吻合;仿真破坏形态与试验现象一致;计算所得荷载、位移、延性和耗能等全部指标中有81%的误差在20%以内。