UNSTRUCTURED TETRAHEDRAL MESH GENERATION FOR THREE-DIMENSIONAL VISCOUS FLOWS

A method of generating general tetrahedral meshes suitable for use in viscous flow simulations is proposed. The approach which is followed consists of the initial generation of a number of unstructured layers of highly stretched elements, in the vicinity of solid walls, followed by the discretisation of the remainder of the domain, by a standard advancing front procedure. The numerical performance of the proposed methodology is demonstrated by the generation of meshes suitable for viscous flow analysis over a number of three-dimensional aerodynamic configurations of current practical interest.     

A SET OF HYBRID EQUILIBRIUM FINITE ELEMENT MODELS FOR THE ANALYSIS OF THREE-DIMENSIONAL SOLIDS

In this paper an approach to the formulation of equilibrium elements for the analysis of three-dimensional elasticity problems is presented. This formulation is an extension of the approach previously proposed for the analysis of two-dimensional elasticity problems. The general aspects of the formulation remain unchanged when applied to the new problem, but new points are considered, namely the way to perform volume integrations for general elements and the techniques used to obtain the self-equilibrated three-dimensional stress approximation functions. The numerical behaviour of such elements is presented and discussed.     

高层结构计算的有限元-有限条杂交法

本文提出用插值法改进传统有限条法的横向局部位移。这种改进过的方法用于高层结构计算中,很好地解决了传统方法遇到的剪力失真问题。该方法较传统有限条法计算精度高,结果可靠,未知量却增加很少。     

A NEW FORMULATION OF ISOPARAMETRIC FINITE ELEMENTS AND THE RELATIONSHIP BETWEEN HYBRID STRESS ELEMENT AND INCOMPATIBLE ELEMENT

A new method of formulating isoparametric finite element is developed, and the element strains are proposed to be resolved into two parts, constant part and higher-order one. The new method indicates two important properties of isoparametric finite element, and the equivalent relationship between hybrid stress elements and incompatible elements. © 1997 by John Wiley & Sons, Ltd.     

HYBRID-TREFFTZ FINITE ELEMENT FORMULATION FOR SIMULATION OF SINGULAR STRESS FIELDS

An equilibrium hybrid-Trefftz formulation based on the direct approximation of the stress and boundary displacement fields is presented. The general solution of the governing differential equations is used to approximate the stress field and the boundary displacements are represented by polynomial functions. When singular solutions are implemented to model local high stress gradients due to concentrated loads or to the presence of wedges or cracks, rational functions are used to approximate the boundary displacements in the neighbourhood of such singular stress points. The equilibrium conditions and the kinematic boundary conditions are locally satisfied. The remaining fundamental relations—the compatibility conditions, the static boundary conditions and the constitutive relations—are enforced in a weighted residual form so designed as to preserve the duality and constitutive reciprocity. The resulting governing system is symmetric and all intervening structural operators have boundary integral expressions. Numerical applications are presented to illustrate the performance of the formulation.     

THE s-VERSION OF FINITE ELEMENT METHOD FOR LAMINATED COMPOSITES

The s-version of the finite element method is developed for laminated plates and shells. By this technique the global domain is idealized using 2-D Equivalent Single Layer model. The regions where ESL model errs badly in capturing localized phenomena are superimposed by a stack of 3-D elements. Assumed strain formulation and selective polynomial order escalation in the two models, as well as fast iterative procedures, are employed to maintain a high level of computational efficiency.     

FORMULATION AND EXPERIMENTAL VERIFICATION OF A PNEUMATIC FINITE ELEMENT

Many engineering structures completely surround and enclose gas filled volumes. The enclosed gas adds additional stiffness to the surrounding structure. This paper shows how to account for this effect by means of an augmented virtual work principle. The additional term augmenting the virtual work equilibrium statement for the structure is the virtual boundary work done by the pressure of the enclosed gas. The augmented equations are discretized using standard finite element methods, and the additional terms are discussed. The resulting ‘pneumatic’ finite element is shown to be analogous to regular structural finite elements. To assess the accuracy and efficiency and also to illustrate the applicability of the present formulation, a series of four examples was selected. In two of the examples, the behaviour of the end cap of a partially filled plastic food product container is studied. The numerical results using the pneumatic element compare well with an alternative Rayleigh–Ritz solution of the end cap behaviour. The other two examples represent the behaviour of a double bellows air spring shock absorber under static isothermal and dynamic adiabatic conditions. For the static isothermal case, an experimental study was performed with results in good agreement with the pneumatic element solutions. For the dynamic adiabatic loading case, the dynamic stiffness of the air spring was predicted using the pneumatic element. The numerical results agree with experimental data published in an air spring application guide. The examples illustrate that the pneumatic element formulation can be applied to the large deflection analysis of structures that enclose gas filled volumes.     

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.     

一个有效的厚薄板通用COONS曲面矩形元

本文采用板壳有限元Coons曲面法和挠度位移与转角位移导数相关构造法构造出一个有效的厚薄板通用矩形单元,并直接给出位移场形函数;其推导简单易行,灵活多样,几何意义直观,力学概念清晰,并具有一般性。在薄板极限情况下,本文厚薄板通用单元自动退化为一个性能良好的薄板Coons曲面矩形元,不出现剪切闭锁现象。数值计算表明:本文构造的厚薄板通用单元具有较高的计算精度和良好的收敛性。     

复合材料细观结构三维有限元网格模型的建立

提出了针对颗粒夹杂为椭球形状并呈随机分布的多相复合材料的三维有限元网格的建立方法,为复合材料细观结构研究提供了一种全自动的建模工具。引入了以体积为标度的任意两椭球骨料侵入的判别准则,实现了一种三维随机骨料的投放算法;在基于映射法的颗粒表面有限元网格生成算法中通过扫描线布点和局部连接技术较好地解决了网格极化现象;采用改进的三维AFT方法生成基体的四面体网格,并利用AFT特性一次生成所有颗粒夹杂的四面体网格;为进一步的复合材料细观结构与宏观力学性能的多尺度计算打下了基础。最后用几个算例验证了算法的有效性。     

膜结构有限元分析中的平面单元与曲面单元的比较

在对膜结构进行有限元模拟时,通常采用两种面单元形式——平面常应变三角形单元和六结点曲面三角形等参元,究竟哪一种单元形式更优一直是存在争议的问题。首先就这两种单元的有限元格式进行探讨,比较了它们在位移模式、几何方程及刚度矩阵等方面的力学本质差异;然后,通过一些典型算例,比较了它们在计算精度和计算效率等方面的优劣。分析结果表明:在有限元格式方面,曲面三角形等参元较之平面常应变三角形单元更为完备,更加符合结构的实际受力特征;在计算精度和计算效率方面,曲面三角形等参元也要优于平面常应变三角形单元;因此,从结构精细化分析的角度来看,宜采用曲面三角形等参元来进行膜结构有限元分析。     

等效体积单元(RVE)在砌体有限元分析中的应用

本文回顾了砌体有限元分析中的常用单元模型;提出了等效体积单元(RVE)的概念;详细分析了等效体积单元(RVE)的力学特性、破坏与失效模式;并应用等效体积单元(RVE)进行墙体的有限元分析.     

A MIXED-HYBRID FINITE ELEMENT MODEL BASED ON ORTHOGONAL FUNCTIONS

A mixed-hybrid formulation for stress finite elements is presented. The stresses and the displacements in the domain of the element and the displacements on the boundary are simultaneously and independently approximated using orthogonal functions. The stress approximation functions are used as weighting functions in the weighted residual enforcement of the local compatibility and constitutive equations. Similarly, the displacement approximation functions in the domain and on the boundary are used as weighting functions in the weighting residual enforcement of the local equilibrium equation and of the static boundary conditions, respectively. Legendre polynomials and Fourier series are used to illustrate the performance of the finite element formulation when applied to elastostatic problems.     

统一滑移线与有限元求解路基极限荷载

应用统一强度理论和统一平面应变滑移线场理论对路基的极限荷载进行了分析,得到了统一滑移线解,此结果考虑了材料的拉压异性和中间主应力的效应,对于岩土类材料有很好的适用性.同时用大型有限元软件Ansys进行了数值分析并与统一滑移线场的计算结果进行了比较,二者接近,证明了统一平面应变滑移线场理论能较真实地反应岩土结构的受力情况,说明用统一强度理论求解路基极限荷载是可行的.     

基于离散元和有限差分耦合算法的崩塌体和结构碰撞预测分析

采用离散元和有限差分耦合计算方法,对龙洞子崩塌挡墙结构碰撞进行了预测分析。构建了3种崩塌挡墙结构模型,并进行了数值模拟。崩塌体由颗粒模拟,挡墙分别由刚性墙、颗粒、FLAC中的实体单元模拟。基于离散元和有限差分耦合算法的数值模拟,分析了不同模型的挡墙动力响应和变形。通过数值模拟结果的对比分析,选出了最优的结构模型和参数,为有效防御崩塌的防护结构设计提供理论依据。     

板桁组合结构空间计算的板桁梁段有限元法

本文考虑了板桁组合结构桥面板的局部屈曲，剪力滞后和板桁梁段截面畸变、翘曲、扭转与剪切变形的影响，利用横向有限条带法构造了桥面板板段的局部空间变位模式，提出了板桁梁段有限元法。该方法自由度少，计算精度高，能用于大型板桥组合结构的空间计算。     

REFINED CONSISTENT FORMULATION OF A CURVED TRIANGULAR FINITE ROTATION SHELL ELEMENT

The present paper considers a finite rotation formulation for curved shell elements with rotations about the element sides as nodal degrees of freedom. Attention is mainly on the derivation of a consistent finite rotation formulation. Significant simplifications of the governing equations are presented. These simplifications lead to more efficient finite element implementations. Numerical examples demonstrate the differences between the present consistent and previous approximate formulations.     

ON OPEN BOUNDARIES IN THE FINITE ELEMENT APPROXIMATION OF TWO-DIMENSIONAL ADVECTION–DIFFUSION FLOWS

A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection–diffusion equation for practical river surface flow simulations. Essentially, the space–time Crank–Nicolson–Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, namely Cauchy and Open, were theoretically and numerically analysed. Steady-state and transient numerical tests investigated the accuracy of boundary conditions on inflow, noflow and outflow boundaries where diffusion is important (diffusive boundaries). With the proper choice of boundary conditions, the steady-state Galerkin and the transient Crank–Nicolson–Galerkin finite element schemes gave stable and precise results for advection-dominated transport problems. Comparisons indicated that the present approach can give equivalent or more precise results than other streamline upwind and high-order time-stepping schemes. Diffusive boundaries can be treated with Cauchy conditions when the flow enters the domain (inflow), and with Open conditions when the flow leaves the domain (outflow), or when it is parallel to the boundary (noflow). Although systems with mainly diffusive noflow boundaries may still be solved precisely with Open conditions, they are more susceptible to be influenced by other numerical sources of error. Moreover, the treatment of open boundaries greatly increases the possibilities of correctly modelling restricted domains of actual and numerical interest. © 1997 by John Wiley & Sons, Ltd.     

A BRIEF HISTORY OF THE BEGINNING OF THE FINITE ELEMENT METHOD

This paper presents summaries of the works of several authors associated with the invention of the analysis technique now referred to as the finite element method. It stresses the notion of first development from which subsequent ideas evolved and gives what is believed to be an accurate record of the historical sequence of published papers in the international literature.     

重载径向轴承三维弹性流体润滑的有限元和边界元耦合数值分析

本文采用有限元和边界元技术分析了重载径向轴承的三维弹性流体润滑(EHL)问题,并提出了一种精度高、收敛快的加权迭代计算模式,用该计算模式成功地求解了由二阶Reynolds方程、粘压方程和三维弹性方程组成的非线性方程组,得到了在各种大偏心率下轴承材料分别为钢、铜和巴氏合金的径向轴承的弹流静特性参数。