APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARANIETRIC HYBRID FINITE ELEMENT ANALYSIS

IntroductionSince T.H.H.Pain firstly puts forward hybrid element method[1]in1964, the researchand application of hybrid element have got great development. T.H.H.Painet al.havemade important pioneer works in the domain of the research on incompatible displacementstructure hybrid elementstress pattern[2,3]in recentdecades. Reference [4] had provided theoptimizing design concept of hybrid element further and established standardization methodof incompatible displacement structure hybrid eleme…     

层合板的非线性有限单元分析

对层合板引入小应变中转动几何非线性假设，位移模式考虑了横向剪切应力及其连续性，有采用罚单元的方式构造了简单，协调的八节点等参单元，并应用于层合板的应力分析，取得了很好的数值结果。     

横观各向同性轴对称问题的非协调元和杂交应力元计算

基于变分原理得出各向同性轴对称问题下的非协调元和杂交应力元方法仍然适用于分析横观各向同性轴对称问题的结论，同时对应用于各向同性问题的罚平衡优化方法进行了修改，使之能够应用于横观各向同性问题的分析。文中给出了分析算例。并对各种单元结果进行了比较，计算结果表明非协调元和杂交应力元方法不但适用于横观各向同性轴对称问题分析，而且将提高其数值解的精度，改善单元内部应力分布。     

含多椭圆孔(核)复合材料加筋层板的应力集中研究

基于各向异性体平面弹性理论中的复势方法,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元,采用该杂交应力有限元来描述层板的椭圆核区域,采用杆单元来描述加强筋(杆单元的刚度取为层板沿筋条方向的刚度),其余区域采用常规8节点等参单元进行模拟,建立起分析含多椭圆核复合材料加筋壁板问题的力学分析方法,详细讨论了椭圆核大小、位置、筋条尺寸、相对位置、铺层比例等诸参数的影响规律,得到了一些有益的结论。     

Application of the quadrilateral area coordinate method： a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-processing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. The project is supported by the National Natural Science Foundation of China (10502028), the Special Foundation for the Authors of the Nationwide (China) Excellent Doctoral Dissertation (200242), and the Science Research Foundation of China Agricultural University (2004016).     

等参元——修改等参元——最佳等参元

本文以二维问题为模型,建立了等参元、修改等参元和最佳等参元间的相互关系.给出了最佳等参元附加节点方程的解法.其数值解与理论分析一致.显示出修改等参元的许多良好特性.     

基于加权残量法的多变量等参元简明列式及其应用

根据作者提出的建立多变量有限元模型的系统化方法，应用加权残量法的基本原理，给出了建立多变量等参元模型的简明列式。然后应用该列式，构造了简明有效的平面四结点多变量等参元MQ4和MQ5前者不含内部自由度，后者含有内部自由度。文中结合若干典型算例对所构造的单元性能进行了考核，并与若干典型协调与非协调等参元的数值结果进行了比较。数值结果表明，无论是在规则网格还是在不规则网格情况下，本文构造的多变量等参元，不仅能通过分片检验的要求，而且表现出了良好的性能。     

Stream function finite element solution of Stokes flow with penalties

A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C⁰) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.     

Large deformation of incompressible rubber cylinder under plane strain

The large deformation of incompressible rubber cylinder under inner pressure is analyzed by a kind of new rubber materials strain energy function. The theory formulation for the displacement and stress is presented. The penalty finite element formulation is established in order to analyze nonlinear rubber materials, and the results of finite element method agree well with theoretical ones. A new method for controlling the calculating stability and convergence rates is put forward. The selection of the appropriate penalty factor and its influence on calculated results are discussed.     

Accuracy of Finite Element Based Shape Design Sensitivity Analysis*

ABSTRACT Accuracy of finite element based shape design sensitivity analysis, for use in shape design optimization, is analyzed and tested. A shape design sensitivity formulation that uses stress averaging to treat stress constraint func-tionals is presented. A smooth boundary parameterization is introduced to avoid the "Babuska paradox" and to improve accuracy of design sensitivity analysis. Accuracy of design sensitivity analysis with displacement and hybrid stress finite element formulations is compared. Good accuracy is obtained using higher order displacement finite elements, such as linear stress triangular and 8-noded isoparametric elements.     

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

IntroductionIt is known that standard finite element procedure is unable to simulate the wavepropagation with high oscillations or gradients in space in the media with reasonableefficiency and accuracy due to the nature of polynomial interpolation approxi…     

四节点四边形数值流形方法及其改进

本文对四节点四边形流形元提出了改进措施,将覆盖位移函数用自然坐标表示,使得在一般非规则有限数学覆盖网格下,数值积分变得比较容易,克服了现有四节点四边形流形单元数值积分困难的缺点。数值算例将其应用于复合材料数值模拟,计算结果表明,当覆盖位移函数采用完全一阶等参多项式时,计算精度较传统有限元法有很大改进。在力应集中或应力突变的区域,无需网格加密,只需提高覆盖位移函数的阶次即可。     

张力等参有限单元的构造及其在分离流动计算中的应用

本文利用张力样条函数，构造了一种十二节点张力等参有限单元。它不仅具有等参元的一切特点，而且具有张力可调的独特性质，从而在一定程度上可调整插值函数以达到较好的收敛收和计算精度。在分离流动计算中，尤其可以显示出它独特的优越性。本文的两个分离流动算例说明了这一点。     

用拟协调元直接构造平面任意四边形单元——进入有限元的禁区

利用拟协调元方法,在直角坐标系下直接构造了一族平面任意四边形单元,对其收敛性进行了分析,并与平面等参元进行了对比研究.结果证明平面任意四边形单元可采用多项式基函数直接列式,并可以保障单元的收敛性;拟协调元列式可以使平面问题的有限元方法得到统一.与平面等参元相比,单元列式简单,性能稳定,具有显式的刚度阵,计算量小,这说明对于有限元平面问题拟协调元是一个更正确、有效的做法.      

含两类附加函数的扩展等参有限元法

基于扩展有限元的基本思想,提出一类指数型间断函数来模拟。由于裂纹或节理等非连续结构所导致的位移不连续现象,该附加函数是以到间断处的垂直距离为自变量,且随距离的增大而呈指数衰减,同时,在非连续结构末端引入能反映其奇异场特性的三角基函数。本文用弱解形式推导了扩展有限元格式,并论证了两类附加函数在单元公共边上能够保持位移连续性这一要求。最后,编制了二维4节点和三维8节点的扩展等参有限元程序,并分别给出了算例,结果表明在模拟裂纹追踪时,扩展有限元法可行且有效。     

非协调四结点平面等参位移元新列式方法

本文导出一种等参协调元位移函数的新的表示方法,在此基础上建立起了构造等参非协调元的新方法。作为实例,构造出两个可以给出单刚显式的四结点平面非协调新单元。     

COARSE-MESH-ACCURACY IMPROVEMENT OF BILINEAR Q4-PLANE ELEMENT BY THE COMBINED HYBRID FINITE ELEMENT METHOD

IntroductionByadding‘nodeless’incompatiblebubblemodesandpreservinggeometriccharacteristicofthevariationalprincipleinmechanics,thecombinedhybridmethod[1～4 ]remarkablelyenhancedcoarse_mesh_accuracyofconventionalquadrilateralelementsoflowerorder.ThequadrilateralplaneelasticelementCH(0_1 )proposedinRef.[3 ]isasuccessfulexample.Followingthegeometricpointofviewinmechanicscombinedwithmathematicalanalysis,anovelexpressionofthecombinedhybridvariationalprincipleisintroducedtoclarifyitsintrinsicmecha…     

Spectral/hp penalty least‐squares finite element formulation for unsteady incompressible flows

In this paper, we present spectral/hp penalty least‐squares finite element formulation for the numerical solution of unsteady incompressible Navier–Stokes equations. Pressure is eliminated from Navier–Stokes equations using penalty method, and finite element model is developed in terms of velocity, vorticity and dilatation. High‐order element expansions are used to construct discrete form. Unlike other penalty finite element formulations, equal‐order Gauss integration is used for both viscous and penalty terms of the coefficient matrix. For time integration, space–time decoupled schemes are implemented. Second‐order accuracy of the time integration scheme is established using the method of manufactured solution. Numerical results are presented for impulsively started lid‐driven cavity flow at Reynolds number of 5000 and transient flow over a backward‐facing step. The effect of penalty parameter on the accuracy is investigated thoroughly in this paper and results are presented for a range of penalty parameter. Present formulation produces very accurate results for even very low penalty parameters (10–50). Copyright © 2008 John Wiley & Sons, Ltd.     

A new stable space–time formulation for two‐dimensional and three‐dimensional incompressible viscous flow

A space–time finite element method for the incompressible Navier–Stokes equations in a bounded domain in ?^d (with d=2 or 3) is presented. The method is based on the time‐discontinuous Galerkin method with the use of simplex‐type meshes together with the requirement that the space–time finite element discretization for the velocity and the pressure satisfy the inf–sup stability condition of Brezzi and Babu?ka. The finite element discretization for the pressure consists of piecewise linear functions, while piecewise linear functions enriched with a bubble function are used for the velocity. The stability proof and numerical results for some two‐dimensional problems are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

线性等参单元逆变换的几何二分法及其修正

在证明线性等参单元的一个几何特性的基础上,提出了线性等参单元逆变换的几何二分法。几何二分法简单易行,避免求解高维高次非线性方程组。在几何二分法基础上,提出一种修正措施以消除畸形单元对所求结果的影响,几何二分法及其修正措施克服了以往方法存在的缺点,两个实例验证了由几何二分法及其修正措施进行等参逆变换的正确性。