基于有限差分法的金属复合板冷却过程温度分布预测

目的 研究金属复合板在冷却过程中的温度变化规律以及经过冷却后金属复合板的表面及内部温度分布规律.方法 利用二维有限差分法对金属复合板材冷却过程中的温度变化规律进行了分析,从理论上推导了使用等步长节点法求解温度的差分方程,通过设置合理的边界条件解决了金属复合板基板和复板接触界面互相影响的传热问题.结果 通过设置等步长节点的有限差分法计算得出金属复合板冷却过程的温度变化规律以及冷却后金属复合板的表面及内部温度分布,对比有限元软件模拟计算和有限差分程序计算结果,得出结论.结论 界面处温度高,越靠近两边温度越低,通过与有限元软件模拟计算作对比,验证了差分法计算的准确性.     

Frictional contact of flexible and rigid bodies

 This paper is about planar frictional contact problems of both flexible and rigid bodies. For the flexible case a nonlinear finite element formulation is presented, which is based on a modified Coulomb friction law. Stick-slip motion is incorporated into the formulation through a radial return mapping scheme. Linearly interpolating four node elements and three node contact elements are utilized for the finite element discretization. The corresponding tangent stiffness matrices and residual vectors of the equations of motion are presented. In the rigid body case the contact problem is divided into impact and continual contact, which are mathematically described by linear complementarity problems. The impact in normal direction is modeled by a modified Poisson hypothesis, which is adapted to allow multiple impacts. The formulation of the tangential impact is grounded on Coulombs law of friction. The normal contact forces of the continual contact are such that colliding bodies are prevented from penetration and the corresponding tangential forces are expressed by Coulombs law of friction. Examples and comparisions between the different methods are presented. Received: 10 January 2001     

基于FEPG有限元分析系统的树脂充模过程模拟

为优化复杂预成型体结构的液体成型工艺,基于有限元法/生死节点法模拟了复合材料液体模塑成型过程树脂流动,并针对典型矩形平板、圆板结构、I型加筋壁板充模过程进行了仿真与验证。结果表明:典型矩形平板和圆板结构的充模过程模拟结果与理论解一致性较好,验证了生死节点法跟踪树脂流动前锋的有效性。含有方腔的变厚度圆柱体和正方体三维实体结构的充模过程模拟验证了有限元方法对三维结构的适用性。基于有限元法/生死节点法的液体充模过程模拟方法对于复杂求解区域具有更好适应性,可用于复杂实体结构的液体模塑成型工艺过程树脂流动规律预测、指导模具设计及工艺优化。      

Hybrid finite difference/finite element solution method development for non-linear superconducting magnet and electrical circuit breakdown transient analysis

The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique.     

A suitable low‐order,tetrahedral finite element for solids

To use the all‐tetrahedral mesh generation capabilities existing today, we have explored the creation of a computationally efficient eight‐node tetrahedral finite element (a four‐node tetrahedral finite element enriched with four mid‐face nodal points). The derivation of the element's gradient operator, studies in obtaining a suitable mass lumping and the element's performance in applications are presented. In particular, we examine the eight‐node tetrahedral finite element's behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the eight‐node, mean‐quadrature hexahedral finite element. Comparisons with the results obtained from the mean‐quadrature eight‐node hexahedral finite element and the four‐node tetrahedral finite element are included. Given automatic all‐tetrahedral meshing, the eight‐node, mean‐quadrature tetrahedral finite element is a suitable replacement for the eight‐node, mean‐quadrature hexahedral finite element and meshes requiring an inordinate amount of user intervention and direction to generate. Copyright © 1999 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.     

可动节点复合单元的基本原理及在一维问题中的应用

着重于开发一种以常规线性单元为基底,附加中间移动节点而构成的新型高精度的复合有限单元方法.移动节点复合单元法作为一种高精度有限单元法,通过调节中间可动节点的位置改变其单元内部的场分布,从而只需少量单元即可达到较高的计算精度.由于此种复合单元的中间移动节点的形函数采用计算机图形学常用的Bezier函数,故可简称为‘Bezier复合单元'(BCE).应用此Bezier单元对具有解析解的一维受分布载荷作用的等截面杆问题和受集中载荷作用的变截面杆问题进行模拟,并与解析解及采用常规有限单元法的模拟结果进行对照和分析.     

Effects of internal finite element node placement on field problem solutions

Given herein, in abbreviated form, is a discussion of the effects of element internal and edge node location in the finite element-Galerkin method. The solution dependencies on node placement of many numerical schemes are reviewed. Then, a transient linear one-dimensional heat conduction problem, solved using the finite element-Galerkin method, is used for illustration. Results show that, in contrast to many other numerical techniques, if the finite element-Galerkin method is strictly adhered to with respect to spatial integrations for a given number of nodes in an element, the solution is unaffected by shifting node locations as long as the specific shape of any given element remains unaltered. The reason for this invariance becomes readily apparent upon examining the orthogonality requirements imposed by this method.     

On the relationship between the finite element and finite difference methods

The integral equations which arise from application of the Galerkin-finite element scheme to the convective diffusion equation are examined to illustrate how this method represents differential equations. The formulae obtained are effectively spatial averages of standard finite difference equations written at a node. The truncation error in the finite element solution at a node is obtained for various nodal configurations.     

An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.The authors are grateful to the support of the Australian Research Council via a Discovery Projects grant (grant No: DP0346419).     

复合材料先进网格结构共固化工艺的温度场模拟

基于ANSYS软件开发了用于模拟复合材料固化过程中温度-固化度耦合场变化程序, 并分别采用二维和三维有限元模型对复合材料先进正交网格结构的软模辅助共固化工艺过程进行了数值仿真。计算结果分析表明: 二维有限元模型不考虑网格结构肋骨交叉点的影响, 能以较大时间步长进行共固化工艺的数值模拟, 且分析结果具有较高的精度; 三维精细有限元模型可考虑肋骨交叉点在共固化工艺中对复合材料先进网格结构内温度-固化度耦合场的影响; 肋骨交叉点附近的温度场明显高于结构的其他部位。      

Modeling of interfacial debonding crack in particle reinforced composites using Voronoi cell finite element method

In this paper, Voronoi cell finite element method (VCFEM), introduced by Ghosh and coworkers (1993), is applied to describe the matrix-inclusion interfacial debonding for particulate reinforced composites. In proposed VCFEM, the damage initiation is simulated by partly debonding of the interface under the assumption of the critical normal stress law, and gradual matrix-inclusion separations are simulated with an interface remeshing method that a critical interfacial node at the crack tip is replaced by a node pairs along the debonded matrix-inclusion interface and a more pair of nodes are needed to be added on the crack interface near the crack tip in order to better facilitate the free-traction boundary condition and the jumps of solution. The comparison of the results of proposed VCFEM and commercial finite element packages MARC and ABAQUS. Examples have been given for a single inclusion of gradually interfacial debonding and for a complex structure with 20 inclusions to describe the interfacial damage under plane stress conditions. Good agreements are obtained between the VCFEM and the general finite element method. It appears that this method is a more efficient way to deal with the interfacial damage of composite materials. The financial support by the Special Funds for the National Major Fundamental Research Projects G19990650 and the National Natural Science Foundation of China No. 59871022 are gratefully acknowledged.     

A nine node finite element for analysis of geometrically non-linear shells

A nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger-Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic modes. One version leads to a finite element model which is kinematically stable at element level while the other two give globally stable models. Numerical tests indicate that the finite element model which is stable at element level may reveal the locking effect in certain cases. However, the other two models are free of locking.     

A Treatment of wall boundaries for turbulent flows by the use of a transmission finite element method

A method to connect momentum Navier-Stokes equations with the universal law of the wall using the finite element method is developed for turbulent wall flows. This method is based on a domain decomposition of the fluid into subdomains near a solid boundary where the law of the wall is valid. A transmission formulation is introduced to match these regions and a new class of boundary finite element is used. This finite element takes into account the near-wall profile of the velocity and the transmission conditions. Computational results are presented for Poiseuille flow and flow over a backward-facing step.     

Generalized nodes and high‐performance elements

The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition‐of‐unity‐based finite‐element approximation. Construction of the partition‐of‐unity‐based approximation is accomplished by a physically defined local function of displacements. A 4‐node quadratic tetrahedral element and a 3‐node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition‐of‐unity‐based finite‐element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright © 2005 John Wiley & Sons, Ltd.     

Modelling of short wave diffraction problems using approximating systems of plane waves

This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

发动机机体结构振动模态分析

目的　建立某发动机的有限元模型 ,并进行模态分析 ,为研究机体的优化和动力匹配作准备工作 .方法　用 Ansys5.4有限元分析软件 ,对一 1 2缸 V型发动机进行自由模态分析 ,其中采用 1 0节点 4面体单元构造出较详细的机体离散模型 .结果　求解了机体的自由模态参数 ,与试验模态分析所得到的模态参数相对照 .结论　表明有限元方法对复杂结构的动力分析是一种有效方法 ,为进一步研究机体的优化、动力匹配和响应奠定了基础     

Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber

The present paper deals with the enrichment of 3D low‐order finite elements. The used concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. A consistent stiffness matrix is obtained, allowing a better approximation of the actual solution compared with that resulting from low‐order finite elements. Implemented for two eight‐node hexahedral elements, the performance of the space fiber rotation concept is assessed by running some classical beam, plate, and shell benchmarks, and the obtained results are compared especially with those given by linear eight‐node and quadratic 20‐node hexahedral elements. In particular, it is shown that the developed elements accuracy is significantly superior to that of the classical eight‐node hexahedral element and close to that of the classical 20‐node hexahedral element. Copyright © 2013 John Wiley & Sons, Ltd.     

Linear finite elements with orthogonal discontinuous basis functions for explicit earthquake ground motion modeling

The dynamic explicit finite element method is commonly used in earthquake ground motion modeling. In this method, the element mass matrix is approximately lumped, which may lead to numerical dispersion. On the other hand, the orthogonal finite element method, based on orthogonal polynomial basis functions, naturally derives a lumped diagonal mass matrix and can be applied to dynamic explicit finite element analysis. In this paper, we propose finite elements based on orthogonal discontinuous basis functions, the element mass matrices of which are lumped without approximation. Orthogonal discontinuous basis functions are used to improve the accuracy and reduce the numerical dispersion in earthquake ground motion modeling. We present a detailed formulation of the 4‐node tetrahedral and 8‐node hexahedral elements. The relationship between the proposed finite elements and conventional finite elements is investigated, and the solutions obtained from the conventional explicit finite element method are compared with analytical solutions to verify the numerical dispersion caused by the lumping approximation. Comparison of solutions obtained with the proposed finite elements to analytical solutions demonstrates the usefulness of the technique. Examples are also presented to illustrate the effectiveness of the proposed method in earthquake ground motion modeling in the actual three‐dimensional crust structure. Copyright © 2010 John Wiley & Sons, Ltd.     

A new crack tip element for the phantom‐node method with arbitrary cohesive cracks

We have developed a new crack tip element for the phantom‐node method. In this method, a crack tip can be placed inside an element. Therefore, cracks can propagate almost independent of the finite element mesh. We developed two different formulations for the three‐node triangular element and four‐node quadrilateral element, respectively. Although this method is well suited for the one‐point quadrature scheme, it can be used with other general quadrature schemes. We provide some numerical examples for some static and dynamic problems. Copyright © 2007 John Wiley & Sons, Ltd.