Frictional contact analysis of functionally graded materials with Lagrange finite block method

Based on the one‐dimensional differential matrix derived from the Lagrange series expansion, the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials. In this paper, the formulation of the Lagrange finite block method with boundary type in the strong form is presented and applied to non‐conforming contact problems for the functionally graded materials subjected to either static or dynamic loads. The first order partial differential matrices are only needed both in the governing equations and in the Neumann boundary condition. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate of global system to the normalized coordinate with eight seeds. Time dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin's inversion method is applied to determine all the physical values in the time domain. Conforming and non‐conforming contacts are investigated by using the iterative algorithm with full load technique. Illustrative numerical examples are given and comparisons have been made with analytical solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

Parametric quadratic programming method for elastic contact fracture analysis

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the parametric variational principle and FEM, a linear complementary method is extended to analyze contact fracture mechanics. The near-tip fields are properly modeled in the analysis using special crack tip elements with quarter-point nodes. Stress intensity factor solutions are presented for some frictional contact fracture problems and are compared with known results where available.     

Finite element analysis of substation composite insulators

Composite insulators are rapidly replacing their porcelain counterparts in electrical substation applications. These insulators consist of a glass-reinforced polymer (GRP) rod, with two metal end fittings radially crimped onto the ends of the rod during assembly. In this paper, axisymmetric finite element models are developed to evaluate the mechanical performance of composite insulators under externally applied axial compression. The analyses are performed by assuming both a perfectly bonded interface between the composite rod and the end fittings, and an imperfect interface which permits large relative sliding with Coulomb friction. Results indicate that the perfect interface model is unrealistic since it predicts singular stresses at the interface comer and an overall linear structural response. On the other hand, the imperfect interface model is found to simulate accurately the structural non-linearity caused by relative sliding of the GRP rod within the end fittings. The imperfect interface model has therefore been used to evaluate the effects of interface friction, and the extent of crimping, on the maximum load-bearing capacity of substation composite insulators.     

A contact algorithm for frictional crack propagation with the extended finite element method

We present an incremental quasi‐static contact algorithm for path‐dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non‐linear contact mechanics and embedded within a localized element by penalty method. Newton–Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ‘LATIN’ for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd.     

碳纤维束间的摩擦磨损特性

为了对碳纤维束的磨损程度进行定量分析以及探索碳纤维束间摩擦磨损机制,采用自制的摩擦模拟实验装置,研究了摩擦次数、加载力、摩擦角度对碳纤维束摩擦损伤的影响。通过对比摩擦前后碳纤维束的拉伸断裂强力、毛羽量和表面浆膜形态评价了其磨损程度。结果表明:随着摩擦次数、加载力的增大,碳纤维束的磨损程度逐渐加剧;当摩擦角度在90°~30°范围变化时,碳纤维束的拉伸断裂强力随着角度的减小而小幅度下降;而当摩擦角度为0°时,碳纤维束的拉伸断裂强力急剧下降。同时,结合纤维束接触理论和黏性薄膜压痕法揭示了碳纤维束摩擦损伤机制,发现有效接触面积的变化是导致碳纤维束磨损程度改变的主要因素,且纤维束间的有效接触面积随加载力的增大而增大,随摩擦角度的增大而减小。      

A non‐linear programming approach to kinematic shakedown analysis of composite materials

Using a Representative volume element (RVE) to represent the microstructure of periodic composite materials, this paper develops a non‐linear numerical technique to calculate the macroscopic shakedown domains of composites subjected to cyclic loads. The shakedown analysis is performed using homogenization theory and the displacement‐based finite element method. With the aid of homogenization theory, the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. By means of non‐linear mathematical programming techniques, a finite element formulation of kinematic shakedown analysis is then developed leading to a non‐linear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load of a composite is then obtained. An effective, direct iterative algorithm is proposed to solve the non‐linear programming problem. The effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples. This can serve as a useful numerical tool for developing engineering design methods involving composite materials. Copyright © 2005 John Wiley & Sons, Ltd.     

渐开线齿轮的接触分析

以Hertz应力表达式为基础,将单齿啮合的渐开线齿轮等效为相互挤压的两个圆柱体,推导了齿轮接触应力的理论表达式．建立一套单齿对啮合的有限元分析方法,包括引入渐开线和齿根过渡曲线方程及对应的自变量区间,建立参数化齿廓;模型轮缘厚度取3倍的模数,周向宽度取3倍的齿厚;在接触面上进行网格细化处理;在对应的主、从动齿轮内缘分别施加均匀切向力和固定约束等．计算结果显示,有限元解和理论解吻合较好,最大偏差不超过5%,该方法适用于不同的啮合轮齿参数．由有限元方法得到的渐开线轮齿的接触应力符合Hertz理论中的半椭圆分布规律,Mises应力和剪应力分布也符合接触力学理论,但应力分布的对称中心存在偏离或者偏斜现象,分析认为,是由于轮齿弯曲变形造成的．     

电连接器接触件应力场的数值分析与试验验证

利用ANSYS对某型号电连接器接触件应力场进行分析,以寻找应力变化规律.对接触件应力场分布特点、插孔形变、接触压力随温度升高的变化规律进行了仿真研究,并进行数据分析与接触压力的试验验证.结果表明:随着温度升高,插孔最大形变量增加,最大接触压力和接触压力区域都有所减少;尺寸较小的接触件插孔槽缝底部最大等效应力随温度升高增幅较大,交变载荷作用时易出现疲劳、破裂等,属产品失效薄弱点.通过分析得知最大等效应力值随温度上升而变化的趋势取决于温度软化效应和热应力增强作用的综合结果;仿真结果能较好地反映电连接器的工作应力状态,接触压力试验验证了有限元仿真方法的可行性.     

移动式架车机伸缩托头-托架接触的有限元分析

采用基于接触对的非线性接触分析处理接触问题时,其分析结果更接近工程应用实际,但计算成本比较高且存在不收敛的情况。而自由度节点耦合分析不但能降低计算成本,而且能够保证一定精度。为了探究在一定误差范围内选用自由度节点耦合分析来替代基于接触对的非线性接触分析的可行性,以举升重量为15 t的移动式架车机为研究对象,在ANSYS软件中建立伸缩托头-托架的接触模型与节点耦合模型,在举升高度最大且伸缩托头完全伸出的工况下进行有限元分析,考虑接触刚度系数与摩擦因数对有限元分析结果的影响,分析了2种模型各接触区域等效应力的区别。通过比较2种模型的有限元分析结果可知,2种模型各接触区域的等效应力值存在一定的相对误差,且接触区域内2个接触面的相对滑动程度决定了接触分析的精度。对于精度要求不高的机械结构,可以考虑用自由度节点耦合分析来替代基于接触对的非线性接触分析。     

Frictional contact analysis of multiple cracks by incremental displacement and resultant traction boundary integral equations

Based on the merits of the dual boundary element technique, a modified dual boundary element technique is extended to deal with the frictional contact of a finite plate with arbitrarily distributed multiple cracks. Besides establishing the incremental displacement boundary integral equation on the outer boundary, the resultant traction boundary integral equation on one of the crack surfaces is also developed. Since the resultant traction instead of incremental traction on the crack surface is introduced, the computed resultant contact tractions under sliding condition satisfy the Coulomb's friction law directly. Hence, as compared with the authors' previous work, only very few computation iterations are required by this method to accurately describe the contact situations of crack surfaces. As a result, not only the linear cracks, but also other types of multiple cracks, for example, curved and kinked cracks, can be tackled. The effects of friction and interaction among cracks on the computation of stress intensity factors are also displayed.     

基于Layerwise理论的共固化粘弹阻尼复合材料动特性分析

共固化粘弹性复合材料兼具结构承载和阻尼减振功能。针对传统的混合单元法在应用于粘弹性夹层复合材料结构阻尼性能分析时存在着前处理困难、计算规模大、精度低以及难以考虑正交各向异性铺层自身损耗能力的缺点,推导了一种基于Layerwise离散层理论的四节点四边形复合材料层合板单元,并利用直接复特征值解法建立了共固化粘弹性复合材料结构的阻尼性能分析方法。将该方法应用于不同的阻尼结构,分析结果与文献中已公开结果和混合单元法的计算结果进行了对比验证。结果表明,基于离散层理论的层合板单元具有计算精度高、前处理建模简单和计算规模小的优点,可有效应用于复杂共固化粘弹性复合材料结构的阻尼性能分析和设计。     

准静态压痕力作用下复合材料层压板的损伤阻抗分析

建立了一种复合材料层压板在准静态压痕力作用下的损伤阻抗的预测方法。首先分别针对基体破坏、分层、 纤维断裂等失效模式引入相应的失效变量 , 并建立不同失效模式下的刚度折减方法 , 然后采用基于应变描述的 Hashin和 Yeh失效准则并结合有限元方法 , 对复合材料层压板在准静态压痕力作用下的破坏过程进行渐进损伤分析 , 在此基础上进一步预测了层压板的损伤阻抗。采用商用有限元软件 ABAQUS/ Standard 的 UMAT用户子程序实现数值模拟。计算结果表明 , 分层起始与扩展是导致载荷2位移曲线发生第 1 次卸载的主要原因 , 当接触力达到其最大值时出现较明显的纤维断裂。分层起始载荷和最大接触力的预测结果与实验数据吻合良好。     

Low-velocity impact analysis of composite laminates using linearized contact law

Usually many researchers have used the modified Hertzian contact law or experimental static indentation law to analyze impact response of composite laminates subjected to low-velocity impact. In this study, physical meaning of the analytical method using the laws was investigated and the difference between the analytical results obtained using the two laws was also investigated. Furthermore parametric study on contact coefficient and exponent of the contact law was performed. Finally it could be shown that linearized contact law could be well applied to the low-velocity impact analysis of composite laminates. If this concept is used, any general-purpose finite element method software can be used to solve impact problem without direct developing any FEM code by each researcher. In this paper, some analytical results analyzed using a general-purpose commercial FEM software were also presented.     

温度变化下复合材料层合板的试验模态分析

通过动力测试试验研究了环境条件变化对复合材料层合板振动特性的影响 , 这对于复合材料结构基于动力响应健康监测和振动控制系统设计使用的安全性具有重要意义。在不同温度条件下利用锤击以及激振器实验方法测定复合材料层合板的动力响应 , 采用随机子空间法 (SSI) 识别了其固有频率、 阻尼以及模态振型。研究结果表明 , 复合材料层合板结构固有频率及阻尼比与温度变化存在逆相关关系 , 而所识别的模态振型变化并没有非常清晰的相关关系。分析结果进一步表明 , 复合材料结构振动控制和健康监测系统设计过程中需要考虑上述影响。      

Boundary element analysis of two-dimensional elastoplastic contact problems

A general boundary element formulation for contact problems, capable of dealing with local elastoplastic effects and friction, is presented. Both conforming and non-conforming problems may be analysed. The contact problem is solved by means of a direct constraint technique, in which compatibility and equilibrium conditions are directly enforced in the general system of equations. The contact areas are modelled with linear interpolation functions, and quadratic interpolation functions are used everywhere else. Elastoplasticity is solved by a BEM initial strain approach The Von Mises yield criterion with its associated flow rule is adopted. Both perfectly plastic and work hardening materials are studied in the proposed formulation.

An incremental loading technique is proposed, which allows accurate development of the loading history of the problem. The non-linear nature of these problems demands the use of an iterative procedure, to determine the correct frictional conditions at every node of the contact area and the value of the plastic strains at selected points where local yielding may have occurred. Several numerical examples are presented to demonstrate the efficiency of the proposed formulation.     

Discontinuous deformation analysis handling vertex-vertex contact based on principle of least effort

This study establishes an innovative discontinuous deformation analysis by solving the problem of frictional and cohesive contact using an implicit cone complementary formulation. In order to handle singularity associated with the vertex-vertex contact, resistances to motion trend are firstly estimated by introducing the concepts of total and partial contact forces. Based on principle of least effort, the vertex-vertex contact can be converted to a corresponding vertex-edge contact properly. In addition, unnecessary vertex-vertex contacts can be identified. The numerical scheme fully exploits geometric and dynamic conditions of the polygonal block system. As a result, determination of motion trend in the block system is penalty-free without being affected by the time step. The advantages and application prospects of the presented dynamic framework are demonstrated by using several benchmark examples.     

添加剂对Ag/陶瓷复合触点材料浸润性及电性能的影响

采用固相反应法制备了LaFe0.25Ni0.75O3陶瓷并加入少量添加物作为改性剂,对其与Ag的浸润性,材料的电阻率以及Ag/陶瓷复合电接触材料的电性能分别进行了研究,结果显示,改性剂使陶瓷材料与Ag之间的浸润性发生明显的变化,且作用效果与改性剂的加入方式有关,添加剂的加入使材料的电阻率增大,同时一定程度上改变了陶瓷在银基体中的分布状态,从而对电接触材料的使用性能产生较大的影响.     

圆柱斜齿轮齿面接触动应力计算与分析研究

为了有效计算动态工况下斜齿圆柱齿轮副的齿面接触应力,建立了考虑时变啮合刚度激励和啮入冲击激励的滚动轴承支撑的斜齿圆柱齿轮副啮合型弯-扭-轴耦合六自由度振动模型,通过其计算了齿面啮合动载荷。提出了综合考虑轮齿动载荷、齿间载荷分配系数以及齿面赫兹接触的斜齿圆柱齿轮齿面接触动应力计算方法,同时也利用Abaqus有限元软件动力学模块分析了齿面接触动应力。分别计算了800 N·m、1 200 N·m、1 600 N·m三种负载扭矩下的齿面接触动应力变化过程,基于承载接触分析法的最大接触应力与AGMA标准计算值最大相差为11.6%,基于Abaqus有限元法的最大接触应力与AGMA标准计算值最大相差13.8%,而两种方法的齿面接触动应力变化曲线最大偏差11.3%,从而证实了本文提出的斜齿圆柱齿轮齿面接触动应力计算方法合理有效。     

Fatigue crack closure analysis of bridged cracks representing composite repairs

This article presents an analytical and numerical study of the fatigue crack‐closure behaviour of a bridged crack representing a crack that has been repaired by a composite patch. It is shown that, provided that the plate stress beneath the patch is less than 40% of the material’s yield stress, the crack‐closure stress of a patched crack is approximately equal to that of an unbridged crack under small‐scale yielding, depending only on the stress ratio. Furthermore, it is shown that the transient crack‐closure behaviour of a patched crack subjected to variable amplitude loading can be determined by analysing an unpatched crack subjected to the same stress intensity factor history. Based on these findings, it is proposed that the fatigue crack closure of a patched crack can be determined by analysing an unpatched centre crack subjected to an adjusted stress, for which an explicit expression is given. Predictions based on the proposed method are shown to correlate very well with experimental results obtained under two aircraft loading spectra.