基于高阶板理论的有限单元及其在压电智能结构中的应用研究

带有分布式压电驱动器 /传感器的自适应智能材料结构在振动控制、形状控制、精确定位等方面具有很大潜力而受到广泛的关注。本文把x ,y方向的位移定义为厚度坐标的三次多项式 ,利用板上下自由表面的力边界条件及正交异性复合材料的特性 ,导出了改进的高阶板理论。依据该理论建立了 4节点 2 0自由度矩形板高阶有限单元 ,并对一些算例进行了分析。通过与文献结果的对比 ,验证了改进的高阶板理论和所建立单元的正确性。最后利用所建立的单元 ,分析了压电悬臂梁中压电层在不同脱胶长度情况下板的频率变化 ,计算结果与试验结果相吻合     

Development of high speed computation algorithm for transient analysis of rectangular plates

A new transient analysis method for a rectangular plate structure comprised of a large number of plate elements was developed in order to significantly reduce computational time and memory. This algorithm was derived from the combination of the transfer technique of the transfer mass coefficient method, the modeling technique of the finite element method, and the numerical integration technique of Newmark’s method. In this paper, the algorithm for the transient analysis of a rectangular plate structure is formulated by the proposed method. In order to verify the computational accuracy and efficiency of the proposed method, the results obtained by the proposed method were compared with those obtained by the finite element method and the finite element-transfer matrix method. The proposed method, the finite element-transfer mass coefficient method, could considerably reduce the computation time without the loss of accuracy, in spite of using small computation memory, by using the transfer rules successively.     

Analysis of laminated anisotropic plates and shells using symbolic computation

The extension of classical isotropic plate and shell solutions and finite element formulations to cope with orthotropic/monoclinic laminated and shear deformable structures often involves very complex intermediate stages and final results within the derivations. This paper examines four case studies covering the use of symbolic computation to manage this complexity. These case studies comprise the derivation of a catalogue of solutions to orthotropic circular plate problems, the formulation of two axisymmetric shell finite elements (respectively using Flügge’s shear-rigid shell assumptions and the shear-flexible assumptions of Soldatos) and the derivation of the eighth-order governing differential equation for a laminated monoclinic or orthotropic shell. The emphasis is placed upon the techniques required to achieve these derivations using symbolic computation, and the considerable effort involved in putting the results into publishable form is noted.     

Free vibration analysis of perforated plate submerged in fluid

An analytical method to estimate the coupled frequencies of the circular plate submerged in fluid is developed using the finite Fourier-Bessel series expansion and Rayleigh-Ritz method. To verify the validity of the analytical method developed, finite element method is used and the frequency comparisons between them are found to be in good agreement. For the perforated plate submerged in fluid, it is almost impossible to develop a finite element model due to the necessity of the fine meshing of the plate and the fluid at the same time. This necessitates the use of solid plate with equivalent material properties. Unfortunately the effective elastic constants suggested by the ASME code are found to be not valid for the modal analysis. Therefore in this study the equivalent material properties of perforated plate are suggested by performing several finite element analyses with respect to the ligament efficiencies.     

复合材料加筋结构的神经网络响应面优化设计

针对复合材料加筋结构优化设计的复杂性,提出利用人工神经网络结构近似分析响应面来反映结构设计输入与结构响应输出的全局映射关系的优化方法。通过正交试验设计选取合适的结构有限元分析样本点,进行神经网络响应面的构建和训练;将神经网络响应面作为目标函数或者约束条件,汇同其他常规约束条件完成优化模型的建立,并应用遗传算法(GA)进行优化,从而形成一套适应性强的的高效优化方法。以复合材料翼身融合体帽型加筋板的质量优化为实例,建立加筋板模型的重量响应面目标函数、强度和翘曲稳定性响应面约束条件;通过PATRAN/NASTRAN有限元软件进行有限元计算,获取用于响应面训练的样本点数值。算例结果表明,该方法能以很少的有限元分析次数取得高精度的响应面近似模型,并且使优化计算耗时大为减少,优化效率大大提高。     

Vibration analysis of corrugated Reissner–Mindlin plates using a mesh-free Galerkin method

A mesh-free Galerkin method for the free vibration analysis of unstiffened and stiffened corrugated plates is introduced in this paper, in which the corrugated plates are simulated with an equivalent orthotropic plate model. To obtain the corresponding equivalent elastic properties for the model, a constant curvature state is applied to the corrugated sheet. The stiffened corrugated plates are treated as composite structures of equivalent orthotropic plates and beams, and the strain energies of the plates and beams are added up by the imposition of displacement compatible conditions between the plate and the beams. The stiffness matrix of the whole structure is then derived. The proposed method is superior to the finite element methods (FEMs) because no mesh is needed, and thus stiffeners (beams) do not need to be placed along the mesh lines and the necessity of remeshing when the positions of the stiffeners change is avoided. To demonstrate the accuracy and convergence of the proposed method, several numerical examples are analyzed both with the proposed method and the finite element commercial software ANSYS. Examples from other research are also employed. A good agreement between the results for the proposed method, the results of the ANSYS analysis, and the results from other research is observed. Both sinusoidally and trapezoidally corrugated plates are studied.     

Modelling the cutting forces in micro-end-milling using a hybrid approach

This paper presents the development of a cutting force model for the micro-end-milling processes under various cutting conditions using a hybrid approach. Firstly, a finite element (FE) model of orthogonal micro-cutting with a round cutting edge is developed for medium-carbon steel. A number of finite element analyses (FEA) are performed at different uncut chip thicknesses and velocities. Based on the FEA results, the cutting force coefficients are extracted through a nonlinear algorithm to establish a relationship with the uncut chip thickness and cutting speed. Then, the cutting force coefficients are integrated into a mechanistic cutting force model, which can predict cutting forces under different cutting conditions. In order to account for the cutting edge effect, an effective rake angle is employed for the determination of the cutting force. A comparison of the prediction and experimental measured cutting forces has shown that the developed method provides accurate results.     

角膜移植中缝针刺入角膜的有限元仿真

利用微力材料试验机进行新鲜猪眼球角膜组织的力学性能测试试验。试验选用医用眼科2号缝针(直径0.2 mm),以 1 mm/s的临床手术平均刺入速度,在正常眼压下刺入角膜组织,得到了缝针针尖在刺入过程中的位移—针轴力关系。在此基础上,采用线性三角形单元建立角膜的平面有限元分析模型,并根据缝针与角膜软组织接触表面间相互作用的粘—滑理论,建立缝针刺入角膜的有限元仿真算法。以试验测得的针尖位移和针轴力的关系为边界条件,在Matlab环境下利用迭代算法对所建立的有限元方程进行求解,实现了缝针刺入角膜过程的实时仿真,同时得到缝针刺入角膜过程中节点的位移图和位移—针轴力的关系曲线,为角膜移植手术机器人的设计和缝合作业的任务规划提供了重要的依据。     

Some advances and applications in quadratic programming method for numerical modeling of elastoplastic contact problems

This paper reviews briefly some advances and applications in parametric quadratic programming (PQP) method for numerical modeling of elastoplastic contact problems. The parametric variational principle (PVP) and the corresponding finite element model for numerical simulation of 3D elastoplastic frictional contact problems with isotropic/anisotropic (orthotropic) friction law are presented. The finite element software JIFEX is then developed with the application-oriented concept for nonlinear analysis of complex structures in general purposed engineering. Some typical engineering applications such as compressor impeller and the railway wheel/rail contact analysis are shown to illustrate the potential of the software developed.     

Dynamic response and damage of composite shell under impact

The dynamic response and damage of laminated composite cylindrical shell subjected to impact load is numerically investigated using the finite element method. A nine-node isoparametric quadrilateral element based on Sander's shell theory is developed, in which the transverse shear deformation is considered. A semi-empirical contact law that accounts for the permanent indentation is incorporated into the finite element program to evaluate the contact force. The Newmark time ingegration algorithm is used for solving the time dependent equations of the shell and the impactor. The Tsai-Wu failure criterion is used to estimate the failure of the laminated shell. Numerical results, including the contact force history, interlaminate damage zone, and failure indices in the shell are presented. Effects of curvature, impact velocity and mass of impactor on the composite shell behaviors are discussed.     

超声红外热像技术中预紧力对金属平板振动特性的影响

在超声红外热像检测过程中,超声脉冲激励下被测对象的振动状态直接决定了缺陷区域的生热效果,而工具杆与被测对象之间的预紧力是影响被测对象振动状态的重要因素之一。试验结果表明:预紧力的增大使得振动能量呈上升趋势并伴随着小范围不稳定,同时被测对象的振动频谱由混沌振动开始,经历次谐波、准次谐波后达到超谐波振动状态。针对上述现象,采用显式动力学方法建立了与试验条件相对应的有限元模型,并进行了瞬态动力学分析。模型采用压电-力类比方法来模拟压电陶瓷的逆压电效应,同时引入了动态松弛来更准确模拟试验工况。仿真结果验证了试验观察到的现象,并进一步揭示了预紧力的增大将改变超声工具杆和被测平板之间的接触力状态,从而改变被测试件的振动能量分布和振动频谱。研究成果有助于实现通过预紧力来控制被测对象振动状态,进而达到优化超声红外热像检测的目的。     

Development of a force controlled nanocutting system using a flexible mechanism for adaptive cutting of microstructures on non-planar surfaces

A force controlled nanocutting system based on a flexible mechanism was developed. Instead of utilizing force sensors, the force sensing and control in the developed system is realized by sensing and controlling the deformation of the flexible mechanism. With force feedback control for controlling the cutting force in real time, this system could achieve adaptive cutting along non-planar surfaces without prior knowledge about the surface shape. The finite element method was used to model the flexible mechanism and a Pareto-based multi-objective optimization algorithm with the goals of high force resolution and stability was used to obtain the geometric parameters of the flexible mechanism. During the cutting processing, a capacitive displacement sensor was used to detect the deformation of the flexible mechanism to measure the force in real time, and a piezoelectric ceramic actuator was used to adjust the feed position of the tool to control the cutting force. Nanocutting experiments of microstructures were successfully carried out on inclined and curved surfaces of ductile as well as brittle materials without prior knowledge of their surface forms.     

Welding residual stress in roots between deck plate and U-rib in orthotropic steel decks

Fatigue cracks have recently been observed at weld roots between the deck plate and U-rib in orthotropic steel decks. Some cracks initiated from the weld roots and then propagated through the deck plate. The welding residual stress at the root appears to have a considerable influence on crack initiation and propagation. However, the stress has not yet been efficiently clarified in previous studies. In this study, the residual stress of model specimens with or without weld penetration and root gap were measured using the cutting method and magnetostriction method. In addition, thermo-elastic-plastic finite element analyses were carried out on parametric models of actual welded joints.     

板材软模成形二维断面有限元分析界面接触摩擦处理

板材软模成形是板材和柔性传力介质耦合变形过程,存在板材和刚性模具及板材和柔性传力介质两种类型的界面接触。采用罚函数法计算接触力,推导了Mindlin轴对称壳单元和实体单元两种不同单元类型之间接触摩擦的有限元列式。采用静力显式的时间积分方法,通过控制载荷步长保持接触状态稳定。粘弹塑性软模材料的板材变形数值算例表明该算法是有效的。该算法也适用于其他类型软模材料的板材变形接触摩擦问题的处理。     

A simple finite element analysis of axisymmetric vibration of annular and circular plates

The axisymmetric vibration of annular and circular plates, isotropic or polar orthotropic, is analysed by an axisymmetric finite element. The features of the present study are that: (i) the formulation of the finite element is based on elasticity theory and has no assumptions as in the conventional plate theory-based analysis, yet is still simple and ready for use, and (ii) the boundary conditions are satisfied exactly and the significant effect of boundary conditions on the vibration frequency is demonstrated. Comparisons with alternative solutions show the accuracy of the present approach and the inadequacy of conventional methods in dealing with the vibration of annular and circular plates with simply supported boundary conditions.     

Strength calculation for forged straight bevel gear teeth having a linking web

When bevel gears are forged, a thin web results on the back of the teeth. This web, which results from the clearance between the dies, gives an additional strength not accounted for when the Lewis design criteria is used. To account for this extra strength a plate model is developed. The solution for this plate model can be obtained by assuming a polynomial deflection function. Using the Galerkin variational method the constants in this assumed deflection function can be calculated. The plate model is compared with a finite element model, using a general purpose program and also with experimental strain measurements. This proposed plate solution indicates an increase in strength of more than 25% in excess of that suggested by the cantilever beam model of Lewis when compared with the finite element results.     

Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method

In this paper, a finite element formulation is developed for analyzing the axisymmetric thermal buckling of FGM annular plates of variable thickness subjected to thermal loads generally distributed nonuniformly along the plate radial coordinate. The FGM assumed to be isotropic with material properties graded in the thickness direction according to a simple power-law in terms of the plate thickness coordinate, and has symmetry with respect to the plate midplane. At first, the pre-buckling plane elasticity problem is developed and solved using the finite element method, to determine the distribution of the pre-buckling in-plane forces in terms of the temperature rise distribution. Subsequently, based on Kierchhoff plate theory and using the principle of minimum total potential energy, the weak form of the differential equation governing the plate thermal stability is derived, then by employing the finite element method, the stability equations are solved numerically to evaluate the thermal buckling load factor. Convergence and validation of the presented finite element model are investigated by comparing the numerical results with those available in the literature. Parametric studies are carried out to cover the effects of parameters including thickness-to-radius ratio, taper parameter and boundary conditions on the thermal buckling load factor of the plates.     

胶囊机器人磁驱动力建模与测量

可吞式无线磁驱胶囊机器人在胃肠道内的诊疗效果与机器人受到的外部磁驱动力密切相关。本文建立了外部磁驱动力的理论模型,基于等效磁荷模型推导了两径向充磁环形永磁体相互作用的数学表达式,采用自适应递归式计算方法开展了数值计算。此外,发展了环形永磁体间磁力实时测量方法,并开发了磁力-间距同步测量仪器开展实验研究,且建立了3D环形永磁体有限元仿真模型。实验测量磁力-间距关系曲线与理论计算和有限元仿真结果吻合较好,误差小于4%,验证了理论模型和有限元仿真模型的准确性和可靠性。通过参数分析,揭示了胶囊机器人内置永磁体长度、厚度和体积对磁力的影响规律。研究结果为精准驱动胶囊机器人在胃肠道内运动奠定了理论基础。     

基于LS—DYNA的分条圆盘剪剪切力的计算研究

通过对分条圆盘剪剪切力计算公式的讨论,按实际生产需求设计了圆盘剪三维模型。利用LS—DYNA,建立铜板分条圆盘剪的有限元模型,进行非线性计算研究,获得了铜板剪切过程中的应力一应变状态、剪切力。与理论公式计算结果对比分析,肯定了铜板分条剪切模拟中应力一应变分布与塑性变形的准确性,得到的剪切力变化曲线,较好地反应分条圆盘剪剪切过程中剪切力的变化规律,文章采用的有限元动力学分析可以为薄板分条圆盘剪的设计与实际生产提供了理论支持。     

道岔侧板变形装置刚柔耦合动力学仿真分析

考虑电动推杆的推力、车辆通过时的离心力以及各构件间的相互作用,结合基于有限元法的柔性体模态计算,建立了轻轨道岔的侧板变形装置的刚柔耦合动力学模型,采用ADAMS软件对该装置进行多体动力学仿真计算,得出各构件的载荷、位移时间历程以及侧板和凸轮组的应力云图,可为道岔侧板变形装置的结构设计提供理论依据。