杂交元假设应力模式的变形刚度分析

通过本征变形模式提出识别杂交元零能变形模式和假设应力场中零能应力模式的新方法,同时给出了在假设应力场中增加应力模式时杂交元变形刚度的计算公式．从而从理论上阐明了在假设应力场中增加零能应力模式不仅不能抑制单元零能变形模式而且可能增加非零能变形模式的刚度,因此不宜用来假设应力场;同时进一步指出寄生应力模式将使单元产生虚假应变能而使单元显得过刚,因此即使它能够抑制单元零能变形模式也不宜用来假设应力场,从而为假设应力场提供了合理的建议．数值算例说明了包含零能应力模式和寄生应力模式时单元的性能．     

杂交应力元的应力子空间和柔度矩阵H对角化方法

证明了：1）杂交元假设应力模式线性无关是柔度矩阵非奇异的充分必要条件;以及2）等价假设应力模式形成相同的杂交元,在此基础上建立了假设应力模式的希尔伯特应力子空间,从而可以持方法简单地得到等价的正交归一化应力模式,实现了柔度矩阵对角化,使得杂交元形成过程中完全避免了繁杂的矩阵求逆运算,极大地提高了杂交元分析的计算效率,数值算例表明该方法是确实有效的。     

平面弹性裂纹分析的一种有效边界元方法

提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法．该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界．算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的．此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析．这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响．     

正交各向异性轴对称位势问题的Trefftz有限元分析

Trefftz有限元法（Trefftz finite element method, TFEM）因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元．在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入修正变分泛函并利用Gauss散度定理消除区域积分,最后根据驻值原理导得只含边界积分的单元刚度方程．数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.     

多变量有限元:相容性与模式优化

本文给出基于非协调试解函数的多变量有限元的非线性相容分析,导出能量相容条件和单元优化条件.提出了实施这些条件的杂交元的优化方法,建立了单元优化格式和多变量参数匹配原理.研究结果已应用于弹性力学等问题.     

基于曲率插值的大变形梁单元

线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题．该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.     

一种h型自适应有限单元

ｈ型自适应有限单元在网格局部细划时．会产生非常规节点，从而破坏了一般意义上的单元连续性假定．本文利用参照节点对非常规单元进行坐标和位移插值．为保证单元之间坐标和位移的连续性，本文提出了一组修正的形函数，常用的形函数是它的一个特例．本方法应用于有限元程序时，除形函数外无须做任何改动．算例表明水文的方法具有方法简单、精度高、自由度少、计算量小等优点．     

无锁定的退化的等参壳元

构造了一个无锁定的8节点退化的等参壳元。在自然坐标系中,对横向剪应变项插值修正使单元满足必要的模式(平移、转动和纯弯曲)以消除"剪切锁定";在局部坐标系中,对薄膜应变插值修正以消除"薄膜锁定"。这样构造的8节点单元的刚度矩阵具有正确的秩,同时具有恰当的零特征值和相应的刚体位移模式。这种单元对大跨-厚比情形既无"剪切锁定"又无"薄膜锁定",无虚假的零能模式和机构出现,可用于厚壳和薄壳。     

多边形应力杂交单元的接触算法研究

针对单元较小的情况下,现有的非均匀模型难以得到精确应力场和应力集中现象的问题,采用直接约束法,提出了一种基于多边形应力杂交单元的优化接触算法.多边形应力杂交单元在应力函数的构造以及积分区域划分上的优势,使其能适应复杂的模型边界与材料边界,更易划分网格.根据上述理论研究成果编制了完整的计算程序,算例结果发现该方法能够得到粉末压制过程的宏观非线性力学响应、高精度的应力场以及明显的应力集中现象,为复杂优化问题的求解提供了有效手段.     

惩罚函数法在三维等参杂交元的应用

提出在等参杂交元中用惩罚函数法引入平衡约束条件,具体讨论了惩罚函数法在三维等参杂交元中的运用,并提出采用分项罚数的方法,建立最佳的罚平衡杂交元模型．罚平衡法可以在不增加自由度的前提下,有效地扼制寄生应力．数值实验表明,新建立的单元,可以有效地抑制单元畸变对计算精度的影响,从而大幅度提高畸变网格下的计算精度,方法带有普遍性．     

干气密封环端面结构参数正交优化及热变形研究

泄漏是干气密封失效的主要形式,而密封环端面又是主要的泄漏通道.针对特定工况,利用密封环的结构参数对密封气膜性能的影响程度,通过有限元正交仿真,来优选密封环的端面结构参数;另外,利用稳态热分布的有限元仿真,通过热-结构耦合,获得密封动环的热变形及动环材料属性对密封特性的影响关系.研究结果显示,除弹性模量之外,导热系数、Poisson(泊松)比和热膨胀系数均与密封动环的热变形成拟线性关系.研究结果对干气密封环的优化设计具有指导和参考价值.     

昆虫翼拍动中受载变形的粘弹性本构模型

昆虫翼拍动受载时发生被动变形,被看作为有助于改善飞行性能的机制之一．决定这种被动变形大小的一个关键因素是昆虫翼的材料本构关系,至今缺乏研究．基于蜻蜓翼(离体)的应力松弛实验和模型翼拍动时受载变形的有限元数值分析,揭示了粘弹性本构关系是昆虫翼材料性能的合理描述,并研究了粘弹性参数对被动变形的影响．     

Mode hunting through active information

We propose a new method to find modes based on active information. We develop an algorithm called active information mode hunting (AIMH) that, when applied to the whole space, will say whether there are any modes present and where they are. We show AIMH is consistent and, given that information increases where probability decreases, it helps to overcome issues with the curse of dimensionality. The AIMH also reduces the dimensionality with no resource to principal components. We illustrate the method in three ways: with a theoretical example (showing how it performs better than other mode hunting strategies), a real dataset business application, and a simulation.     

Spectral finite element analysis of elastically connected double-beam systems

A spectral finite element method for two parallel beams connected to each other by the vertical springs uniformly distributed along the beam length is introduced in this paper. The effects of the shear deformation and rotary inertia of the beams are accounted for. The coupled equations of motion are derived by using Hamilton's principle and the spectral element matrix is established based on the exact solutions of the governing equations. The use of the proposed spectral element formulation to investigate the free vibration characteristics of the particular double-beam systems is demonstrated by applying the Muller root search algorithm. Once the natural frequencies and mode shapes are obtained, a spectral element based normal mode method is introduced to compute the dynamic response of the double-beam systems subjected to various kinds of concentrated and distributed loads. Numerical results of the present method are verified by comparing with those available in the literature.     

时间序列的经验模态频率分解EMFD

在经验模态分解的基础上,提出了经验模态频率分解.经验模态频率分解是正交分解,有很好的性质和频率意义.     

政府规制下制造商实施EPR的模式研究

根据消费者对新产品和再造品的偏好不同,考虑产品的需求差异性,本文研究在政府规制下,制造商实施EPR的模式选择问题。文章首先构建了制造商实施EPR的两种模式——闭环模式和外包模式,然后比较研究了两种模式下的最优结果,最后进行了数值分析。研究表明当消费者的环保意识δ较小时,实施闭环模式对制造商有利,而当δ较大时,实施外包模式对制造商更有利,并且外包模式有利于提高废旧品的回收量。但是消费者环保意识的增强给制造商带来了压力,而给第三方再造商带来了商机。     

A new element for analyzing large deformation of thin Naghdi shell model. Part II: Plastic

In this paper a new element is developed that is based on Cosserat theory. In the finite element implementation of Cosserat theory shear locking can occur, especially for very thin shells. In the present investigation the director vector is constrained to remain perpendicular to the mid surface during deformation. It will be shown that this constraint yields accurate results in very large deformation of thin shells also the rate of convergency is very good. For plastic formulation, the model introduced by Simo is used and it has been reduced for constrained director vector and the consistent elasto-plastic tangent moduli is extracted for finite element solution. This model includes both kinematic and isotropic hardening. For numerical investigations an isoparametric nine node element is employed then by linearization of the principle of virtual work, material and geometric stiffness matrices are extracted. The validity and the accuracy of the proposed element is illustrated by the numerical examples and the results are compared with those available in the literature.     

Stabilized Mixed Tetrahedrals with Volume and Area Bubble Functions at Large Deformations

In this contribution, stabilized mixed finite tetrahedral elements are presented in order to avoid volume locking and stress oscillations. Geometrically non-linear elastic problems are addressed. The mixed method of incompatible modes is considered. As a key idea, volume and area bubble functions are used for the method of incompatible modes [1], thus giving it the interpretation of a mixed finite element method with stabilization terms. Concerning non-linear problems these are non-linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two-field method, the method of incompatible modes in finite deformation problems is derived for a hyper elastic Neo-Hookean material. In the representative examples Cook's membrane problem and a block under central pressure illustrate the good performance of the presented approaches compared to existing finite element formulations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of shear stiffness and concrete wedge cone failure on fracture of a fiber-reinforced plastic rod at an intersection with a concrete crack

Experimental results of model speciments in which FRP rods fractured due to local deformation at a crack intersection in a concrete member were analyzed by a 3D nonlinear finite element method in which orthogonal anisotropy of the FRP rod was considered. The analytical results indicated that accurate prediction of shear modulus of the FRP rod and size of concrete wedge cone failure around the FRP rod was significant to predict deformation and fracture of the FRP rod. FRP rods as reinforcement in concrete members, the small shear modulus, because of the orthogonal anisotropy and the wedge cone failure, may prevent the FRP rod from fracturing at a very low tensile stress due to the local deformation at the crack intersection.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 21, No. 2, pp. 158–166, March–April, 1996.