轴对称实体迴转杂交应力元

用杂交应力法导出一系列新的八节点、四边形轴对称实体迴转元,对每种元,边界二次位移插值函数相同,内部应力场各异,对两类不同选择假定应力场的方法进行了对比研究,以內压力作用下的厚壁筒及厚球为例,对各种应力场进行了数值比较,并选出了一种较好的元,该元给出了远较传统的八节点轴对称假定位移元准确的应力分布。     

Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. Moreover, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.     

含一个无外力圆柱面带转动的三维杂交应力元

根据一种修正的余能原理,建立了一类具有一个无外力圆柱表面及结点含转动自由度的8 结点新型三维杂交应力元. 单元边界位移场选择二次位移插值函数,且与相邻元协调;单元内假定应力场满足以柱坐标表示的平衡方程及圆柱面上无外力边界条件. 数值算例表明,这种特殊杂交应力元在相当粗的网格下即能十分准确地分析圆弧形槽口附近及曲梁的三维（及二维）的孔边应力分布.      

含一个无外力圆柱面带转动的三维杂交应力元简

根据一种修正的余能原理,建立了一类具有一个无外力圆柱表面及结点含转动自由度的8 结点新型三维杂交应力元. 单元边界位移场选择二次位移插值函数,且与相邻元协调;单元内假定应力场满足以柱坐标表示的平衡方程及圆柱面上无外力边界条件. 数值算例表明,这种特殊杂交应力元在相当粗的网格下即能十分准确地分析圆弧形槽口附近及曲梁的三维（及二维）的孔边应力分布.     

一类新的具有无外力圆柱表面的杂交应力元

根据Hellinger-Reissner原理,建立了进一步改进的具有一个无外力圆柱表面三维杂交应力元.元内假定应力场满足以柱坐标表示的平衡方程,及圆柱面上的无外力边界条件.当退化为二维时,也满足协调方程.数值算例表明,当分析带圆弧的槽孔板、块时,在稀疏的有限元网格下,这类单元即可提供较以前各类特殊元、一般假定位移元及一般假定应力元远为准确的三维及二维应力分布.     

变宽度板在拉伸和弯曲作用下的三维应力集中

根据一种修正的余能原理，建立了具有一个无外力圆柱面的三维杂交应力元，元内假定应力场满足三维柱坐标表示的平衡方程及无外力圆柱面上的外力边界条件；当元退化为二维时，也满足协调条件。单元位移场选择与相邻单元协调。数值算例表明这种特殊杂交应力元在相当粗的网格下，能十分有效地分析变宽度薄／厚板在拉伸与弯曲作用下的三维(及二维)应力集中。     

组合杂交法与ANSYS软件计算精度比较研究

为探索8节点六面体组合杂交元方法(CHH(0-1))的计算效率和精度, 并正确认识ANSYS 软件计算结果的可靠性, 本文以板弯曲模型为例, 分别用CHH(0-1)元、ANSYS软件中的8节 点brick元、20节点brick元对该模型进行求解．经过对位移及应力计算结果的比较分析, 得知ANSYS软件中的8节点brick元实际是Wilson brick元, 当网格规则时位移计算结果可靠, 但应力计算结果精度差, 20节点brick元计算 非常耗时, 应力计算精度也不高, 而CHH(0-1)元用较少的计算量便可得到高精度的位移、应 力计算结果．     

扩展的Hellinger-Reissner原理及特殊层合杂交应力元

建立了一种非匀质材料新的、扩展的Hellinger-Reissner原理,发展了当一个单元域划分为不同材料特性子域、其元内应力场沿子域表面不连续、且位移场在子域表面也急剧变化时,一个非匀质有限元刚度列式便利方法。这种列式亦可用于对每层横向剪应变均独立处置的厚层板。基于此变分原理建立了新的具有一个无外力圆柱表面的层合杂交应力元,单元各层独立假定的应力场通过以自然坐标表示的非协调位移为权函数使齐次平衡方程变分满足的理性方法及严格满足给定圆柱面上无外力条件得到,位移场在元间及层间连续条件则分别通过Lagrange乘子进行了松弛。数值算例表明：这类新型元可有效地分析具有多类圆柱形槽孔的厚、中厚及薄层板自由孔边应力分布。     

Theoretical basis and general optimal formulations of isoparametric generalized hybrid/mixed element model for improved stress analysis

By the modified three-field Hu-Washizu principle, this paper establishes a theoretical foundation and general convenient formulations to generate convergent stable generalized hybrid/mixed element (GH/ME) model which is invariant with respect to coordinate, insensitive to geometric distortion and suitable for improved stress computation. In the two proposed formulations, the stress equilibrium and orthogonality constraints are imposed through incompatible displacement and internal strain modes respectively. The proposed model by the general formulations in this paper is characterized by including assumed stress/strain, assumed stress, variable-node, singular, compatible and incompatible GH/ME models. When using regular meshes or the constant values of the isoparametric Jacobian Det in the assumed strain interpolation, the incompatible GH/ME model degenerates to the hybrid/mixed element model. Both general and concrete guidelines for the optimal selection of element shape functions are suggested. By means of the GH/ME theory in this paper, a family of new GH/ME can be and have been easily constructed. The software can also be developed conveniently because all the standard subroutines for the corresponding isoparametric displacement elements can be utilized directly. Modified version of a conference paper presented at Int. Conf. on EPMESC IV, July 29–Aug. 3, 1992, Dalian, China     

QUADRILATERAL 4-NODE QUASI-CONFORMING PLANE ELEMENT WITH INTERNAL PARAMETERS

在拟协调框架之下,利用新的内参形函数构造了一个四边形四节点拟协调平面单元. 新的内参位移函数也可以添加到等参单元Q4 中来构造新的内参型等参单元. 新构造的拟协调单元QC6N 具有显式刚度矩阵,因而效率更高. 数值例子表明相比于四节点等参单元,新构造的单元可以提高计算精度和抗网格畸变的能力.     

内参型四边形四节点拟协调平面单元

在拟协调框架之下,利用新的内参形函数构造了一个四边形四节点拟协调平面单元. 新的内参位移函数也可以添加到等参单元Q4 中来构造新的内参型等参单元. 新构造的拟协调单元QC6N 具有显式刚度矩阵,因而效率更高. 数值例子表明相比于四节点等参单元,新构造的单元可以提高计算精度和抗网格畸变的能力.      

Buckling analysis of laminated cylindrical shells by 3-D multilayer hybrid element

A 3-D multilayer hybrid element is developed for the analysis of thick laminated plates and shells. The stresses are assumed independently in each sublayer element and the stress continuity between adjacent sublayers is applied to form the stress pattern of the multilayer element. Both interlaminar stress concentration and global structure response can be adequately predicted by the element model. The buckling analysis of orthotropic cylindrical shells under the external pressure is performed and the results show that the plane strain assumption is not applicable to the buckling of long orthotropic cylindrical shells.     

A penalty-hybrid finite element analysis of stokes flow

A type of penalty-hybrid variational principle is suggested for the analysis of Stokesian flow. On such a basis, a finite element model is formulated featuring, among others, a priori satisfaction of the deviatoric stress and hydrostatic pressure on linear momentum balance equations. Also in the present scheme the hydrostatic pressure is successfully eliminated at the element level, leaving only nodal velocities as solution unknowns. A series of 4-node and 8-node quadrilateral elements are derived and examined. Numerical examples demonstrating their characteristic behaviors are also included.The project Supported by National Natural Science Foundation of China     

基于Hellinger-Reissner变分原理的应变梯度杂交元设计

从一般的偶应力理论出发，基于Hellinger-Reissner变分原理，通过对有限元 离散体系的位移试解引入非协调位移函数，得到了偶应力理论下有限元离散系统的能量相容 条件，并由此建立了应变梯度杂交元的应力函数优化条件. 根据该优化条件，构造了一 个C0类的平面4节点梯度杂交元，数值结果表明，该单元对可压缩和不可压缩状态的 梯度材料均可给出合理的数值结果，再现材料的尺度效应.     

杂交元本征应力模式和应力子空间的性质研究

详细讨论了有限元本征应力模式和应力子空间的性质，并着重讨论和进一步完善了与杂交应力有限元应力子空间有关的一些定理，为提出新方法提供了理论基础，主要包括：（1）证明了杂交元特征值不大于对应位移元的特征值；（2）证明了矩阵H非奇异的充分必要条件是假设应力模式线性无关；（3）证明了杂交元所对应位移元的本征应力模式形成的杂交元与该位移元相同；（4）证明了等价假设应力模式形成相同的杂交元；（5）证明了确定杂交元本征应力模式的充分必要条件是其范数平方等于所形成杂交元的变形模态特征值；（6）证明了杂交元假设应力模式与变形模态的能量一一对应的充分必要条件是假设应力模式彼此正交且与所对应位移元的本征应力模式除了一一对应者之外都正交。     

平面Cosserat模型有限元分析的4和8节点单元与分片试验研究

经典连续体理论不包括物质内部尺度,当考虑应变软化问题时,有限元结果对网格具有很强的依赖性。与经典连续介质力学理论不同,Cosserat连续体模型在传统平动自由度的基础上添加了一独立的旋转自由度,在本构模型中引入了内尺度参数。本文研究了基于Cosserat理论的平面4和8节点等参元以及8（4）节点线、角位移混合插值等参单元,给出Cosserat单元分片试验的实施过程。最后将单元运用到小孔应力集中问题的分析当中,通过计算结果与理论解的比较,表明了4和8节点以及8（4）节点等参元的适用性,为问题的非线性分析打下基础。     

隐格式近似不可压四面体4节点大变形单元

由于在处理体积自锁方面的优势,近似不可压问题的大变形求解多采用六面体单元/网格,但对于复杂工程问题,由于网格剖分上的限制,往往更需要一种可以很好解决体积自锁的四面体单元。Bonet和Burton的平均节点压力4节点四面体单元是为数不多能够较好处理体积自锁问题的四面体单元之一,但是该单元目前主要用于显式计算。利用单元平均压力对位移增量的精确方向导数,得到了严格的一致切线阵,保证了Newton-Raphson迭代的二阶收敛,从而使得该单元可以用于隐式计算。该单元的压力平均计算会耦合相邻单元的节点自由度,从而增加切线刚度阵的非零带宽,但不增加自由度总数。分别采用线性六面体选择缩减积分单元、标准线性四面体单元和本文的单元计算了3个近似不可压的典型算例。算例表明,本文推导的单元可以有效克服体积自锁,达到与常用六面体单元相近的效果,使得四面体网格可以方便地用于不可压问题的大变形隐式求解。     

两个相等圆孔板弯曲时的三维应力集中

根据Hellinger-Reissner原理建立了具有一个无外力圆柱表面的三维八节点杂交应力元,其假设应力场严格满足柱坐标下三维平衡方程及圆柱面上无外力边界条件;当元退化为二维时也满足协调方程。数值算例表明,这种特殊杂交应力元可高效地分析具有两个圆孔薄板和厚板的应力集中,特别是三维应力集中。     

A 17-node quadrilateral spline finite element using the triangular area coordinates

Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.