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.      

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.     

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。     

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.     

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。     

新的一个求解带孔薄板弹性问题的二维杂交应力单元

建立了一个新的求解带圆孔薄板弹性问题的二维杂交应力单元,该单元为四节点四边形平面单元,名为P-HS4-8β。由极坐标系下的物理方程和几何方程求解出了一个极坐标方向的应力,通过将这个应力带入由Hellinger-Reissner原理推导的极坐标系下平面应力问题的能量方程中,得到了消除了该应力的能量方程,基于这个能量方程建立了杂交应力单元列式。根据圆孔边无外力条件和相容方程,推导了适用于求解带圆孔薄板问题的极坐标系下的二应力插值矩阵,并将此矩阵应用于新的有限单元列式中。数值算例表明新单元在求解孔边附近的应力时具有较高的精度。     

一种新的弹塑性杂交应力元法

本文基于一个改进的弹塑性的Hellinger/Reis■ner 混合变分原理构造了一种用于解弹塑性问题的四节点等参杂交应力元.新的模型中,在单元内增加了等效应力增量、塑性等效应变增量及不协调位移变量,从而使单元内的屈服准则及流动法则平均得到满足,不协调位移改进了单元应力精度.计算表明,新的模型可以提高弹塑性杂交法的精度和计算效率.     

多参量断裂力学广义杂交/混合裂纹有限元法

通过研究广为人知的断裂力学单变量八节点位移裂纹QPE元和Akin族奇异单元法，本文运用经典局部裂纹解析解，与非协调假设应力杂交-混合元列式方法相结合，提出用于分层各向异性材料的多变量半解析假设应力奇异广义杂交／混合裂纹有限元法，能克服现有位移裂纹元法的域应力分布精度低和高次单元所需计算容量大的局限性，互为补充，更有利于结构裂纹扩展分析和应用研究。文中设计了一个半解析奇异裂纹平面单元，各向同性材料板算例验证了退化二次八节点协调位移裂纹元及六节点非协调奇异应力裂纹元，说明采用稀疏及加密单元网格，两类裂纹单元分别从上下逼近收敛于实验和理论参考解，可得到吻合程度较好的1／√r奇异应变和应力分量以及应力强度因子值，表明了本文奇异裂纹单元理论的优越性。     

横观各向同性轴对称问题的非协调元和杂交应力元计算

基于变分原理得出各向同性轴对称问题下的非协调元和杂交应力元方法仍然适用于分析横观各向同性轴对称问题的结论，同时对应用于各向同性问题的罚平衡优化方法进行了修改，使之能够应用于横观各向同性问题的分析。文中给出了分析算例。并对各种单元结果进行了比较，计算结果表明非协调元和杂交应力元方法不但适用于横观各向同性轴对称问题分析，而且将提高其数值解的精度，改善单元内部应力分布。     

具有均匀受压圆柱面的三维杂交应力元

1.前言 应用具有圆柱表面的特殊杂交应力元分析具有圆柱面的物体时,将给出较一般的假定位移元、及一般的杂交应力元远为准确的结果。本文研究圆柱面上承受均匀法向力时的三维杂交应力元,它将用于更准确地分析一些弹性力学不易解决的压力管道等问题。     

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work, the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is estab-lished to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method (FEM). The convergent stresses have good agreements with those results obtained by three dimensional (3D) FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kan-torovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.     

Practical Green's function for the thermal stress field induced by a heat source in plane thermoelasticity

The classical Green’s functions used in the literature for a heat source in a homogeneous elastic medium cannot lead to finite remote thermal stresses in the medium, so that they may not work well in practical thermal stress analyses. In this paper, we develop a practical Green’s function for a heat source disposed eccentrically into an elastic disk/cylinder subject to plane deformation. The edge of the disk/cylinder is assumed to be thermally permeable and traction-free. The full thermal stress field induced by the heat source in the disk/cylinder is determined exactly and explicitly via the Cauchy integral techniques. In particular, a very simple formula is obtained to describe the hoop thermal stress on the edge of the disk/cylinder, which may be conveniently useful for analyzing the thermal stresses in microelectronic components.     

Hybrid Thermoelastic Stress Analysis of a Pinned Joint

Mechanical joints such as bolted or pinned connections are commonly used to fasten mechanical or structural members together. Inadequate knowledge of the stresses at the edge of the loaded holes can render it difficult to stress analyze such mechanical fasteners theoretically or numerically. Thermoelastic stress analysis (TSA) is utilized here to analyze a plane-stressed pin-loaded plate. The approach combines the recorded temperature information with an Airy stress function, plus imposes the traction-free conditions on the non-contacting edge of the hole and on the external boundaries of the plate. Individual components of stress are determined full-field as well as on the pin-plate interface. In addition to agreeing with the frequently assumed interface contact stresses in mechanical connections having zero clearance, the TSA results satisfy force equilibrium, are compatible with residual markings on the contacted surfaces of the pin and the hole, and correlate with FEM predictions. Significant advantages of TSA here include neither needing to know the elastic modulus nor to differentiate the recorded information.     

A quadrilateral membrane hybrid stress element with drilling degrees of freedom

A new kind of quadrilateral assumed stress hybrid membrane element with drilling degrees of freedom and a traction-free inclined side has been developed based on an extended Hellinger-Reissner principle which is established by expanding the essential terms of the assumed stress field as polynomials in the natural coordinates of the element. The homogeneous equilibrium equations are imposed in a variational sense through the internal displacements which are also expanded in the natural coordinates, while the tractionfree conditions along the inclined side are satisfied exactly. The use of such special element in the finite element solution is shown to be highly accurate when only a very coarse element mesh is used for plates with V-shaped rounded notches or inclined sides.     

部分应力杂交动力分析模型的混合变分原理

本文通过对具有单重卷积积分的二类变量的Ｇｕｒｔｉｎ型混合变分原理进行修正，采用“部分应力杂交”的概念，建立了线弹性动力分析 部分应力杂交变分格式，并在此基础上构造出时间有限元模型，这种模型对于分层复合板的动力分析尤其适用。