结构地震反应分析的频域传递矩阵法

本文将传递矩阵法的应用范围由结构的固有振动分析推广到频域内的地震反应分析。文中具体给出了弯剪梁结构的单元传递矩阵的频域形式。用这种频域内的传递矩阵，结合离散傅里叶变换，即可求得多自由度弯剪梁体系的地震反应。同样地，可用这种方法计算各种串联多自由度体系在其它动力荷载下的反应。该方法精度良好且比相应的有限元法节省计算机ＣＰＵ时间。     

变截面高层框筒结构的矩阵传递法

以连续化数学模型和能量变分原理导出的变截面高层框简结构的微分方程组为基础；根据变截面框简结构的截面沿高度为阶形变化的特点，以每个相同截面的层作为一个计算单元，每个单元由微分方程组导出其单元矩阵、截面矩阵和传递矩阵。进而采用传递矩阵法进行分析。此法概念清楚，计算简单．并以算例说明其应用。     

求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法

利用Laplace—Hankel联合积分变换，推导出了单层粘弹性半空间轴对称问题在动荷载作用下，层间完全接触情况的刚度矩阵，然后按传统的有限元方法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程就可解出动荷载作用下多层粘弹性半空间轴对称问题的矩阵。由于刚度矩阵的元素中只含有负指数项，计算时不会出现溢出的现象。本文还成功地应用了Durbin的Laplace逆变换的数值方法，求解出了多层粘弹性体的时域解。最后，文中还给出了路面动弯沉的计算结果与实测结果的对比来证明推导结果的准确性。     

关于结构刚度方程病态问题的疑难分析

本文围绕矩阵位移法求解结构位移的误差，讨论了结构刚度矩阵的病态问题，指出了计算上的病态常常是结构刚度分布和结构拓扑的不合理，而不一定是计算本身的问题。首先，文章依据误差界的概念和范数的性质推导了衡量结构刚度矩阵病态程度的条件数的公式。然后，阐明了基于不同范数的条件数在衡量矩阵病态程度上的等价性。最后，通过两个具有代表性的算例，分别从结构构件的刚度差异和结构几何拓扑两方面，计算和分析了结构刚度矩阵的病态程度随结构本身性质的改变而改变的规律。在特定的算例中，还有使结构刚度矩阵的病态程度降到最低的最佳刚度分布。     

一种与传递矩阵结合的配点法

本文改进和发展了文献(1)、(2)中提出的广义传递子结构法和配点法,提出了一种新的有效的直接求解结构动力学平衡方程的配点法与传递矩阵法相结合的数值计算方法。在此方法中修正的传递矩阵可用于每个短时间增量中的动态反应分析中。进一步提出了广义传递矩阵的新概念,建立能计算任何动荷载作用下结构的动力反应的一般递推公式。文中给出数字实例证明所建议方法是正确的和可行的。     

矩阵摄动理论在六轴机车横向运动稳定性分析中的应用

本文提出了一种分析机车横向运动稳定性的方法,即利用复膜态的矩阵摄动法来计算临界速度,该方法避免了反复计算矩阵的特征值从而可节约大量的计算时间,对矩阵摄动法计算精度的研究结果表明,该方法的的精度是足够的。     

利用复矩阵的高阶直接积分算法

本文提出一个直接积分结构动力学方程的高阶无条件稳定算法,并给出于利用复矩阵运算的实现方法。用本文算法,每个时间步中只需求解 N×N 阶复值线性代数方程组一次。此法的算法特性和作者以前发表的 DC 法(1990)完全相同,但缩短了计算时间并解除了对系统矩阵的若干限制(经典阻尼等)。通过几个算例对方法的精度作了考察。     

多体系统齐次矩阵方法在浮桥运动响应中的应用研究

浮桥的抗弯刚度和受弯变形位移波的传播速度都比一般钢桥或混凝土桥小得多。在快速移动重载作用下,荷载移动速度有可能接近甚至超过浮桥位移波的传播速度,这样就会造成移动荷载前方浮桥位移波的堆积效应。介绍了多体系统齐次矩阵方法,并用齐次矩阵方法对浮桥进行建模和求解,通过数值模拟和已有的模型试验表明:当荷载的移动速度较大时,浮桥多体系统的运动呈现明显的波动现象,速度越大位移波的堆积越明显。     

无单元法分析薄板自由振动问题

提出了分析四边简支和四边固定薄板自由振动问题的无单元法，推导了无单元法的插值函数，从变分原理出发导出薄板自由振动的质量矩阵和刚度矩阵，编制了相应的计算程序，通过计算实例与其它方法的结果进行比较．数值结果表明无单元法具有一系列优点。     

土性参数各向异性随机场的表征与建模方法

土性参数在空间上的相关性具有各向异性,因此对各向异性随机场表征与建模方法的研究具有重要的意义.本文首先通过对相关函数的分析,将各向异性相关的问题归结到相关距离函数的探讨上,给出了一种描述参数各向异性相关的方法;其次分析了 目前常用的两种随机场反演方法在处理各向异性问题所面临的问题,(1)局部平均划分法只适合横观各向同性随机场的生成,难以处理任意的各向异性问题,(2)矩阵分解法反演随机场时,随机场网格数会受到计算机计算能力的限制,难以处理大型的随机场反演问题.针对以上两点问题,基于相关函数的快速衰减特性改进了矩阵分解法,并将改进的矩阵分解法与局部平均划分法进行了反演精度对比,同时用改进的矩阵分解法反演了旋转横观各向同性随机场,结果表明用改进的矩阵分解法处理各向异性问题是适用的.     

对称变截面平面曲杆的单元刚度矩阵

本以一种新的思路和做法对变截面曲杆进行单元分析,直接把变截面曲杆作为单元,采用弹性中心法导出了单元刚度矩阵通用公式,确定了截面按余弦规律变化时,轴线分别为圆弧形、抛物线形、半椭圆形平面曲杆的单元刚度矩阵精确式,供结构设计参考使用。     

Finite displacement static analysis of thin plate with an opening––a variational approach

A generalized work–energy method for the linear and geometrically nonlinear static analysis of thin isotropic plate with a cutout is presented. The plate geometry is divided into few quadrilateral segments. Each segment is defined by four curved edges and the natural coordinates in conjunction with the Cartesian coordinates are used in formulating the stiffness matrix and the load vector. Two different sets of interpolating functions are used for the geometric and displacement representations respectively. The matrix equation of equilibrium is derived from the variational principle. By exploiting the geometric symmetry, numerical results are obtained for the following examples: (a) square plate with circular opening at the centre and (b) circular plate with circular or square inner boundary. The plates are subjected to uniformly distributed load and both the pinned and fixed outside boundary conditions are considered. Very good comparison is observed between the present results and those published in the literature for the fixed square plate without an opening. Effects of the opening size on the displacement are examined in detail.     

曲线裂纹和反平面圆形夹杂相交问题

建立了和反平面圆夹杂界面相交的曲线裂纹的弱奇异积分方程,利用Cauchy型奇异积分方程主部分析方法研究了穿过反平面圆夹杂界面的曲线裂纹在交点处的奇性应力指数以及交点处角形域内的奇性应力,并根据奇性应力定义了交点处的应力强度因子。通过对弱奇异积分方程的数值求解,可得裂纹端点和交点处的应力强度因子。     

Elastica of a variable-arc-length circular curved beam subjected to an end follower force

This paper presents postbuckling behaviors of a variable-arc-length (VAL) circular curved beam subjected to an end follower force. One end of the VAL circular curved beam is hinged while the other end is supported by a frictionless slot, which is fixed horizontally and vertically but is allowed to rotate corresponding to loading direction. When the VAL circular curved beam is deformed, the total arc-length of the circular curved beam varies. Two approaches have been applied for the solution of this problem. The first approach is an elliptic integrals method based on elastica theory, which yields the exact closed-form solution in terms of the first and second kinds of elliptic integrals. For validation of the results, the shooting method is employed for a numerical solution by developing the set of nonlinear governing differential equations together with boundary conditions, and then integrating them by using the fourth-order Runge–Kutta algorithm. The results from both approaches are in very good agreement. From the results, it is found that the VAL circular curved beam subjected to an end follower force can be deformed in many mode shapes. For the first and third modes, the beam exhibits both stable and unstable configurations, whereas for the second mode only an unstable configuration exists. The influences of initial curvature on the critical load and the deformed configurations are highlighted.     

Out-of-plane responses of a circular curved Timoshenko beam due to a moving load

For the cases of using the finite curved beam elements and taking the effects of both the shear deformation and rotary inertias into consideration, the literature regarding either free or forced vibration analysis of the curved beams is rare. Thus, this paper tries to determine the dynamic responses of a circular curved Timoshenko beam due to a moving load using the curved beam elements. By taking account of the effect of shear deformation and that of rotary inertias due to bending and torsional vibrations, the stiffness matrix and the mass matrix of the curved beam element were obtained from the force–displacement relations and the kinetic energy equations, respectively. Since all the element property matrices for the curved beam element are derived based on the local polar coordinate system (rather than the local Cartesian one), their coefficients are invariant for any curved beam element with constant radius of curvature and subtended angle and one does not need to transform the property matrices of each curved beam element from the local coordinate system to the global one to achieve the overall property matrices for the entire curved beam structure before they are assembled. The availability of the presented approach has been verified by both the existing analytical solutions for the entire continuum curved beam and the numerical solutions for the entire discretized curved beam composed of the conventional straight beam elements based on either the consistent-mass model or the lumped-mass model. In addition to the typical circular curved beams, a hybrid curved beam composed of one curved-beam segment and two identical straight-beam segments subjected to a moving load was also studied. Influence on the dynamic responses of the curved beams of the slenderness ratio, moving-load speed, shear deformation and rotary inertias was investigated.     

ANTIPLANE CIRCULAR INCLUSION WITH A CURVED CRACK CROSSING THE BOUNDARY

The weakly singular integral equation used to solve the problem of the curved crack crossing the boundary of the antiplane circular inclusion is presented. Using the principal part analysis method of the Cauchy type integral equation, the singular stress index at the intersection and the singular stress of angular regions near the intersection are obtained. By using the singular stress obtained, the stress intensity factor at the intersection is, defined. After the numerical solution of the integral equation, the stress intensity factors at the end points of the crack and intersection are obtainable. The research is supported by National Natural Science Foundation of China (No. 59879012) and is the project of Chinese Foundation of State Education Commission (No. 98024832).     

二维高亚音速Laval喷管流场的有限元计算

本文使用了八节点曲四边形等参元，通过变分有限元法，对二维高亚音速Ｌａｖａｌ喷管位势流场进行了计算，结果是满意的，并和一维结果进行了对比。文中还使用了有限元法特有的局部线化理论，取单元中心点密度去处理迭代过程中单元系数阵的计算，其结果与通常的有限元法计算相一致，但计算时间却大大减少了。     

高效的三维曲梁单元

三维井眼中延伸数千米的三维细长圆截面钢钻柱应力分析问题是一个复杂的力学问题,通常使用有限元数值分析方法对其进行受力分析。而在进行有限元分析时,现有的圆弧曲粱单元和空间直粱单元在几何上都不能很好地模拟三维曲线形状的钻柱。为了确保计算精度．其单元划分势必不能过大,结果是计算时间长,收敛性差。为了解决这一问题,显然必须构建一种新的较有效的曲梁单元。基于自然坐标系,依据圆截面空间曲粱单元节点有6个自由度——3个线位移和3个角位移,利用包含全部刚体位移模式和常应变的形函数,忽略剪切变形,假设变形后的梁轴线的弯曲曲率改变为线性变化,建立起了保证收敛性的具有12个自由度的有初始曲率和挠率的圆截面空间曲梁的有限元模型。为了证明给出的有限元模型的高效性,分析了几个静态问题,并与现有文献中的解析解或数值结果进行了比较。基于所给出的结果,可望该有限元模型可以作为分析三维空间曲粱结构的有效工具。     

Hypersingular integral equation for multiple curved cracks problem in plane elasticity

The complex variable function method is used to formulate the multiple curved crack problems into hypersingular integral equations. These hypersingular integral equations are solved numerically for the unknown function, which are later used to find the stress intensity factor, SIF, for the problem considered. Numerical examples for double circular arc cracks are presented.     

Analysis of curved beams using a new differential transformation based curved beam element

Differential transformation method is used to obtain the shape functions for nodal variables of an arbitrarily non-uniform curved beam element including the effects of shear deformation considering axially functionally graded material. The proposed shape functions depend on the variations in cross-sectional area, moment of inertia, curvature and material properties along the axis of the curved beam element. The static and free vibration of axially functionally graded tapered curved beams including shear deformation and rotary inertia are studied through solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal beams (both forms—prime and quadratic) with hinged-hinged, hinged-clamped and clamped-clamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross section are studied. Out of plane vibration is studied and the lowest natural frequencies are calculated and compared with the published results. Out of plane buckling is investigated for circular beams due to radial load.