有限元病态刚度方程的解法研究

本文在文献〔１〕、〔２〕的基础上，对有限元局部节点位移构成准刚体运动这种情况进行了研究，提出了一种新的改性转换矩阵〔Ｑ〕，并给出了两种简单易行的计算〔Ｑ〕￣Ｔ〔Ａ〕〔Ｑ〕的方法。所提方法对直接法和迭代法求解有限元病态方程都是适用的，算例表明，得到了较好的计算结果。     

用da／dN=〈C〉（△K）^〈m〉估算平均裂纹扩展速率的误差及其控制

本文分析了以〈Ｃ〉和〈ｍ〉作为Ｐａｒｉｓ公式参数估算疲劳裂纹平均扩展速率的误差与控制参量，研究表明这样处理的结果偏于安全，估算的相对误差主要受方差Ｖａｒ〔ＬｏｇＣ〕的控制，且随Ｖａｒ〔ＬｏｇＣ〕的增大而增大。     

层状地基轴对称问题的Mindlin解

本文在文献〔１〕的基础上，对层状地基应力和位移的计算方法做了一些创新的工作，首先作者提出求解传矩阵的逆矩阵的简便公式。并在应力、位移的计算上，对荷载作用面上下分别采用二种不同的传递矩阵。加快了计算速度，避免了层状体系计算中常见的溢出问题及大数减大数造成的计算困难。     

几何非线性混合应变元的构造及应用

本文基于由文献〔１〕导出的几何非线性混合应变元一般公式，构造了三个八节点六面体几何非线性混合应变元和Ｓｉｍｏ－Ｒｉｆａｉ的二维四边形线性应变元的几何非线性混合应变元。数值结果表明，所构造的二维及三维几何非线性混合应变元具有理想的性能。它们通过分片试验，且没有虚假剪切现象和不可压缩材料的自锁。同时，它们对歪扭网格不敏感，在利用粗疏网格离散时对线性和非线性（几何和材料）问题具有很高的精度。     

各向异性和各向同性介质的反平面剪切问题的相似性

在最近的文章〔1〕及所引的文献中,对正交各向异性介质的反平面剪切问题作了研究计算。其实各向异性介质的反平面剪切问题的解很容易从各向同性介质的对应问题导出,所需附加的计算仅仅是一个坐标变换。我们知道,反平面剪切问题和柱体扭转问题的基本方程具有完美的相似性。因此这两个问题只要已解决了其中的一个,另一个的解就随即得到了。早在1956年,本人在专著〔2〕     

非等距时间序列的GM（1，N）模型及其在地下工程中的应用

文献〔１〕给出了等距时间序列的灰色预测ＧＭ（１，Ｎ）模型，本文把它推广到非等距时间序列，得到了相应模型，并应用于地下工程的几个实例     

简支梁非线性响应的三维路径积分法分析

采用基于Gauss-Legendre积分公式的三维路径积分法，分析了在过滤高斯白噪声激励下的简支梁非线性随机振动响应的概率密度函数；联立一阶滤波方程与简支梁一阶模态的振动模型，得到在过滤高斯白噪声激励下的简支梁随机振动模型，基于Gauss-Legendre积分公式的积分法和短时高斯近似法求解响应的概率密度函数值。结果表明，三维路径积分法计算值与蒙特卡洛模拟值符合良好，即使在尾部区域也符合良好。三维路径积分法比等效线性化法的计算精度更高。     

疲劳载荷下的裂纹张开位移

自Wells提出裂纹张开位移〔COD〕概念以来,作为一种工程断裂准则,在结构的断裂分析中已经得到了广泛的应用。然而,由于实际裂纹顶端张开位移〔CTOD〕难于直接测量,现在所用的方法多数是在塑性铰的假设模型下,测量裂纹咀张开位移〔CMOD〕,再换算成名义裂纹张开位移的。当然,在较大范围屈服的情况下,作为近似,这种假设是成功的。在疲劳载荷下,裂纹顶端的塑性区通常很小,塑性铰模型将不能正确地描叙裂纹顶端的张开位移。本文所探讨的就是测量和计算小范围屈服下裂纹顶端张开位移的方法。     

等几何壳体分析与形状优化

首先基于Reissner-Mindlin理论进行了三维壳体等几何分析，而后基于此对三维壳体进行形状优化，提出了形状优化中灵敏度的全解析计算方法，包括位移应变阵、雅克比阵和刚度阵等相对控制顶点位置的灵敏度解析计算公式；通过实例验证了壳体等几何分析和灵敏度全解析计算方法的有效性。与传统的基于网格的灵敏度半解析计算方法相比，基于NURBS的灵敏度全解析计算具有精确、计算效率高的特点，且可以避免优化迭代中的网格畸变。     

宾汉流体阻力近似解公式精度的优化提高

针对前苏联学求解宾汉流体布金汉方程的阻力近似解公式，其与精确解最大偏差为6．7％，首次通过数学分析和三维优化计算，改变公式中的参数，使偏差大幅度降低．偏差是参数和核心流相对半径r^-O的函数，用极限判定了在r^-O闭区间内的连续性和间断点，为降低偏差提供了依据．绘制了偏差三维变化图，应用切片平面解决了多峰曲面的极值问题．最终优化出的参数使公式的最大偏差为2．6％，比6．7％降低了4．1％，优化后的公式，在管道输送阻力计算中更有实用价值．     

单试样法测金属材料JR曲线及其条件起裂值

在单试样卸载柔度法及三曲线法基础上，提出了一种更简便的测定金属材料JR曲线及其条件起裂值的单试样三点柔度法，并用该方法测定了1Cr1/2Mo钢、16MnR钢和WCF62钢的JR曲线及其条件起裂值，与标准的多试样法相比，误差均在工程许可范围内。     

一种计算三维裂纹应力强度因子的新方法

构造了一种新的三维奇异单元，提出了一种有效计算三维裂纹应力强度因子新的数值方法。该方法的计算结果与理论解和Newman解结果一致；与Panson等方法相比所使用的自由度数大大减小。结果表明该方法是一种高效、稳定可靠的计算方法。     

三维裂纹问题的高精度数值解法

提出了一种求解三维均质弹性体中任意形状平片裂纹问题超奇异积分方程组的Chebyshev多项式数值解法。数值计算结果表明：文中方法不仅收敛快，而且精度高。     

疲劳裂纹扩展曲线的正交多项式与三参数指数函数拟合法

回顾了疲劳裂纹扩展a -N曲线的拟合方法。对三参数幂函数拟合方法进行了改进 ,这种方法避免了原方法搜索范围受局限的特点 ;提出了两种新的a-N曲线拟合方法 :正交多项式法和指数函数法 ,并给出了参数估计算法。正交多项式法拟合a -N曲线 ,其相关系数随最高次数的增加而提高 ,指数函数法比改进三参数幂函数拟合精度高 ;指数函数法与正交多项式法相比 ,各个参数具有更为明确的物理意义     

Symplectic solution for three dimensional couple stress problem and its variational principle

A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.     

New Statement of the elasticity problem for a layer

The problem on the equilibrium of an inhomogeneous anisotropic elastic layer is considered. The classical statement of the problem in displacements consists of three partial differential equations with variable coefficients for the three displacements and of three boundary conditions posed at each point of the boundary surface. Sometimes, instead of the statement in displacements, it is convenient to use the classical statement of the problem in stresses [1] or the new statement of the problem in stresses proposed by B. E. Pobedrya [2]. In the case of the problem in stresses, it is necessary to find six components of the stress tensor, which are functions of three coordinates. The choice of the statement of the problem depends on the researcher and, of course, on the specific problem. The fact that there are several statements of the problem makes for a wider choice of the method for solving the problem. In the present paper, for a layer with plane boundary surfaces, we propose a new statement of the problem, which, in contrast to the other two statements indicated above, can be called a mixed statement. The problem for a layer in the new statement consists of a system of three partial differential equations for the three components of the displacement vector of the midplane points. The system is coupled with three integro-differential equations for the three longitudinal components of the stress tensor. Thus, in the new statement, just as in the other statements in stresses, one should find six functions. In the new statement, three of these functions (the displacements of the midplane points) are functions of two coordinates, and the other three functions (the longitudinal components of the stress tensor) are functions of three coordinates. It is shown that all equations in the new statement are the Euler equations for the Reissner functional with additional constraints. After the problem is solved in the new statement, three components of the displacement vector and three transverse components of the stress tensor are determined at each point of the layer. The new statement of the problem can be used to construct various engineering theories of plates made of composite materials.     

基于Surfer平台的FLAC3D 复杂三维地质建模研究

复杂三维地质体模型的建立一直是FLAC^3D软件前处理过程中的一个难题。因此,提出以Surfer软件为过渡平台,通过对地表及岩层分界面三维地质信息的提取、转换,并将Surfer输出的数据经由FLAC^3D软件内嵌的Fish语言编制的程序的二次转换,生成FLAC^3D软件可以直接读取的模型数据文件,从而实现了该软件前处理过程中复杂三维地质模型的快速、准确建立。同时结合工程实际,检验了该方法的可行性和仿真效果,结果表明,建模过程简捷、实用,可操作性强,是FLAC^3D软件前处理的一种新方法。     

The application of evolutionary and maximum entropy algorithms to photoelastic spectral analysis

Over the past 10 years, spectral analysis has been shown to have the potential to be a reliable means of automating photoelasticity. However, the four methods of analyzing the spectra that have previously been proposed are slow and, in some cases, inaccurate. This paper describes three new methods for spectral analysis based on the maximum entropy method, a genetic algorithm and a memetic algorithm. Thirty-five spectra for known fringe orders were recorded and used in testing the four existing methods and the three new ones. It was found that the new methods were all considerably faster than the existing methods, although less accurate than the best existing method. By combining the maximum entropy method with either the genetic algorithm or the memetic algorithm, spectra could be analyzed up to 30 times as fast as they could with any of the existing methods and with comparable accuracy.     

砂岩全应力应变试验曲线阶段特征的Kolmogorov熵分析

应用K o lm ogorov熵评价准则,进行砂岩全应力应变曲线阶段特征的非线性动力学研究,定量描述了峰前、峰后和全程三个层次的分段特征。通过与功率谱分析结论的比较研究,得出砂岩全应力应变曲线阶段特征的K o lm ogorov熵分析具有高度的可靠性,是对功率谱分析方法的科学验证与有益补充,开辟了岩石全应力应变曲线分段特征定量研究的新途径,具有一定的理论意义。     

Mesh deformation based on artificial neural networks

In the article a new mesh deformation algorithm based on artificial neural networks is introduced. This method is a point-to-point method, meaning that it does not use connectivity information for calculation of the mesh deformation. Two already known point-to-point methods, based on interpolation techniques, are also presented. In contrast to the two known interpolation methods, the new method does not require a summation over all boundary nodes for one displacement calculation. The consequence of this fact is a shorter computational time of mesh deformation, which is proven by different deformation tests. The quality of the deformed meshes with all three deformation methods was also compared. Finally, the generated and the deformed three-dimensional meshes were used in the computational fluid dynamics numerical analysis of a Francis water turbine. A comparison of the analysis results was made to prove the applicability of the new method in every day computation.