激光捷联惯组的双轴位置转台标定仿真

研究了利用双轴位置转台标定时，水平基准误差和北向基准误差对激光捷联惯组（LSIMU）标定精度的影响。首先建立了LSIMU标定模型和生成惯性器件信息的仿真算法，接着设计了LSIMU标定方案和数据处理方法，最后对LSIMU标定进行仿真和分析。仿真结果表明：水平基准误差为0．4’时，加速度计标定误差将达到116×10^-6；当北向基准误差大于5°时，陀螺标定误差将超过0．0001。     

三维裂纹体应力强度因子的计算

本文采用塌缩三棱柱形奇异单元的位移计算应力强度因子，给出了一个新的全三维外推公式，它是Ｃｈｅｎ和Ｋｕａｎｇ公式〔１３〕的全三维推广，特例证明，它的精度比Ｉｎ－ｇｒａｆｆｅａ和Ｍａｎｕ的公式〔８〕高一阶。数值计算表明，结果稳定和对单元尺寸改变不敏感     

三维有限体中平片裂纹的超奇异积分方程方法——Ⅰ、理论分析

本文利用单个平片裂纹的基本解,将三维有限体中的平片裂纹问题,归为解一组超奇异积分方程,然后使用主部分析方法,对这组方程的求解作了理论分析,其结果在本文的第Ⅰ部分给出,关于这组方程的数值法求解,则给出于本文的第Ⅱ部分。     

ADAPTIVE MESHLESS METHOD BASED ON LOCAL FIT TECHNOLOGY

An h-adaptive meshless method is proposed in this paper. The error estimation is based on local fit technology, usually confined to Voronoi Cells. The error is achieved by comparison of the computational results with smoothed ones, which are projected with Taylor series. Voronoi Cells are introduced not only for integration of potential energy but also for guidance of refinement.New nodes are placed within those cells with high estimated error. At the end of the paper, two numerical examples with severe stress gradient are analyzed. Through adaptive analysis accurate results are obtained at critical subdomains, which validates the efficiency of the method.     

三维非规则非均匀边界元网格的简便的高精度算法

对三维直接边界元中一阶奇异积分、一阶近奇异积分以及非奇异积分进行统一处理，给出了一种提高积分计算精度的简便有效的方法，对非规则非均匀边界元网格可获得比一般方法高得多的计算精度，非常适合边界形状比较复杂的三维实际问题的边界元分析．     

Sine-Gordon方程中混沌跳跃行为的机制

定性研究了Sine-Gordon方程在其广义近似惯性流形上的一个四维常微分方程。通过奇异扰动理论得到Silnikov同宿轨道存在的一个解析判定，然而在以往数值模拟中使用过的参数条件下，上面的判定不完全成立。于是进一步利用能量差方法，在这些参数条件下证明了至少存在四条结构稳定的脉冲轨道，它们正好反映了在Sine-Gordon方程的数值模拟中观察到 的混沌跳跃行为。     

弹性地基上四边自由的各向异性矩形板

通过叠加法得到了弹性地基上的各向异性矩形板的一般解。每个叠加解被展成重傅立叶级数，其自身或其一阶导数在边界上的值被展成单傅立叶级数。利用控制微分方程和一些边界条件，每个叠加解被简化成用边界值的级数的系数表示的傅立叶级数。文后给出了弹性地基上的方板的挠曲面图。     

新型各向异性核工业石墨断裂力学行为的实验研究和数值分析

本文分别采用激光和白光DSCM(数字散斑相关测量)方法对一种新型各向异性核工业石墨的裂纹尖端位移、应变场进行了实验研究，两种方法都取得了较好的结果。考虑核工业石墨制备过程形成的各向异性特点，本文构建了三维各向异性有限元模型，采用奇异单元，计算模拟石墨裂纹尖端的变形和应力场，通过对实验结果和有限元计算结果的比较可以发现两者具有相近的趋势。     

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.     

Piecewise analysis of oblique vibro-impacting systems

A great number of studies have shown the complex nonlinear dynamics of mechanical systems with repeated normal impacts. An oblique frictional impact introduces even more complicated dynamics such as stick-slip motions to those systems. Hence, the dynamics of oblique vibro-impacting systems with possible sliding motion is an open problem. Based on a hybrid analysis of vibro-impact dynamics, kinematics and complementary conditions, a piecewise analysis method is developed in the paper to describe the sliding motion during an oblique impact. Thereby, a parametrically excited planar pendulum between two parallel rigid walls is studied as an illustrative example. The example, together with the corresponding numerical results, shows that the sliding impacts occur in such a system with a set of properly selected parameters. The project supported by the National Natural Science Foundation of China (59905010) and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education, China