薄板的多变量小波有限元分析

基于区间B样条小波和广义变分原理,提出了多变量小波有限元法,构造了一种新的薄板多变量小波有限单元.由广义变分原理推导结构的多变量有限元列式,区间B样条小波尺度函数作为插值函数构造的多变量小波有限元法中,广义应力和应变被作为独立变量进行插值,避免了传统方法中应力应变求解的微分运算,减小了计算误差.区间B样条小波良好的数值...     

Solutions for a Mode Ⅲ Growing Crack in a Piezoelectric Plane Under Two Kinds of Electric Boundary Conditions ＊

The solutions for a mode Ⅲ crack growing along an arbitrary propagation path in a piezoelectric plane are studied under the impermeable surface condition and the electrical contact surface condition respectively. According to the two kinds of electric boundary conditions, the Hilbert and Riemann boundary value problems in a half-plane including opening smooth arc are obtained from the theoretical analysis. Moreover, the equipollence of the solution formed under these two electric boundaries is proved, and unified solutions for the stress and electric displacement distribution in the crack-tipfield of the piezoelectric plane are achieved.     

GENERALIZED CANONICAL TRANSFORMATION AND SYMPLECTIC ALGORITHM OF THE AUTONOMOUS BIRKHOFFIAN SYSTEMS

The Birkhoff systems are the generalization of the Hamiltonian systems. Generalized canonical transformations are studied. The symplectic algorithm of the Hamiltonian systems is extended into that of the Birkhoffian systems . Symplectic differential scheme of autonomous Birkhoffian systems was structured and discussed by introducing the Kailey Transformation .     

基于哈密顿原理的两种材料界面裂纹奇性研究

研究了两种材料组成的弹性体在交界面上含裂纹时的裂纹尖端奇异场。通过变量代换及变分原理，将平面弹性扇形域的方程导向哈密体系，从而可通过分离变量及共轭辛本征函数展开法解析法求解扇形域方程，得到求解双材料界面裂纹尖点奇性的一般表达式，由此为该类问题的求解开辟了一条新途径。     

关于线性动力系统可化为线性自治Birkhoff动力系统的条件

本文研究一般性自治动力系统何时转化为线性自治Birkhoff动力系统的问题，给出线性自治Birkhoff动力系统与线性自治Hamilton动力系统等价性的定理，并推导出2n维线性动力系统转化为线性自治Birkhoff动力系统条件；通过运用若当块对转化条件进行分析，分情况给出Birkhoff张量非退化的条件。     

自治Birkhoff系统的广义正则变换和辛算法研究

研究了自治Birkhoff系统的广义正则变换,将Hamilton系统的辛算法推广到Birkhoff系统,通过引入凯莱变换和生成函数法构造Birkhoff方程的Birkhoff的辛差分格式,同时讨论了Birkhoff差分格式的辛算法.