一类非线性算子方程解存在性的注记

利用不动点指数理论,讨论了非线性算子方程Ax=μx解的存在性并给出了方程解的存在性定理,推广了某些文献已有的结果.     

悬臂半无限大板弯曲的边界积分公式

根据双调和方程边值问题的边界积分公式,求得了一般载荷作用下悬臂半无限大板的弯曲解,在此基础上求解了不同边界条件下几种半无限大板的弯曲问题.其解式收敛速度快、计算精度高,计算过程相对简单,并与相应有限元解进行了对比分析.     

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature （DQ） approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.     

A class of singular perturbation solutions to semilinear equations of fourth order

A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied, In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer.     

半刚性连接钢框架的拟动力实验研究

在钢框架结构的设计中, 通常将梁柱节点处理为完全刚接或理想的铰接.但是在实际框架中, 梁柱节点表现出半刚性.目前的实验研究基本都基于结构和构件的静力分析.本文对半刚性连接钢框架结构进行了拟动力实验研究,得出了在地震波激励作用下,半刚性节点初始刚度对钢框架的楼层刚度、基底剪力、楼层位移和楼层加速度的影响.对实验结果进行对比分析可以看出,在结构侧向位移满足的前提下半刚性连接刚度的减弱会引起结构作用效应的降低.实验总结出的节点半刚性对结构动力性能影响的一些结论,将为高层钢结构设计规范的修改提供实验基础.     

一种求解有限元问题结点平衡方程的快速方法

目前随着工程实际问题复杂程度的增加及分析的要求,特别是材料非线性分析的引入,尽管计算机的运算速度、内存、外存容量等不断提高,但并不能完全满足大规模计算的需要,更快、更节省存贮空间的算法一直是有限元法分析过程中的一项核心技术要求。本文针对一些结点及单元均规律化地排列的有限元问题,提出可以透过其相邻结点的关系记录结点平衡方程中系数矩阵的非零元素,无需再像等带宽存贮那样去记录带宽内大量的零元素。此方法可以大大地减少系数矩阵元素的存贮量,从而可以提高计算机读取数据的速度及改善利用迭代法求解的效率。     

极大子群的性质对有限群结构的影响

设H为有限群G的一个子群。称H在G中是s-半正规的,若对任意的素数p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G);称H在G中是c-可补的,若存在G的子群N,使得G=HN且H∩N≤HG=CoreG(H)。证明了下面定理设F是一个包含超可解群类U的饱和群系,H△G,且G/H∈F。则G∈F,若下列条件之一成     

Singularly perturbed solution to semilinear reaction diffusion equations with two parameters

A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied.     

EFFECT OF SURFACE ENERGY ON DISLOCATION-INDUCED FIELD IN HALF-SPACE WITH APPLICATION TO THIN FILM-SUBSTRATE SYSTEMS

In this work the elastic field of an edge dislocation in a half-space with the effect of surface energy has been obtained. The elastic field is then used to study the image force on the dislocation, the critical thickness for dislocation generation in epitaxial thin films with strain mismatch and the yielding strength of thin films on substrates. The results show that the image forces on the dislocation deviate from the conventional solutions when the distance of the dislocation from the free surface is smaller than several times of the characteristic length. Also due to the effect of surface energy, the critical thickness for dislocation generation is smaller than that predicted by the conventional elastic solutions and the extent of the deviation depends on the magnitude of mismatch strain. In contrast, the effect of surface energy on the yielding strength for many practical thin films can be neglected except for some soft ones where the characteristic length is comparable to the thickness.     

含有部分脱胶的浅埋圆衬砌对SH波的散射

采用复变函数法研究了含有部分脱胶的浅埋圆形衬砌对SH波的散射问题.首先,将所研究的区域分成两个域,在圆形衬砌中构造一个满足脱胶部分应力自由的散射波函数,将其展开为含有一个待定系数的Fourier级数;而在介质半空间中应满足脱胶部分应力自由,公共边界处位移和应力连续的边界条件.然后,在"公共边界"上实施"契合",与此同时,可构造出脱胶结构,进而得到求解该同题的无穷代数方程组.最后,针对目前工程上应用较广的两种典型浅埋衬砌进行算例分析,给出了地表位移的数值结果,并讨论了入射波参数、脱胶位置以及埋深对地表位移的影响结果.