With the aid of the " pseudo - traction " method , the superposition technique and the arrived fundamental solution , a method for getting the stress intensity factor ( sif ) for material such as rock with center inclined crack under compressive loading are given 采用“伪力法”和叠加原理,结合所求的基本解,给出了含中心斜裂纹的岩石类材料在压缩荷载作用下的应力强度因子( sif )的解法。
Based on the fundamental solution of two perfectly bonded elastic halfspaces , and using the boundary integral equation method and the finite - part integral concepts , the problem is reduced to a hypersingular integral equation in which the unknown function is the crack opening displacement discontinuity 首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程。
The boundary integral equation for elasticity is derived through the general green ’ s formula and the corresponding fundamental solution . the paper represents the contact conditions , which are essential for the coupling of the boundary integral equations of the two different elastic contact bodies , in a local coordinate system properly chosen 利用广义格林公式和基本解得出弹性问题的边界积分方程,采用循环迭代的方法,通过寻求与接触条件相协调的接触边界位移及面力增量来确定接触区域的大小。
In the paper , computational sophistication is applied to compute the basic solution matrix of a sort of two - dimensional periodic differential equation which contains two parameters . the matrix makes it realizable to study the stability of two - dimensional periodic differential equation , here , the following is proved in the paper : only if a ( t ) , b ( t ) , c ( t ) , d ( t ) satisfy some quantity conditions , is exponentially asymptotically stable <中文摘要> =本文应用计算技巧,计算出一类含双参数的二维周期系统的基本解方阵,以这个基本解方阵为依据,研究二维周期系统的结构稳定性。所得结论是:只要之间满足一定的数量关系,则该系统指数型渐近稳定。
The works in detail are as follows : 1 . base on the essential solution for a complete elastic half space impacted by antiplane line source loading at horizontal surface , the essential solution of displacement field for an elastic half space with an arbitrary - shape - canyon impacted by antiplane harmonic line source loading at horizontal surface is constructed by using the method of complex function and conformal mapping 从完整的弹性半空间表面承受线源荷载作用问题的基本解出发,用复变函数的保角映射方法获得含有任意形凹陷的弹性半空间在其水平面上任意一点承受时间谐和的反平面线源荷载作用时位移场的解答,即本文的green函数。
We reduce the cauchy problem of equations ( 8 ) , ( 9 ) to an equivalent integral equations by the fundamental solution of a second order partial differential equation . then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution 先是通过一个二阶偏微分方程的基本解,把imbq型方程组归) , p )的初值问题转化为等价的积分方程组,然后利用压缩映射原理、解的延拓定理等证明了归) ,问的初值问题的整体广义解和整体古典解的存在唯一性
By comparison , it was clear that the bem could solve the problem not only effectively but also precisely . in the second chapter the theory of weighted residual technique is illustrated and the boundary integral function of the potential problem is deduced by it . methods of obtaining green ' s function fundamental solutions in infinite region and semi - infinite region are presented 第二章首先说明了加权余量法的原理,并由此推出了势问题的边界积分方程,还介绍了无限域和半无限域中格林函数基本解的求法,以及多介质域和第三类边界条件的处理方法,最后说明了边界积分方程的数值解法。
Also according to the basic solution matrix , hopf bifurcation of is investigated by creating subsequence functions , the measure of which differs from that of autonomous system . in the paper i apply myself to seek out a new idea to investigating heteronymous system that is no longer stickled in autonomous system 同样以这个基本解方阵为依据,本文接着研究二维周期系统的hopf分支,所用方法是构造后继函数法,但在具体构造方法上,与自治系统的hopf分支不同,本文致力于探索一种不再拘泥于自治系统的,研究非自治系统hopf分支的新思路。
The green ' s function for point - source excitation is also very simple in homogeneous media . however , since global basic functions like plane waves occupy the entire domain and point source excitation radiates to all directions , their evolution through a non - homogeneous medium constitutes a problem that may become at least as difficult to solve as that of the propagation of the total field 例如dirac函数(点源)在空间域可以有精确的定位,但在传播方向上(波数域)却毫无确定性;而平面波(波数域的基本解)则具有精确的传播方向,但其波前却是无限延伸的,不具任何空间局域性。
By using the arrived fundamental solution , combined with the " pseudo - traction " method and the boundary collocation , the stress intensity factor for crack in a finite plate under compressive loading are solved , the effects of crack direction and boundary condition on the stress intensity factor are analyzed , and the varying curves of the sif along with the width are given 将所得的基本解与“伪力法” 、边界配置法相结合,得到了有限板在压缩荷载作用下应力强度因子的解法,分析了裂纹方向和边界条件对应力强度因子的影响,给出了应力强度因子随板宽的变化曲线。