关于基础力学课程教学改革的思考

基于对我国基础力学课程教学现状的思考,针对教学内容、专业体制和师资培训等方面提出了若干改革设想．     

三维基体裂纹与界面垂直接触的线奇异分析

使用三维断裂力学的超奇异积分方程方法,对两相材料中出现的三维基体裂纹与材料分界面垂直接触的应力线奇异问题作了理论分析,求得了线奇异界面应力的表达式     

方孔对裂纹尖端应力强度因子的影响

方孔对裂纹的影响,在理论和应用上都是很重要的。但由于数学上的困难,迄今还未解决。本文在作者前一工作的基础上,讨论图1所示无限弹性平面上方孔(边长为     

GENERAL SOLUTION OF MULTI-VALUED DISPLACEMENT PROBLEM OF AN ECCENTRIC CIRCULAR RING

In this paper.by using N.I.Muskhelishvili’s method a mul-ti-valued displacement problem is Considered for an eccentriccircular ring.The gereral expression of stress function isderived in the bipolar coordinate system and its application isexplained.     

有限圆板上的径向裂纹系分析

本文在工作和■的复函数法的基础上,对有限圆板上的径向裂纹系作了讨论,得到了单裂纹的基本解,并利用此解给出了解决这类问题的一般方法.为了说明方法的应用,这里使用奇异积分方程的数值解法和Gauss-Chebyshev 求积公式作了例题计算,数值结果绘制了函数图,它们指出了应力强度因子随裂纹几何和作用力变化的关系,这可供工程应用.     

三维界面裂纹的理论分析

使用界面裂纹的基本解及有限部积分的方法 ,将三维界面裂纹问题 ,归为解一组以裂纹面位移间断为未知函数的超奇异积分微分方程 ,然后为此组方程的求解作了系统的理论分析     

带有椭圆孔的裂纹系问题

本文通过引入折算载荷,结合使用的复函数方法,对含有一个椭圆孔和一组任意裂纹系的问题作了讨论,将问题归结为解一组混合型的积分方程,其中既有Fredholm方程,也有Cauchy型奇异积分方程。并对其数值求解作了系统讨论。这里建议的数值方法对于求解一般的混合型积分方程组具有普遍的意义。为了验证并说明方法的应用,文中作了例题计算,所得结果绘制了函数图,它们指出了椭圆孔对裂纹的影响,可供工程应用。     

带裂纹圆柱体的Saint-Venant扭转

横截面上带有任意径向裂纹系的圆柱体的Saint-Venant扭转,还无一般的解析解法。本文采用裂纹二侧应力差和位移差的混合边界条件提法,通过Mellin变换,在求解了一组三节积分方程和一个Neumann问题后,精确地求得了单裂纹基本解,利用此解给出了解决这类问题的一般方法。文中还使用奇异积分方程的数值理论,对二条非共线的等长径向裂纹的应力强度因子和抗扭刚度作了数值计算。     

The Bending of Elastic Circular Ring of Non-homogeneous and Variable Cross Section under the Actions of Arbitrary Loads

On the basis of the stepped reduction method suggested in[1],we investigatethe problem of the bending of elastic circular ring of non-homogeneous andvariable cross section under the actions of arbitrary loads.The general solutionof this problem is obtained so that it can be used for the calculations of strengthand rigidity of practical problems such as arch,tunnel etc.In order to examineresults of this paper and explain the application of this new method,an exampleis brought out at the end of this paper.Circular ring and arch are commonly used structures in engineering.Timo-shenko,S.,Barber,J.R.,Tsumura Rimitsu et al.have studied theseproblems of bending,but,so far as we know,it has been solely restricted to thegeneral solution of homogeneous uniform cross section ring.The only knownsolution for the problems with variable cross section ones has been solelyrestricted to the solution of special case of flexural rigidity in linear functionof coordinates.On account of fundamental equations of the non-homoge     

ON THE TORSION OF A CYLINDER WITH SEVERAL CRACKS

In this paper, based on paper, the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The probtem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations, the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the cr(?)kcutting method is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful.