具有可反测地线的$(\alpha,\beta)$-度量

本文我们得到了$(\alpha,\beta)$-度量的测地系数$G^{i}(x,y)$和其逆$G^{i}(x,-y)$有相同Douglas曲率的充分必要条件.这个充分必要条件恰好是$(\alpha,\beta)$-度量具有可反测地线的充分必要条件.     

应用最小势能原理计算应力强度因子

本文用Williams给出的包含待定系数A_n(n=1,2,…)的应力场和位移场无穷级数解表示裂纹体系统的总势能∏,由最小势能原理,得到含未知数A_n的线性方程组。解此方程组,取主项A_1,即得到相应的应力强度因子K_1=2∏_aA_1~(1/2)。 文中对单边直裂纹拉伸板进行了具体计算。在板的裂纹长度与板宽比a/W=0.5,板半长与板宽比g/W=2.0～2.5的情况下,仅采用了20～30个系数,结果误差小于5％。     

DETERMINING THE STRESS INTENSITY FACTOR BY USING THE PRINCIPLE OF MINIMUM POTENTIAL ENERGY

Expressing the total potential energy of the system of a cracked body Ⅱ byWilliams’infinite series solution of stress and displacement components containingcoefficients A_n(n=1,2,...), we obtain a set of simultaneous linear equations of unknowncoefficients A_n by using the principle of minimum potential energy.When the set ofequutions is solved,the stress intensity factor K_1 can be easily, determined.It is equal to(2πα)~(1/2)A_1.Take a sample plate as an example.A single-edge-cracked plate under tension,withthe ratio of crack length to the width of the plate being 0.5 and the ratio of half plate heightto the wiath of the plate being 2.0 and 2.5, has been calculated Only 20-30 coefficents aretaken,and the errors in stress intensity factors are within 5%.     

具有可反Douglas曲率的Matsumoto度量

本文得到Matsumoto度量具有可反Douglas曲率的充分必要条件,该条件蕴含存在具有可反Douglas曲率的非Douglas的Finsler度量.