一类非均布载荷下中心裂纹圆盘T应力分析

T-Stress in a Centrally Cracked Brazilian Disk Under Nonuniform Pressure Load

实际结构中,岩石常承受非均布载荷作用;并且试验中,集中力作用下往往会存在微小的分布角,这一载荷分布也是非均匀分布的.基于此类情况提出一类非均布载荷,这种载荷为三角函数形式,在分布角的中间压力最大,然后向两边逐渐减小直至为0.运用径向集中压力下中心裂纹巴西圆盘T应力解析公式,在分布角范围内积分获得这类非均布载荷下试件的T应力解析解,并同时进行有限元分析获得数值解.通过比较这两种结果,发现二者非常吻合,相互验证了各自分析的正确性.此外,与均布力作用相比,同等条件下此类非均布载荷作用的无量纲T应力值更接近集中力作用的值,而且两者的数值误差相当小.进一步论证了实际试验中采用集中力加载的T应力公式是正确与合理的.

In an engineering structure,the rock is often subjected to nonuniform load; in addition,there is a small distribution angle under a concentrated force in actual experimental study,and the load distribution also should be nonuniform. Based on this case,a class of nonuniform loads were proposed in the trigonometric function form. Then the maximum loading pressure appeared in the middle of the distribution angle and gradually became small to both sides until 0. By means of the centrally cracked Brazilian disk（ CCBD） T-stress formula under a radial concentrated load,the analytical T-stress solution under this kind of nonuniform load was acquired via the integral in the range of the distribution angle,meanwhile the finite element simulation was conducted to obtain the numerical solution. There is a very good consistency between the numerical results and the analytical results,which verifies the accuracy of each other. Compared with those under the uniform load,the dimensionless T-stress values under this nonuniform load are closer to the values under the concentrated load when the other condition is the same,and the discrepancy between the stresses under the nonuniform load and the concentrated load is very small. The further calculated results show that it is accurate and reasonable to use the T-stress formula for the CCBD subjected to the concentrated forces in actual testing.