具有双曲线边界的各向异性介质的二维问题

文章研究了在纯弯矩M₀作用下,具双曲线边界的各向异性介质的二维变形问题,求得了介质内部的应力应变场的具体形式,在此基础上,以单晶铝板(立方晶系介质)为例,我们求得了沿双曲线边界的环向应力及x₂=0面上的应力分布,当双曲线退化成一双边裂纹时,文章也求得了相应的应力强度因子(k₁,k₂,k₃),并且也发现,k₁与材料的弹性性质无关。

Two-Dimensional Prohlem of AnisotroFic Elastic Bodywith a Hyperbolic Boundary

The general and simplified formula for anisotropic medium with a hyperbolicboundary subjected to pure bending M_0 is provided in this paper. The stress andstrain fields in medium are obtained. Based upon the above results, we analysethe hoop stress along the hyperbolie curve and the stress distributions on theplane x_2=0 for aluminium (cubic crystal). When the boundary curve degeneratesinto an external crack three kinds of stress intensity factors (k_1,k_2,k_3) are obtai-ned,and it. is easily found that the first stress intensity factor k_1 is independentof the rnaterial constants.