受轴向集中压力的椭球体的应力分析

用积分方程法和光弹性方法分析受轴向集中压力的椭球体.在弹性全空间z=-c轴上的a,∞)和-a,-∞)区间上,与z=0平面对称地分布集度为X₁(c)=X₁(-c)的集中力、集度为X₂(c)=X₂(-c)的挤压中心,以及迭加一对平行z轴、等值反向、分别作用于z=α及z=-α上的集中力,就能使受轴向集中压力的椭球体问题归结为两个联立的Fredholm第一种积分方程.然后,便能方便地进行数值计算.三维光弹性“冻结”切片法用于详细分析两个椭球体的模型,给出几个切面的应力分布,所得结果σ_z与积分方程法相近,并将结果应用于分析不规则岩石力学试件实测资料的整理.

Analysis of Ellipsoid Compressed by Two Axial Concentrated Forces at Two Ends

Integral equation method and photoetastic experiment are used for the stress analysis of an axial compressive ellipsoid. Let the concentrated forces and the centers of compression, with symmetrical unknown intensive functions x₁(c)=x2(-c) and x2(c)=x2(-c) respectively, be distributed-symmetrically to z=0 plane along the axis z(=-c) in a,∞) and -a,-∞) of the elastic space, in addition to a pair of equal and opposite axial forces acting on z=a and z=-a. We can reduce the problem of an axial compressive ellipsoid to two coupled Fredholm integral equations of the first kind. Furthermore, numerical calculation is then made. Two photo-elastic models of ellipsoid were analysed by "Freezing and Cutting" method, and the results, in which σ₂ is quite nearly to those obtained by integral equation method, had been used in the analysis of the data of compressive rock specimens.