Yun Tian-quan, Shao Uong-chang, Qiu Chong-guang. Analysis of Ellipsoid Compressed by Two Axial Concentrated Forces at Two Ends[J]. Applied Mathematics and Mechanics, 1981, 2(6): 641-650.
 Citation: Yun Tian-quan, Shao Uong-chang, Qiu Chong-guang. Analysis of Ellipsoid Compressed by Two Axial Concentrated Forces at Two Ends[J]. Applied Mathematics and Mechanics, 1981, 2(6): 641-650.

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

• Publish Date: 1981-12-15
• 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.
•  [1] Broch,E.and Franklin,J.A.,The point-load strength test,International Journal of Rock Mechanics and Mining Science,9,6,1972. [2] Banerjee,P.K.,Integral equation method for analysis of piece-wise non-homogeneous three-dimensional elastic solids of arbitrary shape,Int.J.Mech.Sci.,18,293,(1976). [3] 云天铨,圆柱嵌入半空间的三维问题的一个简便的积分方程方法,固体力学学报,第一卷,第二期,(1980年). [4] 云天铨,轴对称受力问题的积分方程的迭代法,应用数字和力学,第一卷,第一期,(1980),115-123. [5] Frocht,M.M.,Photoelasticity 2,(1948). [6] Kuske,A.,Photoelastic Stress Analysis,(1973).

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