Analysis of ellipsoid compressed by two axial concentrated forces at two ends

Abstract

Integral equation method and photoelastic 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)=X₁(−c) and X₂(c)=X₂(−c) respectively, be distributed symmetrically to =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.