Investigation on the stress displacement field for the plane stress disk,which is also called the Brazilian disk,has an important theoretical and practical value for elastic mechanics,rock mechanics and fracture mechanics.In order to obtain the closed-form solution to stresses and displacements in the Brazilian disk under different loading conditions,based on the theory of elasticity and a series solution of stress for the Brazilian disk subjected to a pair of compressive forces,the explicit expressions of displacements were obtained for the Brazilian disk under diametral-compression loading.The series solutions to stresses were then derived by using mathematical analysis method and the explicit expressions of displacements were obtained subjected to uniformly distributed pressure.The calculated results showed that the stressesσθ,σrand radial displacementuwere symmetric to the loading lineθ=0,and the stressτrθand tangential displacementvwere anti-symmetrictoθ=0.At the loading point of a concentrated force and the starting point or the end point of the distributed pressure,the stress field and displacement field had a abrupt change.For the same condition,the effect of the loading types on the displacements was less than that on the stresses.On the other hand,the loading type only had an important effect on the stress or displacement distributions near the loading point (i.e.,whenρwas larger),and the effect on the stress or displacement distributions was very small at points away from the loading point or loading range (i.e.,whenρis smaller).This conclusion agreed well with the Saint-Venant principle.In addition,the radial displacement increased with the increase ofρ,and it had a maximum value nearρ=0.7.The further analysis showed that the series formula obtained by other researcher can be simplified and combined,and the formula derived from the present paper is the simplest form for the Brazilian disk loaded by pressure.
