Stress state of a hollow round cylinder with side holes under different pressure and temperature impact

The stress–strain state of a hollow cylinder (pipe) with lateral holes is considered. The pipe is under the action of internal and external hydrostatic pressures P₁ and P₂ and also a temperature effect. Such a pipe is used in oil–gas recovery, rocket engineering, chemical machinery industry and etc. There is no detailed analytic solution of this problem in literature to date. The number of holes through which a liquid or gas can flow into the pipe interior (and vice versa) depends on the loads, the size of the cross-section and the material of the pipe. The proper selection of the arrangement of holes and their diameters is determined from an analytic solution. In addition, the maximum boundary loads (of pressures) at which the pipe cracks is also found.