Self-similar solution of the hydraulic fracture problem for two closely spaced beams

The fracture of two closely spaced elastic beams by an incompressible viscous fluid is considered. The beam bending is described in the framework of the Kirchhoff-Love model. The self-similar solutions are sought by the group methods. The numerical results obtained when solving the corresponding system of differential equations with various boundary conditions are graphically illustrated in the form of pressure and velocity distributions within the fluid and in the form of the distance between the beams in the fracture zone.