Uniform rotation of a polygonal plate weakened by two linear crack holes

In the given paper, rotating polygonal plate of the theory of elasticity is considered. From Kosmodamianskii, 1975, Muskheleshvili, 1966 and Timoshenko and Goodyer, 1975 the solution of only elementary simple dynamic problems of the theory of elasticity are known. Solutions of dynamic problems of the theory of elasticity for multi-connected polygonal plates, as well as for the plates with rectilinear cuts are still waiting for their exhaustive answer. For complex domains, especially in the availability of linear cracks, such problems are considered for the first time. Mainly, this was connected with the lack of conformably mapping functions which, for the first time in the scientific world, were discovered by the author of the given manuscript. Owing to the papers Kuliyev, 1991 and Kuliyev, 2004, many questions connected with conformably mapping functions may be settled.Stress state of a polygonal isotropic plate weakened by two linear crack elliptic holes (Fig. 1) is considered. The centers of elliptic holes are on a real axis , the linear cracks reaching the ellipses are symmetrically arranged along a real axis. End points of the crack have the coordinates. Two point masses have been fixed on an imaginary axis at distances from the center of a plate. The plate revolves with constant angular velocity around the axis passing through the center of the plate and perpendicular plane. The origin is at the centre of a polygonal plate. The contours of the plate are free from external forces.We shall obtain the solution of the considered problem by applying the solutions of indicated two problems (two cases of acting loads). Solving each of indicated problems by Muskheleshvili method (determining the functions and that are regular in the plate’s domain for each case) we find the stress fields, and at characteristic points of cuts at the end points of cracks. From these values of stress we can determine the stress intensity coefficient (K) at the end points of cracks, and then to define a critical load at which the fracture of a plate begins. Knowing we find a limiting angular velocity (or limiting member of revolutions per minute). Numerical examples are considered.