The state equations for the first and second fundamental problems of elastodynamics for a cracked medium - D. I. Bardzokas; G. I. Sfyris (National Academy of Sciences of Armenia)
In our work we will derive the state equations the first and second fundamental dynamical problems in the frame of linear elasticity. In the first fundamental dynamical problem we will consider an infinite medium that contains a crack, on the lips of which, the stresses are considered to be known. The second fundamental problem has the same formulation, but in this case, the displacements on the crack lips are known. Beginning from the equations of motion, Hooke’s law and the compatibility equations we will derive the state equations for the above mentioned problems. The derivation of the equations will be based on the Muskhelishvili method of the Complex Potentials, the use of the Sohotsky – Plemely formulas and finally we will get two singular integral equations that are the state equations for the problems.
Keywords: Mechanics of deformable solids; Dynamical problems