Nonclassical biharmonic boundary value problems describing bending of finite and infinite plates with inclusions (Q2730964)

The author studies contact problems of elasticity theory related to the bending of finite and infinite, isotropic or anisotropic plates with an elastic inclusion of variable rigidity. The circular plate and rectangular plate are considered as particular cases. The problems are reduced to integro-differential equations with variable coefficient. The characteristic equation corresponding to these equations is Prandtl integro-differential equation when the coefficient of singular operator possesses zeros of higher order at the end points of the interval of integration. First, the author investigates the properties of the solution of characteristic equation. Then the integro-differential equations are reduced to Fredholm integral equations of the second kind. The author obtains exact and approximate solutions, and examines the behaviour of contact stresses at the ends of contact line. The corresponding problems for anisotropic plates are discussed at the end.