N. Shavlakadze

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

abstract:
Contact problems of the theory of elasticity on bending of finite and infinite, isotropic or anisotropic plates with an elastic inclusion of variable bending rigidity are considered. The problems are reduced to an integro-differential equation with a variable coefficient. When the coefficient turns to zero of higher order at the ends of the interval of integration, the equation is out of the framework of cases already studied. Such equations are studied, exact or approximate solutions are obtained, the bahaviour of unknown contact stresses at the ends of the line of contact is established.

Mathematics Subject Classification: 45J05, 73C02.

Key words and phrases: Elastic inclusion, integro-differential equation, bending of plates, Jacobi polynomials.