G. Monegato and A. Strozzi
Singular integral equations and contact problems in Kirchhoff plates resting on irregular linear supports
Received: 11 February 2008
Mathematics Subject Classification (2000): 74K20 - 74M15 - 45A05 - 45E05
Keywords: Kirchhoff plate, Poisson-Kirchhoff paradox, reaction forces, equivalent shear force, singularity strength, Williams asymptotic approach, contact problem, integral equations.
Supported by the Ministero dell'Istruzione, dell'UniversitÓ e della Ricerca of Italy
Abstract The construction of (boundary) singular integral equation formulations of contact problems for Kirchhoff (thin) plates is addressed. In particular, the need to forecast the singularity strength of the contact reaction is evidenced. It is shown that, when employing the integral formulation to describe contact problems between Kirchhoff plates and irregular linear supports, the equivalent shear force concept may be incompatible with the integral equation approach. In such circumstances the equivalent shear force concept has to be abandoned in favour of, or coupled with, an equivalent twisting moment approach. These concepts are described and applied to two particular contact problems.