Cylindrical bending of a plate by rigid stamps: PMM vol. 39, n≗5, 1975, pp. 876–883

Abstract

A periodic contact problem of the cylindrical bending of a plate by rigid stamps is considered from the aspect of equations of elasticity theory as well as Kirchhoff-Love theory with and without transverse compression of the material in the contact zone taken into account Analysis of the solutions obtained permits illumination of the question of the error and of the possibility of using the classical theory of plates and shells in analyzing contact problems. A comparative analysis is given of the nature of the distribution and of the magnitude of the stresses of the plate in the contact zone, of the character of the contact reaction distribution and the dependence between the magnitude of the contact zone and the force applied to the stamp. The apparatus of integral equations is used in considering the problem from the aspect of elasticity theory, while the solution is obtained in closed form by means of Kirchhoff theory. An analogous problem on the basis of the elasticity theory equations has been solved in [1] also by a method different from that elucidated below. However, only sufficiently thick plates (the ratio between the thickness and the characteristic dimension is not less than 1 20 ) are considered there. But a comparison between the stresses obtained when using different theories can yield the most correct answer about the applicability of any theory.