WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 14, 2019
Two Elementary Problems of Shell Deformation in Plasticity
Author:
Abstract: The two problems of plastic deformation of membrane shells dealt with are, the expansion of a spherical shell by internal pressure, and the shaping of a dome out of a circular disk. The first problem is easily accessible to an analytical solution which overcomes the pressure maximum and establishes the relationship between the expanding sphere radius and the pertaining pressure in dependence of the hardening of the material. This case may be considered in some sense introductory to the second problem, where a flat circular disk, clamped along the periphery, is blown by pressure such that a dome is formed. The proposed solution approximates the deforming shell as part of a sphere throughout, establishes the static equilibrium with the forming pressure, observes the peripheral kinematic constraint as well as the isochoric condition in plasticity and makes recourse on the flow characteristic of the material. The resulting nonlinear equations relating pressure and dome height are treated numerically by two nested iteration loops.
Search Articles
Pages: 153-158
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 14, 2019, Art. #16