Finite, Dynamic lotions of Thin Rate-Dependent Sheets

The transient response of a thin sheet comprised of a rate-dependent solid is determined. The material is assumed to be incompressible, and the constitutive response is governed by a nonlinearly viscous power-law model. The sheet has axially symmetry, but an otherwise arbitrarily varying thickness. Axially symmetric, finite, dynamic motions of the sheet are identified. Introduction In this paper, the finite, transient response of an axially symmetric, thin sheet comprised of a rate-dependent, incompressible solid is determined. A Lagrangian formulation, coupled with a theory of generalized plane stress, is employed. The dependence of the motion on the initial thickness profile of the sheet is explored. Because of its importance in connection with sheet metal forming, plane-stress motions in plastically deforming materials have been the subject of extensive research activity. The prediction of necking in such sheets is a main objective, and several studies, including those by Storen and Rice (1975), Needleman (1976), and Rice (1976), have been carried out using plane-stress approximative assumptions. In this paper, a simple material model is used to describe the dynamic response of finitely-deforming, rate-dependent sheets. In uniaxial tension, the Cauchy stress T is proportional to the rate of strain raised to a power. Using generalized plane stress, axially symmetric motions of a sheet of arbitrary undeformed cross-section are analytically determined

Pressure Dewelopment in the Entrance Region and Fully Deweloped Region of Generalized Channel Turbulent Flows

In this paper, the pressure drops in the developing length of generalized turbulent channel flows are investigated, and the effects of Reynolds number and distance from the channel entrance are examined. The numerical method is also used to predict the pressure drops in simple channel flows for very high Reynolds numbers (of the order of 100,000). Excellent agreement is obtained between experimental data and numerical predictions

Measurements and Predictions of Laminar Mixed Convection Flow Adjacent to a Vertical Surface

Measurements and predictions of laminar mixed forced and free convection airflo