Matti Kurki

Optimization and Analysis of Processes with Moving Materials Subjected to Fatigue Fracture and Instability

We study systems of traveling continuum modeling the web as a thin elastic plate of brittle material, traveling between a system of supports at a constant velocity, and subjected to bending, in-plane tension and small initial cracks. We study crack growth under cyclic in-plane tension and transverse buckling of the web analytically. We seek optimal in-plane tension that maximizes a performance vector function consisting of the number of cycles before fracture, the critical velocity and process effectiveness. The present way of applying optimization in the studies of fracture and stability is new and affords an analytical tool for process analysis.

Dynamic Behaviour of a Travelling Viscoelastic Band in Contact with Rollers

The dynamic behaviour of an axially moving viscoelastic band, in contact with supporting rollers, is studied. A model of a thin, viscoelastic beam (panel) subjected to bending and centrifugal forces is used. An initial-boundary value problem for a fifth-order partial differential equation describing the movement of the band is formulated in detail. In this paper, five boundary conditions in total are used for the first time within the present model. An external force describing the normal force of the roller supports is included. Combining this viscoelastic model with the roller contact simulation is a new approach among moving band behaviour studies. The initial-boundary value problem is solved numerically using the fourth-order Runge-Kutta method and the central finite differences, and the band behaviour is illustrated for different band velocities and degrees of viscosity. It is found that the damping effect of viscoelasticity increases when the band velocity increases, and that the roller contact has a greater effect on the elastic panel behaviour than on the viscoelastic panel behaviour.