Tero Tuovinen

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.

Mechanics of moving materials

1 Introduction 2 Travelling strings, beams, panels, membranes and plates 3 Stability analysis 4 Non-homogeneous tension profile 5 Travelling panels made of viscoelastic material 6 Travelling panels interacting with external flow 7 Fracture and fatigue of travelling plates 8 Some optimization problems References Index

Vibrations of a continuous web on elastic supports

ABSTRACT We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.

Stability of a Tensioned Axially Moving Plate Subjected to Cross-Direction Potential Flow

We analyze the stability of an axially moving Kirchhoff plate, subjected to an axial potential flow perpendicular to the direction of motion. The dimensionality of the problem is reduced by considering a cross-directional cross-section of the plate, approximating the axial response with the solution of the corresponding problem of a moving plate in vacuum. The flow component is handled via a Green’s function solution. The stability of the cross-section is investigated via the classical Euler type static linear stability analysis method. The resulting eigenvalue problem is solved numerically using Hermite type finite elements. As a result, the critical velocity and the corresponding eigenfunction are determined. It is seen that even at very low free-stream fluid velocities, the buckling shape may become antisymmetric in the cross direction.

On Bifurcation Analysis of Implicitly Given Functionals in the Theory of Elastic Stability

In this paper, we analyze the stability and bifurcation of elastic systems using a general scheme developed for problems with implicitly given functionals. An asymptotic property for the behaviour of the natural frequency curves in the small vicinity of each bifurcation point is obtained for the considered class of systems. Two examples are given. First is the stability analysis of an axially moving elastic panel, with no external applied tension, performing transverse vibrations. The second is the free vibration problem of a stationary compressed panel. The approach is applicable to a class of problems in mechanics, for example in elasticity, aeroelasticity and axially moving materials (such as paper making or band saw blades).

Safety Analysis and Optimization of Travelling Webs Subjected to Fracture and Instability

The problems of safety analysis and optimization of a moving elastic web travelling between two rollers at a constant axial velocity are considered in this study. A model of a thin elastic plate subjected to bending and in-plane tension (distributed membrane forces) is used. Transverse buckling of the web and its brittle and fatigue fracture caused by fatigue crack growth under cyclic in-plane tension (loading) are studied. Safe ranges of velocities of an axially moving web are investigated analytically under the constraints of longevity and instability. The expressions for critical buckling velocity and the number of cycles before the fracture (longevity of the web) as a function of in-plane tension and other problem parameters are used for formulation and investigation of the following optimization problem. Finding the optimal in-plane tension to maximize the performance function of paper production is required. This problem is solved analytically and the obtained results are presented as formulae and numerical tables.

Analysis and optimization against buckling of beams interacting with elastic foundation

ABSTRACT We consider an infinite continuous elastic beam that interacts with linearly elastic foundation and is under compression. The problem of the beam buckling is formulated and analyzed. Then the optimization of beam against buckling is investigated. As a design variable (control function) we take the parameters of cross-section distribution of the beam from the set of periodic functions and transform the original problem of optimization of infinite beam to the corresponding problem defined at the finite interval. All investigations are on the whole founded on the analytical variational approaches and the optimal solutions are studied as a function of problems parameters.

Agile Deep Learning UAVs Operating in Smart Spaces: Collective Intelligence Versus “Mission-Impossible”

The environments, in which we all live, are known to be complex and unpredictable. The complete discovery of these environments aiming to take full control over them is a “mission-impossible”, however, still in our common agenda. People intend to make their living spaces smarter utilizing innovations from the Internet of Things and Artificial Intelligence. Unmanned aerial vehicles (UAVs) as very dynamic, autonomous and intelligent things capable to discover and control large areas are becoming important “inhabitants” within existing and future smart cities. Our concern in this paper is to challenge the potential of UAVs in situations, which are evolving fast in a way unseen before, e.g., emergency situations. To address such challenges, UAVs have to be “intelligent” enough to be capable to autonomously and in near real-time evaluate the situation and its dynamics. Then, they have to discover their own missions and set-up suitable own configurations to perform it. This configuration is the result of flexible plans which are created in mutual collaboration. Finally, the UAVs execute the plans and learn from the new experiences for future reuse. However, if to take into account also the Big Data challenge, which is naturally associated with the smart cities, UAVs must be also “wise” in a sense that the process of making autonomous and responsible real-time decisions must include continuous search for a compromise between efficiency (acceptable time frame to get the decision and reasonable resources spent for that) and effectiveness (processing as much of important input information as possible and to improve the quality of the decisions). To address such a “skill” we propose to perform the required computations using Cloud Computing enhanced with Semantic Web technologies and potential tools (“agile” deep learning) for compromising, such as, e.g., focusing, filtering, forgetting, contextualizing, compressing and connecting.

Travelling Panels Interacting with External Flow

This chapter is devoted to the analysis of the travelling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account somehow. The light weight of the material leads to the inertial contribution of the surrounding air to the acceleration of the material becoming significant. In the small displacement regime, the geometry of the vibrating panel is approximately flat, and hence flow separation is unlikely. We will use the model of potential flow for the fluid. The approach described in this chapter allows for an efficient semi-analytical solution, where the fluid flow is solved analytically in terms of the panel displacement function, and then strongly coupled into the partial differential equation describing the panel displacement. The panel displacement, accounting also for the fluid–structure interaction, can then be solved numerically from a single integrodifferential equation. In the first section of this chapter, we will set up and solve the problem of axial potential flow obstructed by the travelling panel. In the second section, we will use the results to solve the fluid–structure interaction problem, and give so me numerical examples.

Non-Homogeneous Tension Profile

In this chapter, we will look at the influence of a skewed tension profile on the divergence instability of a travelling, thin elastic plate. The travelling plate is subjected to axial tension at the supports, but the tension distribution along the supports is not uniform. For the nonuniformity, we will use a linear distribution. First, we will perform a dynamic analysis of small time-harmonic vibrations, after which we will concentrate on the divergence instability problem. We will see that a small inhomogeneity in the applied tension may have a large effect on the divergence modes, and that inhomogeneity in the tension profile may significantly decrease the critical velocity of the plate.