Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid

The out-of-plane instability of a moving plate, travelling between two rollers with constant velocity, is studied, taking into account the mutual interaction between the buckled plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the buckled plate (assumed cylindrical) is described by an integro-differential equation that includes the centrifugal force, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, and the bending force. The aerodynamic reaction is found analytically as a functional of the displacement. To find the critical divergence velocity of the moving plate and its corresponding buckling mode, an eigenvalue…

Dynamic Behaviour of an Axially Moving Plate Undergoing Small Cylindrical Deformation Submerged in Axially Flowing Ideal Fluid

Abstract The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindri…

Nash Equilibrium in a Road Network with Many Groups of Users

In this chapter concentrates on the relationships between individual and group behaviour of drivers in a road network. Such relationships are established by comparing the optimal routing of drivers (system optimum of Wardrop), the competitive drivers’ groups routing (Nash equilibrium), and the selfish drivers routing (user equilibrium of Wardrop). Thus, the boundary conditions for traffic assignment in a road network were recently obtained for the first time. Wide analytical discussion on the topic as well as a survey of relevant references are presented. Moreover, a new behavioural model of traffic assignment in case of simultaneous selfish and group behaviour of drivers in a road network …

Mikrojärjestelmien virtausdynamiikka numeerisen mallintamisen näkökulmasta

Travelling Strings, Beams, Panels, Membranes and Plates

In this chapter, we will introduce in a general manner some of the most common models for axially travelling materials, which will be used in the rest of the book. We will introduce the linear models of travelling strings, panels, and plates. It will be assumed that the material is thin, i.e. its planar dimensions are much larger than its thickness. We will work in the small displacement regime, that is, with linear models approximating the behaviour of the system near the trivial equilibrium. As is well known in the theory of elasticity, this approximation allows for a decoupling of the in-plane and out-of-plane components in the dynamics of the system. We will concentrate on small out-of-…

The curl and fluting of paper : The effect of elasto-plasticity

An in-plane elasto-plastic material model and a hygroexpansivity model were ap­plied for paper. The input parameters for both models are fiber orientation and dry solids content. A finite element model was constructed offering possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior and internal stress situations under through-thickness strain differences. Examples related to the curl and web­fluting phenomena of paper are presented. Both studied cases presented in this paper indicates the usefulness of the hygro-elasto-plastic model in predicting the challenging deformation phe­nomena of orthotropic paper sheets. The application possib…

Transportation Processes Modelling in Congested Road Networks

In this chapter, the models of different transportation processes in a congested road network are considered. The first section is devoted to a signal control problem formulated as a bi-level optimization program. An analytical solution for a two-commodity linear road network offers a practical and illustrative result to be taken into consideration by decision-makers in this sphere. A new algorithm for OD-matrix estimation based on the dual traffic assignment problem is described in the second section. The third section is devoted to the problem of emission reduction. The approaches presented in this book are shown to be well-implemented for coping with such problems. The time-depended vehi…

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 (su…

Stability of Axially Moving Plates

This chapter focuses on the stability analysis of axially moving materials, in the context of two-dimensional models. There are many similarities with the classical stability analysis of structures, such as the buckling analysis of plates. However, the presence of axial motion introduces inertial effects to the model. We consider the stability of an axially moving elastic isotropic plate travelling at a constant velocity between two supports and experiencing small transverse vibrations. We investigate the stability of the plate using an analytical approach. We also look at elastic orthotropic plates, and an elastic isotropic plate subjected to an axial tension distribution that varies in th…

Evolutionary cloud for cooperative UAV coordination

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., em…

Using Wave Propagation Simulations and Convolutional Neural Networks to Retrieve Thin Film Thickness from Hyperspectral Images

Ill-posed inversion problems are one of the major challenges when there is a need to combine measurements with the theory and numerical model. In this study, we demonstrate the use of wave propagation simulations to train a convolutional neural network (CNN) for retrieving sub-wavelength thickness profiles of thin film coatings from hyperspectral images. The simulations are produced by solving numerically one-dimensional wave equation with a method based on Discrete Exterior Calculus (DEC). This approach provides a powerful tool to produce large sets of training data for the neural network. CNN was verified by simulated verification sets and measured reflectance spectra, both of which showe…

Digital Technologies for Transport and Mobility: Challenges, Trends and Perspectives

This white paper aims at presenting the ideas emerging from the different fields pertaining to transport and mobility, to describe the capacities of current state-of-the-art digital technologies and the perspectives that are expected to shape the future of transport and mobility.

Reliable estimates in the anisotropic heat conduction problems

Abstract The heat conduction problems for anisotropic bodies are studied taking into account the uncertainties in the material orientation. The best estimations of the upper and lower bounds of the considered energy dissipation functional are based on developing new approach consisting in solution of some optimization problems and finding the extremal internal material structures, which realize minimal and maximal dissipation. The motivation of this study comes from paper making processes, and more precisely, drying process, which consumes about 50% of the energy fed into the paper machine. The understanding of the effect of uncertainties in the process arises from structural properties of …

On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates

In this paper, we consider the static stability problems of axially moving orthotropic membranes and plates. The study is motivated by paper production processes, as paper has a fiber structure which can be described as orthotropic on the macroscopic level. The moving web is modeled as an axially moving orthotropic plate. The original dynamic plate problem is reduced to a two-dimensional spectral problem for static stability analysis, and solved using analytical techniques. As a result, the minimal eigenvalue and the corresponding buckling mode are found. It is observed that the buckling mode has a shape localized in the regions close to the free boundaries. The localization effect is demon…

Analysis of stability of axially moving orthotropic membranes and plates with a linear non-homogeneous tension profile

Adoption of digital innovations in rural enterprises during COVID-19

The COVID-19 pandemic has rapidly affected the operating conditions of enterprises. Traditional customers and operational models are changing radically in the short term. Digitalisation and digital methods provide an opportunity to re-organise working methods and create a new kind of business to replace old methods and business models. Compared to urban enterprises, rural enterprises have less experience with digital tools and are less likely to adopt digital innovations. This makes rural enterprises especially vulnerable. The purpose of this study is to provide insights into how micro-enterprises and small and medium-sized enterprises in rural areas have addressed the COVID-19 pandemic, th…

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. peerReviewed

Stability of Local Out-of-Plane Deformations of Orthotropic Sheet : Numerical Approach

Dynamic analysis for axially moving viscoelastic panels

In this study, stability and dynamic behaviour of axially moving viscoelastic panels are investigated with the help of the classical modal analysis. We use the flat panel theory combined with the Kelvin–Voigt viscoelastic constitutive model, and we include the material derivative in the viscoelastic relations. Complex eigenvalues for the moving viscoelastic panel are studied with respect to the panel velocity, and the corresponding eigenfunctions are found using central finite differences. The governing equation for the transverse displacement of the panel is of fifth order in space, and thus five boundary conditions are set for the problem. The fifth condition is derived and set at the in-…

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-analyti…

Hygroexpansivity of anisotropic sheets

Dimensional instability, more particularly its component hygroexpansivity, may cause problems in process or end-use situations in which paper or board is in contact with water or subject to changes in ambient relative humidity. Misregistration in printing, curl during copying and calender wrinkles are examples of such defects. In this paper, the in-plane hygroexpansivity of oriented laboratory sheets with different pulps and dried both freely and under restraint is studied. A linear relationship between the drying shrinkage and hygroexpansion coefficient of freely dried laboratory sheets having different fiber orientation anisotropies, was observed. Regardless of both the measurement direct…

A thermoelastic instability problem for axially moving plates

Problems of stability and deformation of a moving web, traveling between a system of rollers at a constant velocity are considered. The plate is subjected to a combined thermomechanical loading, including pure mechanical in-plane tension and also centripetal forces. Thermal strains corresponding to thermal tension and bending of the plate are accounted for. The problem of out-of-plane thermomechanical divergence (buckling) is reduced to an eigenvalue problem, which is studied analytically.

Travelling Panels Made of Viscoelastic Material

In this chapter, our focus is to analyse the behaviour of moving panels using viscoelastic materials. As the reader will have noticed, all the models discussed in previous chapters have concerned the case of a purely elastic material. The deformation of an elastic material depends only on the applied forces; it has no explicit time dependence. Paper, however, is a more complicated material: it is viscoelastic. In addition to elastic properties, it has also time-dependent viscous properties, which cause the phenomena of creep and relaxation (see, e.g., Alava and Niskanen 2006). One of the simplest models for a viscoelastic solid is the Kelvin–Voigt model, which consists of a linear spring an…

Stochastic analysis of the critical velocity of an axially moving cracked elastic plate

In this study, a probabilistic analysis of the critical velocity for an axially moving cracked elastic and isotropic plate is presented. Axially moving materials are commonly used in modelling of manufacturing processes, like paper making and plastic forming. In such systems, the most serious threats to runnability are instability and material fracture, and finding the critical value of velocity is essential for efficiency. In this paper, a formula for the critical velocity is derived under constraints for the probabilities of instability and fracture. The significance of randomness in different model parameters is investigated for parameter ranges typical of paper material and paper machin…

Stability of Thermoelastic Layered Composite in Axial Movement

Design challenges and opportunities of 3D printing

In the future, the number and complexity of products made using additive manufacturing (AM) techniques will increase rapidly. The development of softwares and algorithms related to processes will eliminate extra intermediate steps between the product design and the end product, and will finally give us more intelligent way to manufacture these new products. More efficient 3D printing processes will enable the production of cheaper individual items and, furthermore, they will increase the demand for these high - quality tailored unrivalled solutions. The market potential is huge. However, at present the fundamentals of the area are only lightly studied and several key challenges concerning s…

Laskennallinen tiede - tieteen kolmas menetelmä : tilannekatsaus 2011

Time-Dependent Multiple Depot Vehicle Routing Problem on Megapolis Network under Wardrop's Traffic Flow Assignment

In this work multiple depot vehicle routing problem is considered in case of variable travel times between nodes on a metropolis network. This variant of the classic multiple depot vehicle routing problem is motivated by the fact that in urban contexts variable traffic conditions play an essential role and can not be ignored in order to perform a realistic optimization. Time-travel matrices corresponding to each period of planning horizon were formed by solving the traffic assignment problem in conjunction with shortest path problem. Routing problem instances include from 20 to 100 customers randomly chosen from a road network of Saint-Petersburg. The results demonstrate that taking into ac…

Some Optimization Problems

In this chapter, the problems of safety analysis and optimization of a moving elastic plate travelling between two rollers at a constant axial velocity are considered. We will use a model of a thin elastic plate subjected to bending and in-plane tension (distributed membrane forces). We will study transverse buckling (divergence) of the plate and its brittle and fatigue fracture caused by fatigue crack growth under cyclic in-plane tension (loading). Our aim is to find the safe ranges of velocities of an axially moving plate analytically under the constraints of longevity and stability. In the end of this chapter, the expressions for critical buckling velocity and the number of cycles before…

Added-Mass Based Efficient Fluid–Structure Interaction Model for Dynamics of Axially Moving Panels with Thermal Expansion

The paper considers the analysis of a traveling 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. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel…

Haasteena yritysyhteistyö

Uncertainties in the heat conduction problems and reliable estimates

The heat conduction problems for anisotropic bodies are studied taking into account the uncertainties in the material orientation. The best estimations of the upper and lower bounds of the considered energy dissipation functional are based on the developing new approach consisting in solution of some optimization problems and finding the extremal internal material structures, which realize minimal and maximal dissipation.

Vibrations of a continuous web on elastic supports

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. peerReviewed

Анализ и оптимизация устойчивости балок на сплошном упругом основании часть I (балки конечной длины) [Analysis and optimization of a beam on elastic foundation. Part I (Limited beams)]

Problems of defining the optimal (against buckling) cross section area distribution for beams interacting with elastic foundation are considered. The stability of limited pinned beams and infinite continuous beams is analyzed. For all beams under consideration, the stability analysis is performed as for constant as for variable distributions of strength beam characteristics. The critical length is determined and the variational statement of beam stability problems is presented for this beam type. The exact solution of optimal problem is presented in the case of linear dependence of limited beam bending hardness on beam cross section area. For the case of squared and cubic dependences, the n…

Potku – New analysis software for heavy ion elastic recoil detection analysis

Time-of-flight elastic recoil detection (ToF-ERD) analysis software has been developed. The software combines a Python-language graphical front-end with a C code computing back-end in a user-friendly way. The software uses a list of coincident time-of- flight–energy (ToF–E) events as an input. The ToF calibration can be determined with a simple graphical procedure. The graphical interface allows the user to select different elements and isotopes from a ToF–E histogram and to convert the selections to individual elemental energy and depth profiles. The resulting sample composition can be presented as relative or absolute concentrations by integrating the depth profiles over user-defined rang…

Open benchmark database for multidisciplinary optimization problems

Solving new increasingly complex problems requires development of new methods and tools but verification of their correctness and efficiency in absence of actual experimental data is difficult. In this paper we propose an open database of benchmark cases for multidisciplinary optimization validation that will serve as a reference point for discovery and validation of optimization methods and facilitate adoption of such methods in the industry. The paper describes the goals of the database, the process of acquiring content to the database, its initial content and technical implementation. peerReviewed

Analytical approach for the problems of dynamics and stability of a moving web

Problems of dynamics and stability of a moving web, modelled as an elastic rod or string, and axially travelling between rollers (supports) at a constant velocity, are studied using analytical approaches. Transverse, longitudinal and torsional vibrations of the moving web are described by a hyperbolic second-order partial differential equation, corresponding to the string and rod models. It is shown that in the framework of a quasi-static eigenvalue analysis, for these models, the critical point cannot be unstable. The critical velocities of one-dimensional webs, and the arising non-trivial solution of free vibrations, are studied analytically. The dynamical analysis is then extended into t…

Unicorn-Open science for assessing environmental state, human health and regional economy

Open data and models are becoming increasingly available, but there are not yet good methods and platforms to turn those into systematic evidence-based decision support. Unicorn will produce such an environment based on existing theoretical and practical knowledge about decision support and models. This con sortium possesses the necessary models, data, and skills to set up an environment and demonstrate its func tionality and usefulness with several case studies related to the environmental issues, human health, and economy. The Unicorn environment will be built in a generic and systematic way so that it could even be come an international standard for evidence-based decision support. Devel…

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., em…

Mathematical modelling of sustainable bioresidual concrete

In the production of cement, which is the main component of concrete production, the process generates about 5% of the global carbon dioxide emissions. In addition, bioproduct and pulp mills produce signi_cant quantities of soda ash and bio-ash, which is still largely unused. In this paper we will introduce our study related to improving the environmental friendliness of concrete used in construction by utilizing pulp mill waste while its long-term durability and strength and porosity properties meet the goals set for construction. The project `sustainable bioresidual concrete' is on-going and only preliminary numerical results with measurements are presented here. peerReviewed

Analysis and optimization against buckling of beams interacting with elastic foundation

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. peerReviewed

Bifurcation method of stability analysis and some applications

In this paper a new approach to the analysis of implicitly given function- als is developed in the frame of elastic stability theory. The approach gives an effective procedure to analyse stability behaviour, and to determine the bifur- cation points. Examples of application of the proposed approach for analysis of stability are presented, more precisely we consider the stability problem of an axially moving elastic panel, with no external applied tension, performing transverse vibrations. The analysis is applicable for many practical cases, for example, paper making and band saw blades.

Theoretical study on travelling web dynamics and instability under non-homogeneous tension

Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibration…

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.

Time-Dependent Multiple Depot Vehicle Routing Problem on Megapolis Network under Wardrop's Traffic Flow Assignment

In this work multiple depot vehicle routing problem is considered in case of variable travel times between nodes on a metropolis network. This variant of the classic multiple depot vehicle routing problem is motivated by the fact that in urban contexts variable traffic conditions play an essential role and can not be ignored in order to perform a realistic optimization. Time-travel matrices corresponding to each period of planning horizon were formed by solving the traffic assignment problem in conjunction with shortest path problem. Routing problem instances include from 20 to 100 customers randomly chosen from a road network of Saint-Petersburg. The results demonstrate that taking into ac…

Variational approach for analysis of harmonic vibration and stabiligy of moving panels

In this paper, the stability of a simply supported axially moving elastic panel (plate undergoing cylindrical deformation) is considered. A complex variable technique and bifurcation theory are applied. As a result, variational equations and a variational principle are derived. Analysis of the variational principle allows the study of qualitative properties of the bifurcation points. Asymptotic behaviour in a small neighbourhood around an arbitrary bifurcation point is analyzed and presented. It is shown analytically that the eigenvalue curves in the (ω, V0) plane cross both the ω and V0 axes perpendicularly. It is also shown that near each bifurcation point, the dependence ω(V0) for each m…

An analytical-numerical study of dynamic stability of an axially moving elastic web

This paper is devoted to a dynamic stability analysis of an axially moving elastic web, modelled as a panel (a plate undergoing cylindrical deformation). The results are directly applicable also to the travelling beam. In accordance with the dynamic approach of stability analysis, the problem of harmonic vi- brations is investigated via the study of the dependences of the system’s nat- ural frequencies on the problem parameters. Analytical implicit expressions for the solution curves, with respect to problem parameters, are derived for ranges of the parameter space where the natural frequencies are real-valued, corresponding to stable vibrations. Both axially tensioned and non-tensioned tra…

Fracture and Fatigue of Travelling Plates

In this chapter, problems of fracture and stability of a moving plate, travelling in a system of rollers at a constant velocity, are studied. It is known that in the manufacturing process, there may occur many kinds of defects in the paper web, such as edge cracks and blister and fiber cuts. Our aim is to tackle this problem and analyse theoretically how the defects change the behaviour. We will use the model of a thin elastic plate made of brittle material. A plate with initial cracks is studied, subjected to constant tension and cyclic tension. As a result, we will show how to find safe parameter ranges of transport velocities and in-plane tensions when fracture, stability and constraints…

On displacement-velocity coupling and the origin of in-plane stress in orthotropic moving continua

In this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the solid continuum problem can be transformed to solid a continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in the two-dime…

On some bifurcation analysis techniques for continuous systems

This paper is devoted to techniques in bifurcation analysis for continuous mechanical systems, concentrating on polynomial equations and implicitly given functions. These are often encountered in problems of mechanics and especially in stability analysis. Taking a classical approach, we summarize the relevant features of the cubic polynomial equation, and present some new aspects for asymptotics and parametric representation of the solutions. This is followed by a brief look into the implicit function theorem as a tool for analyzing bifurcations. As an example from mechanics, we consider bifurcations in the transverse free vibration problem of an axially compressed beam. peerReviewed

Mechanics of Moving Materials

Errata to “On the instability of an axially moving elastic plate” [Int. J. Solids Struct. 47 (2010) 91–99]

Stability of moving viscoelastic panels interacting with surrounding fluid

We study a model describing the out-of-plane vibrations of an axially moving viscoelastic panel submerged in flowing fluid. The panel is assumed to travel at a constant velocity between two fixed supports, and it is modeled as a flat panel made of viscoelastic Kelvin-Voigt material. The fluid flow is modeled with the help of the added mass coefficients. The resulting dynamic equation is a partial differential equation of fifth order in space. Five boundary conditions are set for the studied problem. The behavior of the panel is analyzed with the help of its eigenvalues (eigenfrequencies). These characteristics are studied with respect to the velocity of the panel. In our study, we have incl…

Unsupervised Numerical Characterization in Determining the Borders of Malignant Skin Tumors from Spectral Imagery

For accurate removal of malignant skin tumors, it is crucial to assure the complete removal of the lesions. In the case of certain ill-defined tumors, it is clinically challenging to see the true borders of the tumor. In this paper, we introduce several computationally efficient approaches based on spectral imaging to guide clinicians in delineating tumor borders. First, we present algorithms that can be used effectively with simulated skin reflectance data. By using simulated data, we gain detailed information about the sensitivity of the different approaches and how variables defined by algorithms act in the skin model. Second, we demonstrate the performance of the algorithms with spectra…

On the critical velocities and free vibrations of axially moving elastic webs

Optimal Transit Network Design

In this chapter, the optimal transit network design is under investigation. A special kind of transport is assumed to be given the best traffic conditions in a road network (the smallest amount of travel time between origins and destinations). Optimality criteria for transit network design in case of selfish routing are defined in the first section. The Sect. 7.2 is devoted to the estimation of selfish traffic assignment in a network with a transit subnetwork. Optimality criteria for transit network design in case of competitive drivers’ groups routing are defined in the Sect. 7.3. The Sect. 7.4 is devoted to traffic assignment in case of competitive drivers’ groups routing in a network wit…

Prospectives to tractor cabin design with computational acoustics tools

Computational acoustical models allow automated optimization of tractor design with respect to acoustic properties, which could speed up significantly the design process of tractor cabin prototypes. This article gives insightful prospectives to the tractor design process by considering modern computational acoustics technology. Mathematical formulation for a system consisting of vibrating elastic tractor structure and airfilled acoustic enclosure are given and a related numerical solution technique with finite element method (FEM) is presented. Simulation results produced with commercially available software are reviewed. nonPeerReviewed

Анализ и оптимизация устойчивости балок на сплошном упругом основании часть II (бесконечные балки) [Analysis and optimization of a beam on elastic foundation. Part II (Infinite beams)]

Problems of defining of optimal (against buckling) cross section area distribution for beams interacting with elastic foundation are considered. The stability of limited pinned beams and infinite continuous beams is analyzed. For all beams under consideration, the stability analysis is performed as for constant as for variable distributions of strength beam characteristics. The critical length is determined and the variational statement of beam stability problems is presented for this beam type. For infinite continuous beams, the stability problems are investigated as for constant as for periodic distribution of strength characteristics. In the second case, the analysis of infinite beam can…

Hygro-elasto-plastic model for planar orthotropic material

An in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model for paper and board are introduced in this paper. The input parameters for both models are fiber orientation anisotropy and dry solids content. These two models, based on experimental results, could be used in an analytical approach to estimate, for example, plastic strain and shrinkage in simple one-dimensional cases, but for studies of the combined and more complicated effects of hygro-elasto-plastic behavior, a numerical finite element model was constructed. The finite element approach also offered possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior…

A review of the analytical and numerical modeling of composites

This review article is dedicated to the materials that are made from two or more constituent materials with different physical and/or chemical properties. The focus is on the materials, where the individual components remain separate and distinct within the final structure. The new combined material usually have some additional characteristic properties compared to the individual components, or, in other case, some critical properties of combined material may follow almost equally one of the components. Typically, preferred properties of the new material can be such as strength, porosity, conductivity or cheapness. The ultimate goal of this study is to find methods and tools for achieve adequ…

Building trust in the sharing economy: Current approaches and future considerations

The sharing economy could be an answer to the challenge of sustainability; it can facilitate the sharing and reuse of resources, create new ways of earning money, and enhance social connections. For example, by reducing the use of natural resources without having to acquire or own everything, the sharing economy can positively affect sustainability. At the core of this type of economy lies trust among users and between users and the platform—the system cannot reach its full potential without trust. In fact, businesses or organizations in the sharing economy can even fail due to trust issues, although more information is needed to make better use of the existing platforms. The aim of this sy…

Digital innovations in rural micro-enterprises

Digitalization gives micro-enterprises and rural areas new possibilities and it can support their competitiveness. In this paper, we have presented one way of supporting the diffusion and adoption of digital innovations in rural micro-enterprises. First, we examined the challenges and digital competence of the micro-enterprises in the rural areas of Central Finland to better understand what they needed. The second step was to develop a workshop concept. Theories of innovation diffusion and adoption were used as a base for these workshops. The last step was to evaluate the developed concept, its effects and challenges. We found that the workshop concept worked well for spreading information,…

On the instability of an axially moving elastic plate

Problems of stability of an axially moving elastic band travelling at constant velocity between two supports and experiencing small transverse vibrations are considered in a 2D formulation. The model of a thin elastic plate subjected to bending and tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of an analytical approach. In the frame of a general dynamic analysis, it is shown that the onset of instability takes place in the form of divergence (buckling). Then the static forms of instability are investigated, and critical regimes are studied as functions of geometric and mechanical problem param…

Matkalla 3D-tulostettuun maailmaan

3D-tulostus ei ole aivan uusi asia, mutta laajempaan tietoisuuteen ala on noussut vasta viime vuosina. Tällä hetkellä 3D-tulostusta hyödynnetään paljon teollisuuden eri aloilla, kuten esimerkiksi lääketieteessä ja teollisessa muotoilussa, mutta tulostimien hintojen laskettua merkittävästi viime vuosina on niiden pienimuotoinen käyttö lisääntynyt myös tavallisen kuluttajan harrastevälineenä. Mutta mitä 3D-tulostus käytännössä tarkoittaa ja millainen on alan tilanne nyt ja tulevaisuudessa? nonPeerReviewed

Quasi-brittle porous material: Simulated effect of stochastic air void structure on compressive strength

Abstract The effect of porosity comprised of spherical air voids on the compressive strength of quasi-brittle material was studied via simulations. The simulated porous structures were based on pore size distributions of two mortar samples measured by X-ray microtomography. While the simulation method set practical limits on the size of sample, the base of the statistics was established by simulating 128 small structures generated by sampling from pore structures of two mortars. By studying the application of the classical strength-porosity formulas to the simulated data, a new simple model was formed. A linear relationship was achieved between the cubic root of air void fraction (porosity)…

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 eigenfun…

Variational principle and bifurcations in stability analysis of panels

In this paper, the stability of a simply supported axially moving elastic panel is considered. A complex variable technique and bifurcation theory are applied. As a result, variational equations and a variational principle are derived. Anal- ysis of the variational principle allows the study of qualitative properties of the bifurcation points. Asymptotic behaviour in a small neighbourhood around an arbitrary bifurcation point is analyzed and presented. It is shown analytically that the eigenvalue curves in the (ω, V0) plane cross both the ω and V0 axes perpendicularly. It is also shown that near each bifur- cation point, the dependence ω(V0) for each mode approximately follows the shape of …

The origin of in-plane stresses in axially moving orthotropic continua

In this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in th…

Static instability analysis of an elastic band travelling in the gravitational field

Static instability analysis is performed for an axially moving elastic band, which is travelling at a constant velocity in a uniform gravitational field between two supports. The buckling of the band is investigated with the help of admitting small transverse deflections. The model of a thin elastic beam (panel) subjected to bending, centrifugal forces and nonhomogeneous tension (including a gravitational term) is used. Buckling analysis and estimation of the critical velocities of elastic instability are based on variational principles and variational inequalities. As a result, explicit formulas for upper and lower limits for critical velocities are found. It is shown analytically that a c…