Ut Vis Sic Tensio
Giuseppe Saccomandi
Available online 03 November 2017

Abstract
The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

Mathematics Subject Classification
74B20

Keywords
hyper-elasticity, simple extension, phenomenological reduction, non-Gaussian effects

DOI
https://doi.org/10.2298/TAM170703011S

Variational model of scoliosis
Igor Popov, Nikita Lisitsa, Yuri Baloshin, Mikhail Dudin, and Stepan Bober
Available online 07 November 2017

Abstract
Scoliosis, being one of the most widespread spine diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of three-dimensional deformation of human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. The numerical properties of the first stage of scoliosis are investigated, which is shown to have the highest influence on the development of the disease.

Mathematics Subject Classification
92C10; 74L15

Keywords
spine, model, variational method

DOI
https://doi.org/10.2298/TAM170818012P

Locomotion of multibody robotic systems: dynamics and optimization
Felix L. Chernousko
Available online 09 February 2018

Abstract
Locomotion of multibody systems in resistive media can be based on periodic change of the system configuration. The following types of mobile robotic systems are examined in the paper: multilink snake-like systems; multibody systems in quasi-static motion; systems consisting of several interacting bodies; fish-like, frog-like, and boat-like systems swimming in fluids; systems containing moving internal masses. Dynamics of these systems subjected to various resistance forces, both isotropic and anisotropic, are investigated, including dry friction forces obeying Coulomb\mbox{'}s law and forces directed against the velocity of the moving body and proportional to the velocity value or its square. Possible modes of locomotion and control algorithms are discussed. Optimization for various types of mobile robots is considered. Optimal values of geometrical and mechanical parameters as well as optimal controls are obtained that provide the maximum locomotion speed or minimum energy consumption. Results of experiments and computer simulation are discussed.

Mathematics Subject Classification
70E55

Keywords
multibody systems, robotics, locomotion, optimization

DOI
https://doi.org/10.2298/TAM171017001C

An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems
Adebowale Borokinni, Odunayo Fadodun, and Adegbola Akinola
Available online 02 March 2018

Abstract
This article considers a plane strain gradient plasticity theory of the Gurtin--Anand model [M. Gurtin, L. Anand, A theory of strain gradient plasticity for isotropic, plastically irrotational materials Part I: Small deformations, J. Mech. Phys. Solids 53 (2005), 1624--1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin-Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.

Mathematics Subject Classification
74C10

Keywords
plane strain gradient, microstresses, flow rule, weak formulation

DOI
https://doi.org/10.2298/TAM171017002B

Fractional telegrapher's equation as a consequence of Cattaneo's heat conduction law generalization
Dušan Zorica and Stevan M. Cvetićanin
Available online 02 March 2018

Abstract
Fractional telegrapher's equation is reinterpreted in the setting of heat conduction phenomena and reobtained by considering the energy balance equation and fractional Cattaneo heat conduction law, generalized by taking into account the history of temperature gradient as well. Using the Laplace transform method, fractional telegrapher's equation is solved on semi-bounded domain for the zero initial condition and solution is obtained as a convolution of forcing temperature on the boundary and impulse response. Some features of such obtained solution are examined.

Mathematics Subject Classification
35Q79; 35R11; 80A20; 26A33

Keywords
fractional telegrapher's equation, Cattaneo heat conduction law, initial-boundary value problem, Laplace transform

DOI
https://doi.org/10.2298/TAM171211003Z

Estimation of wind turbine blade aerodynamic performances computed using different numerical approaches
Jelena Svorcan, Ognjen Peković, and Toni Ivanov
Available online 17 April 2018

Abstract
Although much employed, wind energy systems still present an open, contemporary topic of many research studies. Special attention is given to precise aerodynamic modeling performed in the beginning since overall wind turbine performances directly depend on blade aerodynamic performances. Several models different in complexity and computational requirements are still widely used. Most common numerical approaches include: i) momentum balance models, ii) potential flow methods and iii) full computational fluid dynamics solutions.
Short explanations, reviews and comparison of the existing computational concepts are presented in the paper. Simpler models are described and implemented while numerous numerical investigations of isolated horizontal-axis wind turbine rotor consisting of three blades have also been performed in ANSYS FLUENT 16.2. Flow field is modeled by Reynolds Averaged Navier--Stokes (RANS) equations closed by two different turbulence models.
Results including global parameters such as thrust and power coefficients as well as local distributions along the blade obtained by different models are compared to available experimental data. Presented results include fluid flow visualizations in the form of velocity contours, sectional pressure distributions and values of power and thrust force coefficients for a range of operational regimes. Although obtained numerical results vary in accuracy, all presented numerical settings seem to slightly under- or over-estimate the global wind turbine parameters (power and thrust force coefficients). Turbulence can greatly affect the wind turbine aerodynamics and should be modeled with care.

Mathematics Subject Classification
76-04; 76F60; 76M23

Keywords
ind turbine, BEMT, vortex methods, turbulence, RANS

DOI
https://doi.org/10.2298/TAM171130004S

Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation
Ratko Pavlović, Ivan R. Pavlović
Available online 14 May 2018

Abstract
The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure.

Mathematics Subject Classification
74H55

Keywords
viscoelastic foundation, transverse shear, Liapunov functional, almost sure stability, Gaussian process, harmonic process

DOI
https://doi.org/10.2298/TAM171103005P

Energy separation in transient and steady-state flow across the cylinder
Jela M. Burazer
Available online 24 May 2018

Abstract
Energy separation is a spontaneous energy redistribution within a fluid flow. As a consequence, there are places with higher and lower values of total temperature in the fluid flow. It is characteristic for many flow geometries. This paper deals with the energy separation in a cylinder wake. Two flow conditions are being considered--transient and steady-state flow in the wake. Two different solvers from the open source package OpenFOAM are used in order to capture the phenomenon of energy separation. One of these solvers is modified for the purpose of calculation in a particular case of the vortex street flow. The energy equation based on the internal energy present in this solver is replaced by the energy equation written in the form of a total enthalpy. The other solver has been previously tested in the vortex tube flow, and can also capture the energy separation in the steady-state wake flow of the cylinder. In both cylinder wake flow conditions, a two-dimensional computational domain is used. Standard \kEps model is used for computations. It is proved that OpenFOAM is capable of capturing the energy separation phenomenon in a proper way in both of the wake flow cases. Good agreement between the experimental results and the ones from computations is obtained in the case of steady-state flow in the wake. Previous research findings are also confirmed in the case of vortex street flow.

Mathematics Subject Classification
76F10

Keywords
energy separation, cylinder, OpenFOAM, turbulence, compressible flow

DOI
https://doi.org/10.2298/TAM171130006B