# International Journal of Mechanics

**E-**ISSN: 1998-4448

Volume 8, 2014

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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**Volume 8, 2014**

Title of the Paper: **Axisymmetric Solution to Time-Fractional Heat Conduction Equation in an Infinite Cylinder under Local Heating and Associated Thermal Stresses**

Authors: **Yuriy Povstenko**

Pages: **383-390**

Abstract: The theory of thermal stresses based on the time-fractional heat conduction equation with the Caputo derivative is used to investigate axisymmetric thermal stresses in an infinite cylinder under local heating of its surface. The representation of stresses in terms of the displacement potential and the biharmonic Love function is employed. The solution is obtained using the integral transform technique (the Laplace transform with respect to time, the exponential Fourier transform with respect to the axial coordinate and the finite Hankel transform with respect to the radial coordinate).

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **The Initial Period of Mixed-Mode Crack Growth in Viscoelastic Composite with Rabotnov’s Relaxation Law**

Authors: **Mikhailo F. Selivanov, Yuri O. Chornoivan**

Pages: **377-382**

Abstract: A numerical algorithm is presented to study the initial period of crack growth in a viscoelastic composite under the mixed-mode loading. Viscoelastic properties of the composite are described using linear viscoelasticity operators with Yu. N. Rabotnov’s kernel. An example of calculation is given for a composite with viscoelastic components.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **Analysis of Energy State of a Discrete Fractionally Damped Spherical Net of Mouse Zona Pellucida before and after Fertilization**

Authors: **Andjelka N. Hedrih, Katica (Stevanović) Hedrih**

Pages: **371-376**

Abstract: Zona pellucida (ZP) is a 3D matrix that surrounds mammalian oocytes and embryo until the stage of early blastocyst. This structure is important for fertilization, polyspermy block, integrity of the growing embryo, guiding the embryo through the oviduct. In the late blastocyst stage, this structure no longer exists. During oocyte maturation, fertilization and embryo development ZP dynamically changes its elasticity. To explain elasticity change of mouse ZP (mZP) during these processes, a discrete fractional order spherical net model of mZP is developed. Elements in the model correspond to ZP glycoproteins that are interconnected with standard light fractional order elements. This model is suitable for modelling different states of the ZP net. Using the part of the ZP spherical net model that still preserves the molar ratio of ZP glycoproteins, we determined characteristic eigen numbers of eigen fractional order oscillations and eigen modes for each chain. Analytical expressions for mechanical energy of the representative part of the ZP net before and after fertilization are defined. Generalised function of energy dissipation for the representative part of the ZP net as well as for the whole ZP net was created. We discussed dynamical change of elasticity of the mZP and dissipation of its energy after fertilisation in biological context.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **Simulation of Oil Recovery Using the Weierstrass Elliptic Functions**

Authors: **Vladimir I. Astaf’ev, Pavel V. Roters**

Pages: **359-370**

Abstract: The objective of this research is to simulate the inflow performance of multiple vertical wells producing from a closed reservoir of constant thickness under pseudo-steady state conditions. For this case we represent, like the method of imaginary sources, a closed reservoir as an element of unbounded doubly periodic array of wells and use the elliptic Weierstrass zeta- and sigma-functions to describe this inflow performance. This approach allows us to find the pressure distribution and the fluid velocity in any shape of reservoir; to calculate the productivity index (PI) and the Dietz’s shape factor (CA) for any shape of reservoir; to analyze the influence of a reservoir shape on the Dietz’s shape factor CA; to establish the multi-well productivity matrix (MPM) for any shape of reservoir; to introduce the multi-well productivity index (MPI) and to find the optimal placement of producing wells in a closed reservoir, based on the maximum MPI condition.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **On the Application of a Viscoelastic Model with Rabotnov’s Fractional Exponential Function for Assessment of the Stress-Strain State of the Periodontal Ligament**

Authors: **Sergei M. Bosiakov**

Pages: **353-358**

Abstract: In the present paper, the mathematical modeling of the viscoelastic periodontal membrane is carried out. Internal surface of the periodontal ligament is adjacent to the outer surface of the tooth root, the geometric shape of which is described by the equation of an elliptic hyperboloid. The external surface of the periodontal membrane is shifted along the normal to the outer surface of the root and fixed on the dental alveolus bone. Relationships between displacements and deformations of the periodontal ligament are formulated with due account for incompressibility of the periodontal tissue. Viscoelastic properties of the periodontium are described by the relaxation kernel with Rabotnov’s fractional exponential function. A system of equations of motion in terms of the translational displacements and rotation angles of the tooth root is obtained. Particular cases of the equations of motion corresponding to the translational motion in the vertical and horizontal directions are formulated.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **Elements of Mathematical Phenomenology in Dynamics of Multi-Body Systems with Fractionally Damped Discrete Continuous Layers**

Authors: **Katica R. (Stevanović) Hedrih**

Pages: **345-352**

Abstract: Dynamics of deformable linear viscoelastic multi-bodies (beams. plates, membranes and belts with the same boundary conditions) coupled by standard light fractional order discrete continuous layers is considered using Petrović’s theory of elements of mathematical phenomenology. Starting with coupled fractional order differential equations in terms of transverse displacements of linear elastic beams which are coupled by fractional order discrete continuous layers with the corresponding boundary conditions, a system of coupled ordinary fractional order differential equations is derived in terms of eigen amplitude functions. Independent main eigen modes and a set of characteristic numbers of the eigen time functions corresponding to eigen amplitude functions are obtained. Using Petrović’s theory of mathematical analogy and qualitative analogy, properties of the main eigen modes and characteristic numbers of the time functions of vibrations of multi-plates as well as multi-membranes coupled by fractional order discrete continuous layers are studied. Energy analysis in a fractionally damped discrete continuous layer is carried out, and a generalized function its energy dissipation is defined.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **Frequency Response of a Viscoelastic Plate under Compressible Viscous Fluid Loading**

Authors: **S. D. Akbarov, M. I. Ismailov**

Pages: **332-344**

Abstract: Forced vibrations of the system consisting of a viscoelastic plate-layer and a half-plane filled with a compressible viscous fluid are studied. The plane-strain state is considered in the case where the lineally-located time-harmonic forces act on the free face plane of the plate, and it is assumed that the mechanical relations for the plate-layer material are described through the Rabotnov fractional exponential operators. The motion of the plate is written by utilizing 2D exact equations of the theory of visco-elasto-dynamics, but the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. It is assumed that the velocities and forces of the constituents are continuous on the contact plane between the plate and fluid. The dimensionless parameters which characterize the creep time and the long-term values of the elastic constants of the plate material are introduced. Moreover, the dimensionless parameters which characterize the compressibility and viscosity of the fluid are introduced as well. The corresponding boundary-value and contact problems which are obtained after employing the dynamical correspondence principle to the equations and relationships related to the plate are solved by applying the Fourier transformation with respect to the coordinate directed along the interface line. The inverse of this transformation is determined numerically. Numerical results on the interface stresses and velocities, and the influence of the foregoing dimensionless rheological parameters on these results are presented and discussed.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **The Simplest Models of Viscoelasticity Involving Fractional Derivatives and Their Connectedness with the Rabotnov Fractional Order Operators**

Authors: **Yury A. Rossikhin, Marina V. Shitikova**

Pages: **326-331**

Abstract: The given paper, the simplest viscoelastic models involving fractional derivatives, namely: fractional derivative Kelvin-Voigt model, Maxwell model, standard linear solid model and Koeller model, which is the generalization of the fractional derivative standard linear solid model, are considered, and their connectedness with the Rabotnov dimensional fractional operators is revealed. It is shown that when the order of the fractional derivative is tending to zero, then some of the enumerated models lose their physical meaning, while the other go over into the models describing pure elastic materials. These results have been achieved only due to the consideration of the resolvent operators, which allow one to express not only the stress in terms of the strain but the strain in terms of the stress as well.

Special Issue: Rabotnov Fractional Operators and their Some Applications

Editors: Yury A. Rossikhin, Marina V. Shitikova

Title of the Paper: **Modeling of Heat Transfer in a Vertical Channel at Bubble Flows by Means a DNS Method**

Authors: **Vladimir V. Chudanov, Anna E. Aksenova, Valerii A. Pervichko**

Pages: **319-325**

Abstract: This paper deals to simulation heat transfer in a vertical channel at bubble flows by means DNS method. The effective numerical CFD algorithm for 3D calculation of two-phase flows with selection of interface boundary explicitly and calculation of surface tension forces is presented. The main attention of this paper is focused on verification of numerical technique with usage of the numerical tests and experiments.

Title of the Paper: **Influence of a Bent or Battered Joint or Welding on the Dynamic Loads due to the Non-Suspended Masses of Railway Vehicles**

Authors: **Konstantinos Giannakos**

Pages: **307-318**

Abstract: Train circulation is a random dynamic phenomenon and, according to the different frequencies of the loads it imposes, there exists the corresponding response of track superstructure. Random dynamic phenomena are generally approached through the probability of occurrence (for stochastic processes see [1]). The railway track is modeled as a continuous beam on elastic support. At the moment when an axle of a railway vehicle passes from the location of a support point of a rail, that is a sleeper, a random dynamic load is applied on the sleeper. The theoretical approach for the estimation of the dynamic loading of a sleeper demands the analysis of the total load acting on the sleeper to individual component loads-actions, which, in general, can be divided into: the static component of the load‚ and the relevant to it reaction/action per support point of the rail (sleeper), the semi-static component of the load, and the relevant to it reaction/action per support point of the rail (sleeper) and the dynamic component of the load, and the relevant to it reaction/action per support point of the rail (sleeper). The motion of a railway vehicle on the rail running table –of the railway track– is described by formulas and it is illustrated through diagrams which have the form of a “signal”. It is a random/ stochastic dynamic phenomenon. The general equation that describes the motion is the second order differential equation (of motion). In the present paper the dynamic component of the Load and the relevant Action/ Reaction on each support point of the rail are investigated through a sensitivity analysis by variating parameters of the second order differential equation of motion of the Non Suspended Masses of the Vehicle ([2], [3]) and specifically the transient response of the reaction/ action on each support point (sleeper) of the rail.

Title of the Paper: **Acoustical Noise Study of a Factory: Indoor and Outdoor Simulations Integration Procedure**

Authors: **Claudio Guarnaccia, Joseph Quartieri, Alessandro Ruggiero**

Pages: **298-306**

Abstract: Industrial settlements are often source of disturbance for the surrounding area. In particular, from an acoustical point of view, the noise emitted by machineries operating in the production line and/or in the logistic activities, is a relevant pollutant to be considered in the environmental impact assessment. For this reason, the field measurement approach is usually preferred, to properly evaluate the noise levels in general conditions. The aid of predictive software may be particularly useful when it is difficult to perform a long term measurement campaign. In this paper, the combination of indoor and outdoor simulations will be presented on a case study in south Italy. The indoor modelling of the sources will help on one hand to understand the acoustic climate of the working environment, on the other hand to assess the overall outdoor noise emission of the factory. The values obtained with the indoor simulation, in fact, will be used to tune the “equivalent source” that simulate the factory emissions. An outdoor noise map will be drawn, in order to assess the impact on the surrounding buildings. Both the indoor and outdoor simulations are tuned with experimental field measurements and compared with results on fixed measurement points.

Title of the Paper: **Numerical Analysis of Bushing of Car Stabilizer**

Authors: **Jakub Javorik, Ondrej Bilek**

Pages: **289-297**

Abstract: The goal of this work is to create numerical model, which will be used for design and optimization of a rubber bushing of stabilizer bar. Thanks this model we are able to predict the mechanical behavior of the bushing. To get material constants for the model, the material of bushing (rubber) was tested in special deformations modes. A hyperelastic material model was set and it was implemented into the numerical model of the bushing. Critical points in the construction of bushing were reveled by the analysis of the numerical model.

Title of the Paper: **Optimal Model through Identified Frequencies of a Masonry Building Structure with Wooden Floors**

Authors: **Mariella Diaferio, Dora Foti, Nicola Ivan Giannoccaro, Salvador Ivorra**

Pages: **282-288**

Abstract: The paper presents the analysis of an important historical building: the Saint James Theater in the city of Corfù (Greece) actually used as the Municipality House. The building, located in the center of the city, is made of carves stones and is characterized by a stocky shape and by the presence of wooden floors. The study deals with the structural identification of such structure through the analysis of its ambient vibrations recorded by means of accelerometers with high accuracy. A full dynamic testing was developed using ambient vibrations to identify the main modal parameters and to make a non-destructive characterization of this building. The results of these dynamic tests are compared with the modal analysis of a complex finite element (FE) simulation of the structure. This analysis may present several problems and uncertainties for this stocky building. Due to the presence of wooden floors, the local modes can be highly excited and, as a consequence, the evaluation of the structural modal parameters presents some difficulties.

Title of the Paper: **Torque Characteristics of Pneumatic Muscle Actuator with Eccentric Pulley**

Authors: **Ján Piteľ, Mária Tóthová, Alena Vagaská, Dagmar Janáčová, Ondrej Líška**

Pages: **276-281**

Abstract: The movement of the pneumatic actuator with artificial muscles in antagonistic connection is typically transmitted through the circular pulley rotating about its center. But torque of such actuator decreases with increasing rotation of the actuator arm due to the non-linear decrease of muscles forces according to their contraction. By application of the eccentric pulley instead of circular pulley a smaller torque decrease can be obtained. In the paper there are described torque characteristics of such pneumatic muscle actuator.

Title of the Paper: **Comparison of Mechanical Properties of Different Particle Sizes of Recycled Polycarbonate at Higher Temperature**

Authors: **Vojtech Senkerik, Michal Stanek, Miroslav Manas, David Manas, Adam Skrobak, Jan Navratil**

Pages: **268-275**

Abstract: This research paper deals with behavior of particles of a recycled material at a higher temperature depending on the particle size. Behavior is tested by mechanical properties. During grinding particles are formed which have a different size, shape and surface, from larger pieces to dust particles. During processing these particles melt at different rates depending on their size. For example they can cause material degradation or lack of melt homogeneity. Several recycled mixtures were prepared that had differed particle size after crushing. The recycled material is always the same as is the original material. The studied material was high-heat polycarbonate. Testing was performed using a tensile test, Charpy impact test and hardness test. Specimens were prepared by the mostly used technology for production products, which is injection molding. Each mixture is one by one loaded by high temperature 100°C and consequently tested. This temperature was chosen because we encounter products made with recycled material additive, which can be used at elevated temperatures. When comparing a virgin polycarbonate with recycled mixtures, the particle size of the recycled material affects some of the material parameters quite substantially, but it had no effect on some other properties.

Title of the Paper: **Analysis of Methods to Evaluate the Noise Reduction due to Acoustic Barriers Installation**

Authors: **Claudio Guarnaccia, Joseph Quartieri, Nikos E. Mastorakis**

Pages: **258-267**

Abstract: Transportation infrastructures represent a relevant noise source in residential areas and have to be carefully taken into account in urban planning. Road traffic is commonly assumed to be the most relevant transportation mean in developed countries. For this reason, road traffic noise can be considered as the most important source of annoyance. The extremely random nature of road traffic makes very difficult to model the phenomenon and give reliable predictions. In the infrastructure design phase, a proper acoustic modelling can be helpful to minimize the noise impact. If the road is already present in the area, it is important to design effective mitigation actions. In this paper, the installation of noise barriers is simulated in a case study. This location, in south Italy, is characterized by several buildings placed in proximity of a motorway. In particular, a new building set has been built just in front of the motorway, without providing any noise mitigation action. In this paper, once the noise map of the area is obtained with a predictive software, the effects of the barriers, measured in terms of noise level reduction, are evaluated by means of literature, regulation and software approaches. The comparison between these approaches will be discussed and will show that, in order to obtain a reliable estimation of the noise reduction, diffraction, reflection and other relevant parameters cannot be neglected.

Title of the Paper: **Assessment of Several Artificial Dissipation Models in 2D and 3D**

Authors: **Edisson S. G. Maciel, Omar Seye**

Pages: **239-257**

Abstract: In this paper, the Euler equations in conservative and integral forms are applied to the solution of the supersonic flow along a compression corner. Five artificial dissipation models are tested, aiming to identify the main vantages and disadvantages of each one. Three isotropic models based on the works of Azevedo, Mavriplis, and MacCormack and Baldwin are implemented. On the other hand, two anisotropic models based on the work of Turkel and Vatsa are studied. The isotropic models are scalar ones, whereas the anisotropic models are scalar and matrix ones. Such studies are performed on a finite volume and structured contexts, in two- and three-dimensional spaces. The algorithms to perform the numerical experiments are the MacCormack, second order, MacCormack, fourth order, and Jameson and Mavriplis, second order, in two-dimensions. In three-dimensions, one studies the MacCormack, second order, and the Jameson and Mavriplis, second order. All schemes are predictor-corrector or symmetrical ones. Convergence is accelerated to the steady state by a spatially variable time step procedure, which has provided excellent results as reported by Maciel. Good results are obtained by all models, especially for the matrix model, and are reported in this paper.

Title of the Paper: **Nano-Indentation Test of PA12 after Radiation Cross-Linking**

Authors: **Martin Ovsik, David Manas, Miroslav Manas, Michal Stanek, Petr Kratky, Vojtech Senkerik**

Pages: **231-238**

Abstract: This article describes the effect of radiation cross-linking on the nano-mechanical properties of polyamide 12. Cross-linking is a process in which polymer chains are associated through chemical bonds. These nano-mechanical properties were measured by the DSI (Depth Sensing Indentation) method on samples which were non-irradiated and irradiated by different doses of the β - radiation. The best results were achieved by the irradiation with doses of 132 kGy. The nano-mechanical properties (nano-hardness, elastic modulus, deformation work, creep) after irradiation was increased up to 67 % compared to untreated material.

Title of the Paper: **Effects of the Distribution and Geometry of Porosity on the Macroscopic Poro-Elastic Behavior: Compacted Exfoliated Vermiculite**

Authors: **Soufiane Belhouideg, Manuel Lagache**

Pages: **223-230**

Abstract: For high temperatures and high pressures applications, materials such as compacted exfoliated clays are interesting materials to substitute asbestos. Because of the thermo-mechanical loadings applied to material, it is fundamental to determine the mechanical properties of such medium. An approach is proposed in order to evaluate the poro-elastic properties of such porous material. The definition of representative elementary volume (REV) is based on scanning electron microscopy (SEM) analysis. Moreover, an approach based on Mori-Tanaka technique, with an iterative process, is proposed because of the specific features of studied porous material: Ellipsoidal porosities with specific orientation distribution, transversely isotropic matrix and porosity volume ratio about 30%. This model is illustrated by an application with the simulation of the behavior of compacted exfoliated clays. In this paper, the elastic properties are determined, but other poroelastic properties could be calculated by the same way.

Title of the Paper: **On the Definition of Seismic Recovery Interventions in R. C. Buildings by Non-Linear Static and Incremental Dynamic Analyses**

Authors: **Domenico Colapietro, Adriana Netti, Alessandra Fiore, Fabio Fatiguso, Giuseppe Carlo Marano**

Pages: **216-222**

Abstract: Incremental Dynamic Analysis (IDA) is a parametric analysis method that allows evaluating the structural performance under seismic loads more accurately than traditional static and dynamic analyses. With respect to a single non-linear analysis, the incremental dynamic analysis has the advantage to evaluate the structural performance under different levels of intensity, scaling proper ground motion records, until the structure collapses or until a fixed level of deformation is reached. In this study the potentialities of incremental dynamic analysis have been investigated in identifying the damaged elements in existing irregular r.c. buildings and a comparison with the results of static Pushover Analyses has been performed. In particular a strongly irregular building has been considered, representative of a particular manufacture and of an historical period of economic growth and speculation; it has not structural problems but suffers from abandonment and weathering effects. An interpretation of IDA procedure has been proposed, with the set of a mean IDA capacity curve, then bi-linearized in order to close the pushover procedure according to the extended N2 method. The aim is to underline in a specific case study how the choice of a methodology can affect the definition of recovery interventions, especially in the case of historical buildings, where the criterion of minimum intervention should be followed in order to preserve the original features.

Title of the Paper: **Dependence of Deformation of a Plate on the Subsoil in Relation to the Parameters of the 3D Model**

Authors: **R. Cajka, J. Labudkova**

Pages: **208-215**

Abstract: The purpose of this paper is to compare the measured subsidence of the foundation in experiments based on FEM calculations. This paper describes how calculated deformations depend on parameters of soil environment modelled by 3D finite elements. When using 3D elements for creation of a 3D model, it is, in particular, essential to choose correctly the size of the model area which represents the subsoil, the boundary conditions and the size of the finite element network. The parametric study evaluates impacts of those parameters on final deformation.

Title of the Paper: **Experimental Determination of the Mechanical Behavior of Compacted Exfoliated Vermiculite**

Authors: **Soufiane Belhouideg, Manuel Lagache**

Pages: **201-207**

Abstract: A series of compacted exfoliated vermiculite (CEV) samples were prepared and their mechanical behavior was experimentally studied. The vermiculite was first exfoliated and after compacted in order to obtain a material with good thermal and mechanical properties. The as-prepared samples have been tested under compressive loading. Some parameters effect was studied, as the porosity and the type of the CEV. The samples of this porous media display two steps for the stress–strain behavior under uniaxial compressive loading, i.e., initial nonlinear deformation, strainhardening ‘pseudo-platform’ stage.

Title of the Paper: **The New Concept of Steel Structure Bracing**

Authors: **R. Fojtík, T. Novotný**

Pages: **195-200**

Abstract: The design of high rise vertical structures that must withstand the actions of horizontal forces consisting primarily of wind actions, earthquake actions etc. puts greater demands on the structure reinforcement resisting to these forces. The structures concerned include masts, towers and high-rise buildings. Many different systems are used as vertical bracing. One of them is a new stiffening system called "circular reinforcing system" presented in this paper. Because it is the new structural system it is now subject to experimental tests to proof its sufficient stiffness and other properties for practical applications.

Title of the Paper: **Unstable Constitutive Law in Continuum Mechanics**

Authors: **D. A. Indeitsev, D. Yu. Skubov, L. V. Shtukin, D. S. Vavilov**

Pages: **190-194**

Abstract: The present paper deals the possibility of obtaining stress-strain relation with a decreasing segment through considering two-component medium. The basic idea lies in the assumption that a crystalline structure consists of two lattices connected by nonlinear interaction force. This force depends on the relative displacement of the lattices. When the displacement reaches its critical value, the system passes to the unstable position leading to a complicated dynamics. In this article the problem of static loading of two-component medium is considered. The problem is limited to one space dimension. The analytic solution obtained by applying the Galerkin procedure is compared with results of numerical calculations.

Title of the Paper: **Modern Sliding Joints in Foundations of Concrete and Masonry Structures**

Authors: **M. Janulikova, P. Mynarcik**

Pages: **184-189**

Abstract: Using of sliding joint is one of the possible options to solution of problem associated with horizontal deformation of the subsoil which causes shear stress in the footing bottom. This horizontal deformation can arise from the effect of undermining but the same effect of foundation also has pre-stressing of foundation or creep or shrinkage of concrete. We can reinforce foundation or we can use the knowledge about sliding joints to solution these effects. Sliding joint is applied between foundation and concrete base layer and it is created from asphalt belt or another material which can help to reduce shear stress on the contact surfaces between foundation and subsoil. Today a lot of new materials exist which can be used for reducing shear stress in foundations. Different types of asphalt belts or other modern materials are tested at the Faculty of Civil Engineering VSB TU Ostrava at different loads and at different temperatures. The effect of ambient temperature is monitored to better description of temperature dependency of all materials. Long-term goal of this research is to simplify process of design buildings with sliding joint and to help designer with right choice of the most advantageous material. The results and conclusion from the test are presented in this paper.

Title of the Paper: **An Experimental and Numerical Analysis of Natural Convection in an Air Filled Square Cavity with an Insulated Baffle**

Authors: **G. Nardini, M. Paroncini, R. Vitali**

Pages: **176-183**

Abstract: An experimental and numerical analysis is carried out in an air filled square cavity. The cavity has the horizontal adiabatic walls and the vertical walls with discrete sources. An insulated baffle is attached to its horizontal wall between the hot sources. The effect of baffle length is experimentally and numerically investigated for Rayleigh numbers in the range of 104 and 105. The dimensionless baffle lengths, Lb, are 0.2, 0.4 and 0.6. It is observed the influence of the baffle on the flow pattern and heat transfer. Interferograms, streamlines, isotherms, velocity maps are shown and heat transfer is analysed. The results clearly demonstrate that the baffle has a significant effect on the heat transfer and flow characteristics of the fluid. The flow field pattern is baffle length and Rayleigh number dependent. It is, in fact, observed that the Nusselt number increases as Rayleigh number increases and always decreases increasing the baffle length. The average Nusselt numbers from Lb = 0.2 to Lb = 0.6 decreases on average by 13.9% on the lower source and 15.6% on the higher source.

Title of the Paper: **Numerical Analysing the Slabs by Means of the Finite Difference Method and the Finite Element Method**

Authors: **O. Sucharda, J. Kubosek**

Pages: **167-175**

Abstract: The article is dealing with computation and optimization of computation of inner forces and deformations of slabs. Finite element method was chosen. Algorithm is written under Matlab. Variant solution of the system of equations is used for optimization. Algorithms were made for chosen numerical methods and functions of Matlab. Comparison is made afterwards. Created algorithms are illustrated using chosen square slab as example.

Title of the Paper: **Dynamics of a Turbojet Engine Considered as a Quasi-Static System**

Authors: **Constantin Rotaru, Mihai Andres-Mihăilă, Pericle Gabriel Matei, RalucaIoana Edu**

Pages: **158-166**

Abstract: Turbojet engine dynamics arise from complex interacting phenomena: gas flow behavior in the compressor and turbine, shaft inertias and losses, fuel flow transport delay, combustion and thermal behavior of the engine and its surroundings. This paper presents a linearized mathematical model of a turbojet engine, based on the Taylor’s series expansion of the torque function, which allows for the engine’s dynamic characteristics study. The numerical solver used in the simulation packages relays on the rotor speed as one of the independent variables. Several approaches of the nonlinear characteristics of the engine model were considered to choose the methodology that better predicts the temperature field in the combustion chamber.

Title of the Paper: **Micromechanical Properties of Surface Layer of HDPE Modified by Beta Irradiation**

Authors: **D. Manas, M. Manas, M. Stanek, M. Ovsik, M. Bednarik, A. Mizera, J. Navratil**

Pages: **150-157**

Abstract: The experimental study deals with the effect of modification of the surface layer by irradiation cross-linking on the microchanical properties of the high-density polyethylene (HDPE) tested using the instrumented nanohardness test. The surface layer of HDPE specimen made by injection technology was modified by irradiation cross-linking using beta irradiation, which significantly influences micromechanical properties of the surface layer. Compared to the heat and chemical-heat treatment of metal materials (e.g. hardening, nitridation, case hardening), cross-linking in polymers affects the surfaces in micro layers. These micromechanical changes of the surface layer are observed in the instrumented nanohardness test.. The subject of this research is the influence of irradiation dosage on the changes of micromechanical properties of surface layer of HDPE.

Title of the Paper: **Assessment of Cooling Rate in Longitudinal Welded Pipelines performed by Submerged Double-Arc Welding**

Authors: **E. Scutelnicu, C. C. Rusu**

Pages: **144-149**

Abstract: Combining the process parameters - from high pressure with low temperature to high temperature with no pressure - a wide range of welding processes by pressure and fusion have been developed in the last decades. Included in the group of fusion welding processes, submerged multi-arc welding is more and more applied to the pipelines manufacturing due to the increased productivity and efficiency of the process. In this case, an overlapping effect of temperature fields is manifested through a major influence on the cooling rate which is responsible for the metallurgical changes and, finally, for deterioration of the joints' mechanical characteristics. It is obvious that good performances of the welded joints ensure the quality and safety of metallic structures and a less impact on the environment is estimated to be achieved. That is why cooling rate should be theoretically and experimentally investigated. Moreover, distance between welding sources could be variable and leads to different values of cooling. The research focuses on the numerical modeling of heat transfer in the welded joints performed by submerged double-arc welding process distances between electric arcs is variable. Temperature field, thermal cycles and cooling rate versus different distances between thermal sources are comparatively analysed and discussed.

Title of the Paper: **Experimental Tests of Pre-Stressed Masonry and Numerical Modeling of Resultant Deformations**

Authors: **M. Stara, V. Buchta**

Pages: **138-143**

Abstract: Due to underground mining and construction of tunnels and collectors in urban areas terrain subsidence occurs with characteristic effects on building structures. In affected areas it is often necessary to detain affected structure with additional pre-stressing of walls and foundations. Pre-stressing masonry is one of the most common and concurrently the most effective method redevelopment. At Faculty of Civil Engineering was constructed laboratory equipment for closer examination of the behavior of tensioned masonry. Specifically for measuring the deformation of brick corner mainly around the anchor plates that used for transmission of tensile forces into masonry. In this masonry corner two pre-stressing bars are placed. These bars are in different height and are anchored to the anchor plates, which transfer pre-stressing forces to the masonry. The masonry was pre-stressed in the both directions. The specimen for laboratory testing is performed in the proportion to the reality of 1:1. Mathematical modeling of the brick corner is based on the finite element method using ANSYS software and then the results are compared with results of the laboratory tests. On the basis of these results it should be possible to improve the models and come closer to achieving an accurate and at the same time, simple procedure for the design of pre-stressed masonry.

Title of the Paper: **Theoretical and Experimental Studies on the Resistance Structure of a Metallurgical Overhead Travelling Crane in Operation**

Authors: **C. Pinca-Bretotean, A. Josan, A. Dascal, G. Chete**

Pages: **128-137**

Abstract: The paper’s purpose is to study the stresses and strains state in the resistance structure of a travelling crane which operates in the steelwork of an integrated iron and steel plant, from ten years. This has been realised through theoretical analysis, based on the resistance structure modelling, using the finite element method, and by experimental measurements, based on electric resistance tensometry. The results of comparative interpretation of the theoretical and experimental studies provide a complete picture of the stresses and deformations found in the resistance structure of an overhead travelling crane, enabling us to understand the behaviour in operation of the resistance structure and, if oversized, to redesign it.

Title of the Paper: **The Thermal Performance of Lightweight Timber Frame Structures during the Summer Period**

Authors: **Iveta Skotnicová, Lenka Lausová, Petra Tymová, Zdeněk Galda**

Pages: **123-127**

Abstract: The paper describes results of experimental and numerical analysis of the thermal performance of lightweight timber frame structures (wall and roof) during the summer period. The aim of this research is to verify the suitability of numerical simulation methods for the prediction of the thermal performance of building structures. The measurements were taken on an experimental timber frame passive house of the VSB-TU Ostrava. The numerical modelling of the external structures is solved using the finite element method in the ANSYS software.

Title of the Paper: **Numerical Modeling of Turbulence Characteristics of Burning Process of the Solid Fuel in BKZ-420-140-7c Combustion Chamber**

Authors: **A. S. Askarova, A. Bekmukhamet, S. A. Bolegenova, M. T. Beketayeva, Yu. V. Maximov, Sh. S. Ospanova, Z. K. Gabitova**

Pages: **112-122**

Abstract: In this paper the results obtained by the numerical method of modeling of Ekibastuz coal burning in BKZ-420 combustion chamber of Kazakhstan Power Plant. There are devoted to the numerical simulation of combustion processes in the furnace boiler BKZ-420. Boiler’s steam generating capacity equal 420 T/h. Boiler (Fig.2) has six vertical pulverized coal burners arranged in two levels with three burners on the front wall of the boiler. High ash, low-grade coal from Ekibastuz burned in the furnace. Its ash content is 40 %, volatile – 24 %, humidity – 5 %, highest calorific value is 16 750 kJ/kg. Milling dispersity of coal was equal to R90 = 15 %. It this research was shown that the most intense burning is observed in the central part of the chamber where the flow temperature reaches about 980 °C and it is seen the temperature reaches a peak in the cross sections of the location of the burners. There combustion reaction occurs more intensively.

Title of the Paper: **Probabilistic Reliability Analysis of High-Performance Reinforced Concrete Beam using Matlab Software**

Authors: **David Pustka**

Pages: **101-111**

Abstract: Significant improvement of computer technology in recent decades brought possibility to exploit fully probabilistic methods for reliability evaluation of structural systems and their members. One of these methods is SBRA (Simulation-Based Reliability Method) using direct Monte Carlo simulation technique. Application of this method allows utilize more precise calculation models, consistent description of random variables using truncated histograms and as well direct quantification of reliability. The following paragraphs of this paper describes application of this method in design and reliability assessment of high-performance reinforced concrete beam.

Title of the Paper: **Energy Balance Equation, Energetic Theorems and Variation Equation for the General Theory of Micropolar Elastic Isotropic Thin Shells**

Authors: **Samvel H. Sargsyan**

Pages: **93-100**

Abstract: In the present paper main equations of three-dimensional theory of micropolar elasticity, energetic relations and general variation equation are introduced. Assumptions are accepted which have asymptotic justification and on the basis of these assumptions general applied theory of micropolar thin shells is constructed. Equation of energetic balance and general variation equation are constructed for micropolar elastic thin shells, theorems of uniqueness, existence, Betty’s and other energetic theorems are proved.

Title of the Paper: **SW and HW Optimization of Injection Molding Process**

Authors: **M. Stanek, D. Manas, M. Manas, J. Navratil, A. Skrobak**

Pages: **85-92**

Abstract: Optimization of injection molding process serves for finding ideal conditions during production of plastic parts and observing their final dimensions, shapes and properties. It is possible to determine the appropriate injection pressure, velocity, value and time of packing pressure, etc. by optimization. The paper is dealing with description of Moldflow Plastics Xpert (MPX) system and its usage in optimization of injection molding process on real part during its production. MPX is integrated with injection molding machines to optimize their operation and to monitor and control the manufacturing process. MPX addresses common manufacturing issues such as machine set-up, process optimization and production part quality monitoring and control. Results generated by MPA and MPI products can be input directly into MPX product to reduce machine set-up time and enhance the efficiency of the injection molding machine.

Title of the Paper: **Boltzmann Entropy of Thermodynamics versus Shannon Entropy of Information Theory**

Authors: **Siavash H. Sohrab**

Pages: **73-84**

Abstract: Some implications of a scale invariant model of statistical mechanics to Boltzmann entropy in thermodynamics versus Shannon entropy in information theory are investigated. The objective versus subjective nature of entropy as well as the fundamental significance of the choice of Shannon measure K as Boltzmann constant k is described. In addition, the impact of the results on Nernst-Planck statement of the third law of thermodynamics is discussed.

Title of the Paper: **Analysis of the Thermoelastic Rod Collision with a Heated Rigid Wall with Due Account for Temperature and Strain Weak Coupling**

Authors: **Yury Rossikhin, Marina Shitikova**

Pages: **62-72**

Abstract: The problem of the collision of a ther- moelastic rod with a heated rigid wall is considered for the case of weak coupling between the strain and temperature fields when the thermoelastic behavior of the rod is described by the Green-Naghdy theory without energy dissipation. The lateral surfaces and free end of the rod are thermally insulated, and free thermal exchange is established within the contact domain with the wall. D’Alembert solution together with the perturbation technique are utilized as the method of solution. The proposed procedure allows one to construct an analytical solution enabling to study the influence of thermoelastic parameters on the contact duration, as well as to obtain the stress, velocity, temperature, and heat flow dependences of time and coordinate.

Title of the Paper: **The Design and Analysis for Shaped Charge Liner Using Taguchi Method**

Authors: **Jen-Hsin Ou, Jen-Bing Ou, Yan-Jing Jhu**

Pages: **53-61**

Abstract: In order to study the shaped jet penetration effect on steel plate after the detonation of shaped charge on armor-piercing projectile, the finite element analysis software is used to do the numerical simulation for liner structure analysis from initiation jet forming to penetrating target plate[1]. In this paper, the liner structural parameters, including cone angle, wall thickness, standoff, detonation point, and their effects on Sunder are also analyzed, and finally the Taguchi method analysis is used to study the influence of various factors on jet forming process and find the optimal solution for effective penetrating depth. The results show that the initiation point contributes nearly 22.61% effect on perforating depth and is the most significant factor. The penetrating effect decreases as the initiation point moves from edge to the center. The wall thickness accounts for 11.09% effect on perforating depth. Based on the results above, we can do a better shaped charge liner design in the subsequent application.

Title of the Paper: **A Fast and Accurate Hybrid Model for Simulating Continuous Pipe Flow Microwave Heating of Liquids**

Authors: **G. Cuccurullo, L. Giordano, G. Viccione**

Pages: **45-52**

Abstract: Use of microwave technology in several industrial heating processes is a relatively new approach. Considering that scaling-up is hard to recover, theoretical simulations can be of help in order to study and optimize the process at hand while reducing the mass of experimental work. This paper aims to speed up prediction of bulk temperatures for an incompressible liquid as it ﬂows continuously in a circular duct that is subjected to microwave heating. Usually, temperature increases are desired which require temperature dependent dielectric permittivity; thus, studying the problem at hand involves the simultaneous solution of the electromagnetic, fluid flow and heat transfer problems. In contrast, a hybrid model is introduced which links numerical results to analytical calculations, providing a tool for accurate prediction of the bulk temperature distribution while noticeably reducing the required computation time. The hybrid solution was obtained by first numerically solving Maxwell equations in correspondence of a fixed average dielectric permittivity; discrete values of the cross-section averaged heat generation arising from such solution were first corrected by a suitable weighting function and then interpolated by a function resulting from the discrete Fourier series. Then the momentum and the energy equations fed by the above calculated heat generation distribution turned out in a linear problem; the related analytical solution was sought as the sum of two partial solutions, each one affected by a single non-homogeneity. The former solution turned out to be the classical Graetz problem, while the latter, driven by the heat generation, was solved in closed form by the variation of parameters method. Fully developed velocity, thermally developing conditions and no phase transition during the heating process were assumed for both the hybrid and the numerical solution. Simulations are intended to validate the hybrid solution when compared to the corresponding numerical one. Results, presented and discussed for different inlet velocities, ensured the accuracy of the proposed model meanwhile showing that computational times are reduced at least by one- tenth.

Title of the Paper: **Nanohardness of Electron Beam Irradiated Polyamide 11**

Authors: **P. Kratky, D. Manas, M. Manas, M. Stanek, M. Ovsik, K. Kyas, M. Reznicek**

Pages: **37-44**

Abstract: The submitted paper presents the assessment of mechanical properties of the surface layer of modified polyamide 11. Hard surface layer was made using the technology of radiation cross- linking, which enables modification of polymer materials and hence the change of their end-use properties. The process of mechanical stress is applied by nanohardness test. The surface layer of polymer material such as polyamide 11 is modified by β – radiation. After the polyamide 11 is subjected to radiation, changes of the surface layer at applied load are observed. Material properties of the created surface layer are measured by nanohardness test using the DSI method (Depth Sensing Indentation).

Title of the Paper: **Mathematical Modeling in the Search for Technological Solutions to Modernize Cold Rolling Mill of Large Diameter Pipes**

Authors: **K. A. Goncharov, Yu. B. Chechulin**

Pages: **30-36**

Abstract: The problem of reconstruction and modernization of manufacturing equipment for the production of large diameter pipes was considered in this paper. To assess the strength and the technical resource of the equipment was used mathematical modeling based on the experimental results and consistent solution of nonlinear boundary value problem of the elasticity theory. The results of solution for the tube cold mill, which were used for design of the new equipment, are given.

Title of the Paper: **An Experimental Research on Nonlinear Roll Hydrodynamic Characteristics of a Composite Trimaran Using ε-SVR**

Authors: **Haitong Xu, Songlin Yang, Qingwei Ma, Baoming Wang, Tianyu Ma, Yuyang Zong**

Pages: **18-29**

Abstract: The rolling motion behaviour of a composite trimaran was studied in the Jiangsu University of Science and Technology Ship hydrodynamic Centre. Series of the free roll decay tests were carried out in the seakeeping tank. The mathematical model of rolling motion mode is established considering both linear and nonlinear ship motion. The overall seakeeping behaviour of the vessel is discussed and particular attention is paid to the roll motion. The results of time-domain nonlinear hydrodynamic identification using ε-Support Vector Regression are validated against the model tests. The error of ε-Support Vector Regression is discussed and the relative error is less than 3%. The results suggest that the ε-Support Vector Regression is a reliable method for identification of the roll motion owning to its inherent benefits. Parametric roll is discussed and test results are presented. The nonlinear effect on the roll motions of the draft, spacing and attitude of side hulls is evaluated. The paper ends with a discussion on configurations of side hull for composite trimaran vessels. This paper can provide technical support in the optimization design of composite trimaran and the research of composite multi-hull ship.

Title of the Paper: **Strength of Bonded Joints at Elevated Temperatures after Radiation Cross-Linking**

Authors: **M. Bednarik, D. Manas, M. Manas, M. Stanek, A. Mizera, M. Ovsik, P. Kratky**

Pages: **10-17**

Abstract: In this study there was found that ionizing beta radiation increased the strength of bonded joints and improved the adhesion properties of low-density polypropylene (LDPE) and high- density polyethylene (HDPE). Bonded joints at elevated temperature (60 °C) were tested. Generally, for the formation of quality bonded joint it is important to wet the adhesive bonding surface well. Wettability is characterized by the contact angle of wetting. The liquid has to have a lower surface tension than the solid in order to be able to wet the solid substance. The measurement results indicated that ionizing beta radiation was a very effective tool for improvement of adhesive properties and increased the strength of bonded joints of studied polymers at elevated temperature (60 °C). Bonded surfaces with ionizing beta radiation doses of 0, 66, 132, 165 and 198 kGy were irradiated. The best results were achieved by irradiation at doses of 165 kGy by which the highest surface energy and the highest strength of bonded joints of HDPE and LDPE were achieved.

Title of the Paper: **Cross Section Optimization of Gravity Type Block work Quay Walls Using Sequential Quadratic Programming Method**

Authors: **M. Shafieefar, A.R. Mirjalili**

Pages: **1-9**

Abstract: Quay walls are waterfront structures for connecting land and sea, berthing and mooring of ships and facilitating loading and unloading cargo. Gravity structures are usually an excellent alternative for waterfront structures where the seabed soil condition is appropriate. Optimum design of block work gravity type quay walls with pre-cast concrete blocks is the object of this paper. The advantages of these quay walls are simple construction technology, preferred costs and good durability. In this research, a procedure for optimization of cross section of a block work gravity type quay wall is introduced and a numerical program for this procedure is developed. The main modes of failure of this gravity structure are: sliding, overturning, deep slip and foundation failure, therefore in the stability calculations settlement, circular slip, bearing capacity of the foundation, Sliding and Overturning at all horizontal surfaces between blocks should be examined. To study the behavior of a block work quay wall and to check the stability against probable different failure modes, a computer program has been developed. This program can easily consider the effects of different parameters such as section geometry of quay wall, material property and loading conditions in design. After reviewing design and construction considerations for such quay walls, available methods for optimum design of such structures are discussed and objective function, constraints and design variables are considered. The main constraints of the optimization problem in the present study are safety factors in various modes of failures. As the relation of safety factor with design variables is unknown, therefore, first a proper method should be used for approximating the objective function and constraints according to design variables. Then, an efficient method should be selected for formulating mathematical optimization of the objective function under existing constraints. For this purpose, the optimization of the cross section is accomplished using Sequential Quadratic Programming (SQP) method in the present work. Results indicate that the cross section of a block work quay wall has an important role in stability of the structure and one can reduce costs of such structures by optimizing the cross section. Finally, some recommendations for optimum design of this type of quay wall are presented.