Search results for: nonlocal elasticity.

Authors: Francesco Marotti de Sciarra, Raffaele Barretta

Abstract:

Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement is presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, Nanobeams, nonlocal elasticity.

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Authors: M.Z. Islam, C.W. Lim

Abstract:

Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which governs the nonlocal material behavior. The new NL-FEM is adopted in such a way that the postulated nonlocal elastic behavior of material is captured by a finite element endowed with a set of (cross-stiffness) element itself by the other elements in mesh. An example with their analytical solutions and the relevant numerical findings for various load and boundary conditions are presented and discussed in details. It is observed from the numerical solutions that the torsional deformation angle decreases with increasing nonlocal nanoscale parameter. It is also noted that the analytical solution fails to capture the nonlocal effect in some cases where numerical solutions handle those situation effectively which prove the reliability and effectiveness of numerical techniques.

Keywords: NL-FEM, nonlocal elasticity, nanoscale, torsion.

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

Abstract:

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: Biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory.

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Authors: J. Ranjbarn, A. Alibeigloo

Abstract:

In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: Nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock.

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

Abstract:

In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in x and y directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors.

Keywords: Feedback control system, magnetostrictive nano-plate, modified couple stress theory, nonlocal elasticity theory, vibration analysis.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

Abstract:

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, nonlocal strain gradient theory, velocity gradient.

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Authors: M.Jalali Azizpour, S.Norouzi, H.mohammadi Majd, M.M.Rabieh, D.Sajedipour, A. Jaderi

Abstract:

The mechanical and tribological properties in WC-Co coatings are strongly affected by hardness and elasticity specifications. The results revealed the effect of spraying distance on microhardness and elasticity modulus of coatings. The metallurgical studies have been made on coated samples using optical microscopy, scanning electron microscopy (SEM).

Keywords: Elasticity modulus, HVOF, Micro-indentation, Thermal spray, WC-Co

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Authors: Klara Krizova, Rudolf Hela

Abstract:

The topic of the article focuses on the evaluation of selected technological factors and their influence on resulting elasticity modulus of concrete. A series of various factors enter into the manufacturing process which, more or less, influences the elasticity modulus. This paper presents the results of concrete in which the influence of water coefficient and the size of maximum fraction of the aggregate on the static elasticity modulus were monitored. Part of selected results of the long-term programme was discussed in which a wide scope of various variants of proposals for the composition of concretes was evaluated.

Keywords: Mix design, water-cement ratio, aggregate, modulus of elasticity.

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Authors: Klara Krizova, Rudolf Hela

Abstract:

The paper reflects current state of popularization of static elasticity modulus of concrete. This parameter is undoubtedly very important for designing of concrete structures, and very often neglected and rarely determined before designing concrete technology itself. The paper describes assessment and comparison of four mix designs with almost constant dosage of individual components. The only difference is area of origin of small size fraction of aggregate 0/4. Development of compressive strength and static elasticity modulus at the age of 7, 28 and 180 days were observed. As the experiment showed, designing of individual components and their quality are the basic factor influencing elasticity modulus of current concrete.

Keywords: Concrete, Aggregate, Strength, Elasticity Modulus, Quality

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Authors: Jiri Brozovsky

Abstract:

Modulus of elasticity is one of the important parameters of construction materials, which considerably influence their deformation properties and which can also be determined by means of non-destructive test methods like ultrasonic pulse method. However, measurement results of ultrasonic pulse methods are influenced by various factors, one of which is the natural frequency of the transducers. The paper states knowledge about influence of natural frequency of the transducers (54; 82 and 150kHz) on ultrasonic pulse velocity and dynamic modulus of elasticity (Young's Dynamic modulus of elasticity). Differences between ultrasonic pulse velocity and dynamic modulus of elasticity were found with the same smallest dimension of test specimen in the direction of sounding and density their value decreases as the natural frequency of transducers grew.

Keywords: Calcium silicate brick, ultrasonic pulse method, ultrasonic pulse velocity, dynamic modulus of elasticity.

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Authors: W. Louhichi, M.Berrima, N. Ben Rajeb Robbana

Abstract:

Elasticity is the essential property of cloud computing. As the name suggests, it constitutes the ability of a cloud system to adjust resource provisioning in relation to fluctuating workloads. There are two types of elasticity operations, vertical and horizontal. In this work, we are interested in horizontal scaling, which is ensured by two mechanisms; scaling in and scaling out. Following the sizing of the system, we can adopt scaling in the event of over-supply and scaling out in the event of under-supply. In this paper, we propose a formal model, based on temporized and colored Petri nets (TdCPNs), for the modeling of the duplication and the removal of a virtual machine from a server. This model is based on formal Petri Nets (PNs) modeling language. The proposed models are edited, verified, and simulated with two examples implemented in colored Petri nets (CPNs)tools, which is a modeling tool for colored and timed PNs.

Keywords: Cloud computing, elasticity, elasticity controller, petri nets, scaling in, scaling out.

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Authors: Lukas Mocek, Alexandros Markopoulos

Abstract:

The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.

Keywords: Linear elasticity, fictitious domain method, Total-FETI, domain decomposition, saddle-point system.

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Authors: M. Chumburidze, D. Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: The couple-stress thermo-elasticity, boundary value problems.

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Authors: E. Jomehzadeh, A.R. Saidi

Abstract:

In the present article, nonlinear vibration analysis of single layer graphene sheets is presented and the effect of small length scale is investigated. Using the Hamilton's principle, the three coupled nonlinear equations of motion are obtained based on the von Karman geometrical model and Eringen theory of nonlocal continuum. The solutions of Free nonlinear vibration, based on a one term mode shape, are found for both simply supported and clamped graphene sheets. A complete analysis of graphene sheets with movable as well as immovable in-plane conditions is also carried out. The results obtained herein are compared with those available in the literature for classical isotropic rectangular plates and excellent agreement is seen. Also, the nonlinear effects are presented as functions of geometric properties and small scale parameter.

Keywords: Small scale, Nonlinear vibration, Graphene sheet, Nonlocal continuum

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Authors: S.F. Tsen, M. Zamin Jumaat

Abstract:

The characteristic bending strength (MOR) and mean modulus of elasticity (MOE) of tropical hardwood red seraya (Shorea spp.) plywood were determined using European Standard EN310 and EN789. The thickness of the test specimen was 4.0mm, 7.0mm, 9.0mm, 12.0mm and 15.0mm. The experiment found that the MOR of red seraya plywood in EN310 is about 12% to 20% and 7% to 24% higher than EN789 whereas MOE were about 28% to 41% and 30% to 36% lower than those obtained from EN 789 for test specimens parallel and perpendicular to the grain direction. The linear regression shows that MOR and MOE for EN789 is about 0.8 times less and 1.5 times more than EN310. The experiment also found that the MOR and MOE of EN310 and EN789 also depend on the wood species that used in the experiment.

Keywords: Bending strength, Modulus of elasticity, EN310, EN789

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Authors: Mohammed Abed, Rita Nemes, Salem Nehme

Abstract:

The present study experimentally investigated the impact of incorporating unprocessed waste fly ash (UWFA) on the residual mechanical properties of self-compacting concrete (SCC) after exposure to elevated temperature. Three mixtures of SCC have been produced by replacing the cement mass by 0%, 15% and 30% of UWFA. Generally, the fire resistance of SCC has been enhanced by replacing the cement up to 15% of UWFA, especially in case of residual modulus of elasticity which considers more sensitive than other mechanical properties at elevated temperature. However, a strong linear relationship has been observed between the residual flexural strength and modulus of elasticity, where both of them affected significantly by the cracks appearance and propagation as a result of elevated temperature. Sustainable products could be produced by incorporating unprocessed waste powder materials in the production of concrete, where the waste materials, CO₂ emissions, and the energy needed for processing are reduced.

Keywords: Self-compacting high-performance concrete, unprocessed waste fly ash, fire resistance, residual modulus of elasticity.

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Authors: M.Jalali Azizpour, S.Norouzi, H.Mohammadi Majd

Abstract:

The mechanical and tribological properties in WC-Co coatings are strongly affected by hardness and elasticity specifications. The results revealed the effect of spraying distance on microhardness and elasticity modulus of coatings. The metallurgical studies have been made on coated samples using optical microscopy, scanning electron microscopy (SEM).

Keywords: HVOF, Micro-indentation, Thermal spray, WC-Co.

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Authors: P. K. Sarkar, Amit Kumar Jain

Abstract:

The demand for Urban transportation is characterised by a large scale temporal and spatial variations which causes heavy congestion inside metro trains in peak hours near Centre Business District (CBD) of the city. The conventional approach to address peak hour congestion, metro trains has been to increase the supply by way of introduction of more trains, increasing the length of the trains, optimising the time table to increase the capacity of the system. However, there is a limitation of supply side measures determined by the design capacity of the systems beyond which any addition in the capacity requires huge capital investments. The demand side interventions are essentially required to actually spread the demand across the time and space. In this study, an attempt has been made to identify the potential Transport Demand Management tools applicable to Urban Rail Transportation systems with a special focus on differential pricing. A conceptual price elasticity model has been developed to analyse the effect of various combinations of peak and nonpeak hoursfares on demands. The elasticity values for peak hour, nonpeak hour and cross elasticity have been assumed from the relevant literature available in the field. The conceptual price elasticity model so developed is based on assumptions which need to be validated with actual values of elasticities for different segments of passengers. Once validated, the model can be used to determine the peak and nonpeak hour fares with an objective to increase overall ridership, revenue, demand levelling and optimal utilisation of assets.

Keywords: Congestion, differential pricing, elasticity, transport demand management, urban transportation.

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Authors: K. Krizova, R. Hela

Abstract:

The paper is focused on monitoring of dependencies of different composition concretes on elastic modulus values. To obtain a summary of elastic modulus development in dependence of concrete composition design variability was the objective of the experiment. Essential part of this work was initiated as a reaction to building practice when questions of elastic moduli arose at the same time and which mostly did not obtain the required and expected values from concrete constructions.

Keywords: Concrete, Compressive strength, Modulus of elasticity, EuroCode 2.

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Authors: I. Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi, Oke Oktavianty, Didik Nurhadiyanto

Abstract:

Contact width and contact stress are important parameters related to the leakage behavior of corrugated metal gasket. In this study, contact width and contact stress of three-layer corrugated metal gasket are investigated due to the modulus of elasticity and thickness of surface layer for 2 type gasket (0-MPa and 400-MPa mode). A finite element method was employed to develop simulation solution to analysis the effect of each parameter. The result indicated that lowering the modulus of elasticity ratio of surface layer will result in better contact width but the average contact stresses are smaller. When the modulus of elasticity ratio is held constant with thickness ratio increase, its contact width has an increscent trend otherwise the average contact stress has decreased trend.

Keywords: Contact width, contact stress, layer, metal gasket, corrugated, simulation.

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Authors: Nidhal Jamia, Sami El-Borgi

Abstract:

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: Functionally graded piezoelectric material, mixed-mode crack, non-local theory, Schmidt method.

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Authors: Geng Xiangren, Liu Lei, Gui Ye-Wei, Tang Wei, Wang An-ling

Abstract:

The malfunction of thermal protection system (TPS) caused by aerodynamic heating is a latent trouble to aircraft structure safety. Accurately predicting the structure temperature field is quite important for the TPS design of hypersonic vehicle. Since Thornton’s work in 1988, the coupled method of aerodynamic heating and heat transfer has developed rapidly. However, little attention has been paid to the influence of structural deformation on aerodynamic heating and structural temperature field. In the flight, especially the long-endurance flight, the structural deformation, caused by the aerodynamic heating and temperature rise, has a direct impact on the aerodynamic heating and structural temperature field. Thus, the coupled interaction cannot be neglected. In this paper, based on the method of static aero-thermo-elasticity, considering the influence of aero-thermo-elasticity deformation, the aerodynamic heating and heat transfer coupled results of hypersonic vehicle wing model were calculated. The results show that, for the low-curvature region, such as fuselage or center-section wing, structure deformation has little effect on temperature field. However, for the stagnation region with high curvature, the coupled effect is not negligible. Thus, it is quite important for the structure temperature prediction to take into account the effect of elastic deformation. This work has laid a solid foundation for improving the prediction accuracy of the temperature distribution of aircraft structures and the evaluation capacity of structural performance.

Keywords: Aero-thermo-elasticity, elastic deformation, structural temperature, multi-field coupling.

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Authors: I. Miličević, M. Hadzima Nyarko, R. Bušić, J. Simonović Radosavljević, M. Prokopijević, K. Vojisavljević

Abstract:

This paper investigates the effects of different treatment methods of rubber aggregates for self-compacting concrete (SCC) on compressive strength and modulus of elasticity. SCC mixtures with 10% replacement of fine aggregate with crumb rubber by total aggregate volume and with different aggregate treatment methods were investigated. The rubber aggregate was treated in three different methods: dry process, water-soaking, and NaOH treatment plus water soaking. Properties of SCC in a fresh and hardened state were tested and evaluated. Scanning electron microscope (SEM) analysis of three different SCC patches were made and discussed. It was observed that applying the proposed NaOH plus water soaking method resulted in the improvement of fresh and hardened concrete properties. It resulted in a more uniform distribution of rubber particles in the cement matrix, a better bond between rubber particles and the cement matrix, and higher compressive strength of SCC rubberized concrete.

Keywords: Compressive strength, modulus of elasticity, NaOH treatment, rubber aggregate, self-compacting rubberized concrete, scanning electron microscope analysis.

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Authors: Bachir Chemani, Rachid Halfaoui, Madani Maalem

Abstract:

The manufacturing technology of band cotton is very delicate and depends to choice of certain parameters such as torsion of warp yarn. The fabric elasticity is achieved without the use of any elastic material, chemical expansion, artificial or synthetic and it’s capable of creating pressures useful for therapeutic treatments. Before use, the band is subjected to treatments of specific preparation for obtaining certain elasticity, however, during its treatment, there are some regression parameters. The dependence of manufacturing parameters on the quality of the chemical treatment was confirmed. The aim of this work is to improve the properties of the fabric through the development of manufacturing technology appropriately. Finally for the treatment of the strip pancake 100% cotton, a treatment method is recommended.

Keywords: Elastic, cotton, processing, torsion.

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: K. N. C. Njoku, Chinwendu Best Eleje, Christian Chukwuemeka Nwandu

Abstract:

One of the problems facing most insurance companies is how best the burden of paying claims to its policy holders can be managed whenever need arises. Hence there is need for the insurer to buy a reinsurance contract in order to reduce risk which will enable the insurer to share the financial burden with the reinsurer. In this paper, the insurer’s and reinsurer’s strategy is investigated under the modified constant elasticity of variance (M-CEV) process and proportional administrative charges. The insurer considered investment in one risky asset and one risk free asset where the risky asset is modeled based on the M-CEV process which is an extension of constant elasticity of variance (CEV) process. Next, a nonlinear partial differential equation in the form of Hamilton Jacobi Bellman equation is obtained by dynamic programming approach. Using power transformation technique and variable change, the explicit solutions of the optimal investment strategy and optimal reinsurance strategy are obtained. Finally, some numerical simulations of some sensitive parameters were obtained and discussed in details where we observed that the modification factor only affects the optimal investment strategy and not the reinsurance strategy for an insurer with exponential utility function.

Keywords: Reinsurance strategy, Hamilton Jacobi Bellman equation, power transformation, M-CEV process, exponential utility.

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Authors: K. Krizova, R. Hela, S. Keprdova

Abstract:

This paper introduces selected composition of conventional concretes and their resulting mechanical properties at different ages of concrete. With respect to utilization of mineral admixtures, fly ash and ground limestone agents were included in addition to pure Portland binder. The proposal of concrete composition remained constant in basic concrete components such as cement and representation of individual contents of aggregate fractions; weight dosing of admixtures and water dose were only modified. Water dose was chosen in order to achieve identical consistence by settlement for all proposals of concrete composition. Mechanical properties monitored include compression strength, static and dynamic modulus of concrete elasticity, at ages of 7, 28, 90, and 180 days.

Keywords: Cement, mineral admixtures, microstructure of concrete, mechanical properties.

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Authors: V. V. Zozulya

Abstract:

New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.

Keywords: Shell, FEM, FGM, legendre polynomial.

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