Search results for: numerical quadrature

Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

Procedia PDF Downloads 424

Authors: Anwar Beg, Sireetorn Kuharat, Rashid Mehmood, Rabil Tabassum, Meisam Babaie

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Nano-polymeric solar paints and sol-gels have emerged as a major new development in solar cell/collector coatings offering significant improvements in durability, anti-corrosion and thermal efficiency. They also exhibit substantial viscosity variation with temperature which can be exploited in solar collector designs. Modern manufacturing processes for such nano-rheological materials frequently employ stagnation flow dynamics under high temperature which invokes radiative heat transfer. Motivated by elaborating in further detail the nanoscale heat, mass and momentum characteristics of such sol gels, the present article presents a mathematical and computational study of the steady, two-dimensional, non-aligned thermo-fluid boundary layer transport of copper metal-doped water-based nano-polymeric sol gels under radiative heat flux. To simulate real nano-polymer boundary interface dynamics, thermal slip is analysed at the wall. A temperature-dependent viscosity is also considered. The Tiwari-Das nanofluid model is deployed which features a volume fraction for the nanoparticle concentration. This approach also features a Maxwell-Garnet model for the nanofluid thermal conductivity. The conservation equations for mass, normal and tangential momentum and energy (heat) are normalized via appropriate transformations to generate a multi-degree, ordinary differential, non-linear, coupled boundary value problem. Numerical solutions are obtained via the stable, efficient Runge-Kutta-Fehlberg scheme with shooting quadrature in MATLAB symbolic software. Validation of solutions is achieved with a Variational Iterative Method (VIM) utilizing Langrangian multipliers. The impact of key emerging dimensionless parameters i.e. obliqueness parameter, radiation-conduction Rosseland number (Rd), thermal slip parameter (α), viscosity parameter (m), nanoparticles volume fraction (ϕ) on non-dimensional normal and tangential velocity components, temperature, wall shear stress, local heat flux and streamline distributions is visualized graphically. Shear stress and temperature are boosted with increasing radiative effect whereas local heat flux is reduced. Increasing wall thermal slip parameter depletes temperatures. With greater volume fraction of copper nanoparticles temperature and thermal boundary layer thickness is elevated. Streamlines are found to be skewed markedly towards the left with positive obliqueness parameter.

Keywords: non-orthogonal stagnation-point heat transfer, solar nano-polymer coating, MATLAB numerical quadrature, Variational Iterative Method (VIM)

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Authors: Pawel Flaszynski, Piotr Doerffer, Jan Holnicki-Szulc, Grzegorz Mikulowski

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Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data.

Keywords: pneumatic valve, transonic flow, numerical simulations, piezoelectric valve

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

Procedia PDF Downloads 342

Authors: Amal Machtalay

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In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

Procedia PDF Downloads 85

Authors: Peng Li, Er-xiang Song

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Numerical analysis of longitudinal tunnel seismic response due to spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical methods for analysis of tunnel longitudinal response under asynchronous seismic wave is extensively studied, including the improvement of the 1D time-domain finite element method, three dimensional numerical simulation technique for the site asynchronous earthquake response as well as the 3-D soil-tunnel structure interaction analysis. The study outcome will be beneficial to aid further research on the nonlinear meticulous numerical analysis and seismic response mechanism of tunnel structures under asynchronous earthquake motion.

Keywords: asynchronous input, longitudinal seismic response, tunnel structure, numerical simulation, traveling wave effect

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Authors: Mohamed Driouich, Kamal Gueraoui, Mohamed Sammouda

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The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications.

Keywords: numerical code, molten polymers, deformable pipes, finite differences

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Authors: Babak Safaei, Ahmad Ghanbari, Arash Rahmani

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In the present study, the free vibration characteristics of double-walled carbon nanotubes (DWCNTs) are investigated. The small-scale effects are taken into account using the Eringen’s nonlocal elasticity theory. The nonlocal elasticity equations are implemented into the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT) to analyze the free vibrations of DWCNTs in which each wall of the nanotubes is considered as individual beam with van der Waals interaction forces. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations of each nonlocal beam model along with four commonly used boundary conditions. Then molecular dynamics (MD) simulation is performed for a series of armchair and zigzag DWCNTs with different aspect ratios and boundary conditions, the results of which are matched with those of nonlocal beam models to extract the appropriate values of the nonlocal parameter corresponding to each type of chirality, nonlocal beam model and boundary condition. It is found that the present nonlocal beam models with their proposed correct values of nonlocal parameter have good capability to predict the vibrational behavior of DWCNTs, especially for higher aspect ratios.

Keywords: double-walled carbon nanotubes, nonlocal continuum elasticity, free vibrations, molecular dynamics simulation, generalized differential quadrature method

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Authors: Yu Liang, Wei Wei

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Spatial representation of numbers and numerical magnitude are important for preschoolers’ mathematical ability. Mental number line, a typical index to measure numbers spatial representation, and numerical comparison are both related to arithmetic obviously. However, they seem to rely on different mechanisms and probably influence arithmetic through different mechanisms. In line with this idea, preschool children were trained with two tasks to investigate which one is more important for approximate arithmetic. The training of numerical processing and number line estimation were proved to be effective. They both improved the ability of approximate arithmetic. When the difficulty of approximate arithmetic was taken into account, the performance in number line training group was not significantly different among three levels. However, two harder levels achieved significance in numerical comparison training group. Thus, comparing spatial representation ability, symbolic approximation arithmetic relies more on numerical magnitude. Educational implications of the study were discussed.

Keywords: approximate arithmetic, mental number line, numerical magnitude, preschooler

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Authors: Ridha Zgolli, Hatem Kanfoudi

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Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A 2D numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier-Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density which is expressed as function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term TEM. The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in details. The numerical simulations are in good agreement with the experimental data for steady flow.

Keywords: cavitation, injection nozzle, numerical simulation, k–ω

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Authors: A. Chellil, A. Nour, S. Lecheb, H.Mechakra, A. Bouderba, H. Kebir

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In this paper, the numerical study for the instability of a composite rotor is presented, under dynamic loading response in the harmonic analysis condition. The analysis of the stress which operates the rotor is done. Calculations of different energies and the virtual work of the aerodynamic loads from the rotor is developed. The use of the composite material for the rotor, offers a good Stability. Numerical calculations on the model develop of three dimensions prove that the damage effect has a negative effect on the stability of the rotor. The study of the composite rotor in transient system allowed to determine the vibratory responses due to various excitations.

Keywords: rotor, composite, damage, finite element, numerical

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Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Saeid Sahmani

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Due to size-dependent behavior of nanostrustures, the classical continuum models are not applicable for the analyses at this submicrion size. Surface stress effect is one of the most important matters which make the nanoscale structures to have different properties compared to the conventional structures due to high surface to volume ratio. In the present study, free vibration characteristics of nanoplates are investigated including surface stress effects. To this end, non-classical plate model based on Gurtin-Murdoch elasticity theory is proposed to evaluate the surface stress effects on the vibrational behavior of nanoplates subjected to different boundary conditions. Generalized differential quadrature (GDQ) method is employed to discretize the governing non-classical differential equations along with various edge supports. Selected numerical results are given to demonstrate the distinction between the behavior of nanoplates predicted by the classical and present non-classical plate models that leads to illustrate the great influence of surface stress effect. It is observed that this influence quite depends on the magnitude of the surface elastic constants which are relevant to the selected material.

Keywords: nanomechanics, surface stress, free vibration, GDQ method, small scale effect

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Authors: Piotr Ciuman, Barbara Lipska

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The aim of presented research was to improve numerical predictions of air parameters distribution in the actual natatorium by the selection of calculation formula of mass flux of moisture emitted from the pool. Selected correlation should ensure the best compliance of numerical results with the measurements' results of these parameters in the facility. The numerical model of the natatorium was developed, for which boundary conditions were prepared on the basis of measurements' results carried out in the actual facility. Numerical calculations were carried out with the use of ANSYS CFX software, with six formulas being implemented, which in various ways made the moisture emission dependent on water surface temperature and air parameters in the natatorium. The results of calculations with the use of these formulas were compared for air parameters' distributions: Specific humidity, velocity and temperature in the facility. For the selection of the best formula, numerical results of these parameters in occupied zone were validated by comparison with the measurements' results carried out at selected points of this zone.

Keywords: experimental validation, indoor swimming pool, moisture emission, natatorium, numerical calculations CFD, thermal and humidity conditions, ventilation

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Authors: H. Ahmed, A. Schlenkhoff

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Recently, permeable breakwaters have been suggested to overcome the disadvantages of fully protection breakwaters. These protection structures have minor impacts on the coastal environment and neighboring beaches where they provide a more economical protection from waves and currents. For regular waves, a numerical model is used (FLOW-3D, VOF) to investigate the hydraulic performance of a permeable breakwater. The model of permeable breakwater consists of a pair of identical vertical slotted walls with an impermeable upper and lower part, where the draft is a decimal multiple of the total depth. The middle part is permeable with a porosity of 50%. The second barrier is located at distant of 0.5 and 1.5 of the water depth from the first one. The numerical model is validated by comparisons with previous laboratory data and semi-analytical results of the same model. A good agreement between the numerical results and both laboratory data and semi-analytical results has been shown and the results indicate the applicability of the numerical model to reproduce most of the important features of the interaction. Through the numerical investigation, the friction factor of the model is carefully discussed.

Keywords: coastal structures, permeable breakwater, slotted wall, numerical model, energy dissipation coefficient

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Authors: Temidayo Otunniyi

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This paper presents a low computational channelization algorithm for the multi-standards platform using poly phase implementation of a critically sampled hybrid Trigonometry generalized Discrete Fourier Transform, (HGDFT). An HGDFT channelization algorithm exploits the orthogonality of two trigonometry Fourier functions, together with the properties of Quadrature Mirror Filter Bank (QMFB) and Exponential Modulated filter Bank (EMFB), respectively. HGDFT shows improvement in its implementation in terms of high reconfigurability, lower filter length, parallelism, and medium computational activities. Type 1 and type 111 poly phase structures are derived for real-valued HGDFT modulation. The design specifications are decimated critically and over-sampled for both single and multi standards receiver platforms. Evaluating the performance of oversampled single standard receiver channels, the HGDFT algorithm achieved 40% complexity reduction, compared to 34% and 38% reduction in the Discrete Fourier Transform (DFT) and tree quadrature mirror filter (TQMF) algorithm. The parallel generalized discrete Fourier transform (PGDFT) and recombined generalized discrete Fourier transform (RGDFT) had 41% complexity reduction and HGDFT had a 46% reduction in oversampling multi-standards mode. While in the critically sampled multi-standard receiver channels, HGDFT had complexity reduction of 70% while both PGDFT and RGDFT had a 34% reduction.

Keywords: software defined radio, channelization, critical sample rate, over-sample rate

Procedia PDF Downloads 101

Authors: Young Hee Geum

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We propose the numerical method defined by xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding

Procedia PDF Downloads 197

Authors: Ju-Hong Lee, Yi-Lin Shieh

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Two-dimensional (2-D) quadrature mirror filter (QMF) banks have been widely considered for high-quality coding of image and video data at low bit rates. Without implementing subband coding, a 2-D QMF bank is required to have an exactly linear-phase response without magnitude distortion, i.e., the perfect reconstruction (PR) characteristics. The design problem of 2-D QMF banks with the PR characteristics has been considered in the literature for many years. This paper presents a transformation approach for designing 2-D two-channel QMF banks. Under a suitable one-dimensional (1-D) to two-dimensional (2-D) transformation with a specified decimation/interpolation matrix, the analysis and synthesis filters of the QMF bank are composed of 1-D causal and stable digital allpass filters (DAFs) and possess the 2-D doubly complementary half-band (DC-HB) property. This facilitates the design problem of the two-channel QMF banks by finding the real coefficients of the 1-D recursive DAFs. The design problem is formulated based on the minimax phase approximation for the 1-D DAFs. A novel objective function is then derived to obtain an optimization for 1-D minimax phase approximation. As a result, the problem of minimizing the objective function can be simply solved by using the well-known weighted least-squares (WLS) algorithm in the minimax (L∞) optimal sense. The novelty of the proposed design method is that the design procedure is very simple and the designed 2-D QMF bank achieves perfect magnitude response and possesses satisfactory phase response. Simulation results show that the proposed design method provides much better design performance and much less design complexity as compared with the existing techniques.

Keywords: Quincunx QMF bank, doubly complementary filter, digital allpass filter, WLS algorithm

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Authors: Alaeddin Ebrahimi, Narasimman Sundararajan, Bernhard Pracejus

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Development of salt domes, often a rising from depths of some 10 km or more, causes an intense faulting of the surrounding host rocks (salt tectonics). The fractured rocks then present ideal space for oil that can migrate and get trapped. If such moving of hydrocarbons passes uranium-carrying rock units (e.g., shales), uranium is collected and enriched by organic carbon compounds. Brines from the salt body are also ideal carriers for oxidized uranium species and will further dislocate uranium when in contact with uranium-enriched oils. Uranium then has the potential to mineralize in the vicinity of the dome (blue halite is evidence for radiation having affected salt deposits elsewhere in the world). Based on this knowledge, the Qarat Kibrit salt dome was investigated by a well-established geophysical method like very low frequency electromagnetic (VLF-EM) along five traverses approximately 250 m in length (10 m intervals) in order to identify subsurface fault systems. In-phase and quadrature components of the VLF-EM signal were recorded at two different transmitter frequencies (24.0 and 24.9 kHz). The images of Fraser filtered response of the in-phase components indicate a conductive zone (fault) in the southeast and southwest of the study area. The Karous-Hjelt current density pseudo section delineates subsurface faults at depths between 10 and 40 m. The stacked profiles of the Fraser filtered responses brought out two plausible trends/directions of faults. However, there seems to be no evidence for uranium enrichment has been recorded in this area.

Keywords: salt dome, uranium, fault, in-phase component, quadrature component, Fraser filter, Karous-Hjelt current density

Procedia PDF Downloads 219

Authors: Dejin Chen, Bin Lin, Xiaohui LI, Haobin Tian

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In order to acquire stable impact performance of cover, the factors influencing the impact force of the cover were analyzed and researched. The influence of impact factors such as impact velocity, impact weight and fillet radius of warhead was studied by Orthogonal experiment. Through the range analysis and numerical simulation, the results show that the impact velocity has significant influences on impact force of cover. The impact force decreases with the increase of impact velocity and impact weight. The test results are similar to the numerical simulation. The cover broke up into four parts along the groove.

Keywords: fragile cover, numerical simulation, impact force, epoxy foam

Procedia PDF Downloads 239

Authors: Hariti Rafika, Fekih Malika, Saighi Mohamed

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During the period storage of liquefied natural gas, stability is necessarily affected by natural convection along the walls of the tank with thermal insulation is not perfectly efficient. In this paper, we present the numerical simulation of heat transfert by natural convection double diffusion,in unsteady laminar regime in a storage tank. The storage tank contains a liquefied natural gas (LNG) in its gaseous phase. Fluent, a commercial CFD package, based on the numerical finite volume method, is used to simulate the flow. The gas is just on the surface of the liquid phase. This numerical simulation allowed us to determine the temperature profiles, the stream function, the velocity vectors and the variation of the heat flux density in the vapor phase in the LNG storage tank volume. The results obtained for a general configuration, by numerical simulation were compared to those found in the literature.

Keywords: numerical simulation, natural convection, heat gains, storage tank, liquefied natural gas

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

Procedia PDF Downloads 433

Authors: Hadi Farhadian, Homayoon Katibeh

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In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above-mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm the high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occurred in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m.

Keywords: water Seepage, Amirkabir Tunnel, analytical method, DEM, SGR

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Authors: Helnaz Soltani, J. N. Reddy

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Presence of fluid medium interacting with a structure can lead to failure of the structure. Since developing efficient computational model for fluid-structure interaction (FSI) problems has broader impact to realistic problems encountered in aerospace industry, ship industry, oil and gas industry, and so on, one can find an increasing need to find a method in order to investigate the effect of fluid domain on structural response. A coupled finite element formulation of problems involving FSI issue is an accurate method to predict the response of structures in contact with a fluid medium. This study proposes a finite element approach in order to study the transient response of the structures interacting with a fluid medium. Since beam and plate are considered to be the fundamental elements of almost any structure, the developed method is applied to beams and plates benchmark problems in order to demonstrate its efficiency. The formulation is a combination of the various structure theories and the solid-fluid interface boundary condition, which is used to represent the interaction between the solid and fluid regimes. Here, three different beam theories as well as three different plate theories are considered to model the solid medium, and the Navier-Stokes equation is used as the theoretical equation governed the fluid domain. For each theory, a coupled set of equations is derived where the element matrices of both regimes are calculated by Gaussian quadrature integration. The main feature of the proposed methodology is to model the fluid domain as an added mass; the external distributed force due to the presence of the fluid. We validate the accuracy of such formulation by means of some numerical examples. Since the formulation presented in this study covers several theories in literature, the applicability of our proposed approach is independent of any structure geometry. The effect of varying parameters such as structure thickness ratio, fluid density and immersion depth, are studied using numerical simulations. The results indicate that maximum vertical deflection of the structure is affected considerably in the presence of a fluid medium.

Keywords: beam and plate, finite element analysis, fluid-structure interaction, transient response

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Fatema-Tuz-Zahura, Raquib Ahsan

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Punching shear failure is usually the governing failure mode of flat plate structures. Punching failure is brittle in nature which induces more vulnerability to this type of structure. In the present study, a 3D finite element model of a flat plate with low reinforcement ratio and without any transverse reinforcement has been developed. Punching shear stress and the deflection data were obtained on the surface of the flat plate as well as through the thickness of the model from numerical simulations. The obtained data were compared with the experimental results. Variation of punching stress with respect to deflection as obtained from numerical results is found to be in good agreement with the experimental results; the range of variation of punching stress is within 5%. The numerical simulation shows an early and gradual onset of nonlinearity, whereas the same is late and abrupt as observed in the experimental results. The range of variation of punching stress for different slab thicknesses between experimental and numerical results is less than 15%. The developed numerical model is useful to complement available punching test series performed in the past. The results obtained from the numerical model will be helpful for designing retrofitting schemes of flat plates.

Keywords: flat plate, finite element model, punching shear, reinforcement ratio

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: A. Kazemi Jouybari, A. Mirabdolah Lavasani

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This paper seeks to the solution of condensation around of a flat plate, circular and elliptical tube in way of numerical and analytical methods. Also, it calculates the entropy production rates. The first, problem was solved by using mesh dynamic and rational assumptions, next it was compared with the numerical solution that the result had acceptable errors. An additional supporting relation was applied based on a characteristic of condensation phenomenon for condensing elements. As it has been shown here, due to higher rates of heat transfer for elliptical tubes, they have more entropy production rates, in comparison to circular ones. Findings showed that two methods were efficient. Furthermore, analytical methods can be used to optimize the problem and reduce the entropy production rate.

Keywords: condensation, numerical solution, analytical solution, entropy rate

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Authors: A. El Amri, M. El Yakhloufi Haddou, A. Khamlichi

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The numerical simulation based on the Finite Element Method (FEM) is widely used in academic institutes and in the industry. It is a useful tool to predict many phenomena present in the classical manufacturing forming processes such as fracture. But, the results of such numerical model depend strongly on the parameters of the constitutive behavior model. The influences of thermal and mechanical loads cause damage. The temperature and strain rate dependent materials’ properties and their modelling are discussed. A Johnson-Cook Model of damage has been selected for the numerical simulations. Virtual software called the ABAQUS 6.11 is used for finite element analysis. This model was introduced in order to give information concerning crack initiation during thermal and mechanical loads.

Keywords: thermo-mechanical fatigue, failure, numerical simulation, fracture, damage

Procedia PDF Downloads 372