Search results for: nonlinear constitutive law

Authors: Azadeh Jafari, Robert G. Owens

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In this study, a geometrical multiscale approach which means coupling together the 2-D Navier-Stokes equations, constitutive equations and 0-D lumped parameter models is investigated. A multiscale approach, suggest a natural way of coupling detailed local models (in the flow domain) with coarser models able to describe the dynamics over a large part or even the whole cardiovascular system at acceptable computational cost. In this study we introduce a new velocity correction scheme to decouple the velocity computation from the pressure one. To evaluate the capability of our new scheme, a comparison between the results obtained with Neumann outflow boundary conditions on the velocity and Dirichlet outflow boundary conditions on the pressure and those obtained using coupling with the lumped parameter model has been performed. Comprehensive studies have been done based on the sensitivity of numerical scheme to the initial conditions, elasticity and number of spectral modes. Improvement of the computational algorithm with stable convergence has been demonstrated for at least moderate Weissenberg number. We comment on mathematical properties of the reduced model, its limitations in yielding realistic and accurate numerical simulations, and its contribution to a better understanding of microvascular blood flow. We discuss the sophistication and reliability of multiscale models for computing correct boundary conditions at the outflow boundaries of a section of the cardiovascular system of interest. In this respect the geometrical multiscale approach can be regarded as a new method for solving a class of biofluids problems, whose application goes significantly beyond the one addressed in this work.

Keywords: geometrical multiscale models, haemorheology model, coupled 2-D navier-stokes 0-D lumped parameter modeling, computational fluid dynamics

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Authors: Moridi Fatemeh, Dasineh Mehdi, Jafari Narges

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The aim of this study was to investigate the relationship between dividends and investment in a condition of cash flow uncertainty. Previous studies have also found some evidence that there is N-shaped relationship between dividends and investment given different levels of cash uncertainly. Thus, this study examines this relationship over the period 2009-2014 in Tehran Stock Exchange (TSE). Based on our sample and new variables, we found reverse N-shaped relationship in different levels of cash flow uncertainly. This shape was descending in cash flow certainly and uncertainly but it is ascending in medial position.

Keywords: dividends, investment, nonlinear relationship, uncertainty of cash flow

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Authors: M. Ezzat, Y. Zaghloul, T. Sorour, A. Hefny, M. Eid

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Ultimate capacity of large diameter bored piles is usually determined from pile loading tests as recommended by several international codes and foundation design standards. However, loading of this type of piles till achieving apparent failure is practically seldom. In this paper, numerical analyses are carried out to simulate load test of a large diameter bored pile performed at the location of Alzey highway bridge project (Germany). Test results of pile load settlement relationship till failure as well as results of the base and shaft resistances are available. Apparent failure was indicated in this test by the significant increase of the induced settlement during the last load increment applied on the pile head. Measurements of this pile load test are used to assess the quality of the numerical models investigated. Three different material soil models are implemented in the analyses: Mohr coulomb (MC), Soft soil (SS), and Modified Mohr coulomb (MMC). Very good agreement is obtained between the field measured settlement and the calculated settlement using the MMC model. Results of analysis showed also that the MMC constitutive model is superior to MC, and SS models in predicting the ultimate base and shaft resistances of the large diameter bored pile. After calibrating the numerical model, behavior of large diameter bored piles under axial loads is discussed and the formation of the plastic zone around the pile is explored. Results obtained showed that the plastic zone below the base of the pile at failure extended laterally to about four times the pile diameter and vertically to about three times the pile diameter.

Keywords: ultimate capacity, large diameter bored piles, plastic zone, failure, pile load test

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Dan James

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The Medial Axis of the Main Canyon of Valles Marineris is determined geometrically with maximally inscribed discs aligned with the boundaries or rims of the Main Canyon. Inscribed discs are placed at evenly spaced longitude intervals and, using the radius function, the locus of the centre of all discs is determined, together with disc centre co-ordinates. These centre co-ordinates result in arrays of x, y co-ordinates which are curve fitted to a Sinusoidal function and residuals appropriate for nonlinear regression are evaluated using the R-squared value (R2) and the Root Mean Squared Error (RMSE). This evaluation demonstrates that a Sinusoidal Curve closely fits to the co-ordinate data

Keywords: medial axis, MAT, valles marineris, sinusoidal

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Ren Zuo Wang

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In this paper, in order to investigate the behavior of the wood structure, the non-linearity of wood material model in LS-DYNA is adopted. It is difficult and less efficient to conduct the experiment of the ancient wood structure, hence LS-DYNA software can be used to simulate nonlinear responses of ancient wood structure. In LS-DYNA software, there is material model called *MAT_WOOD or *MAT_143. This model is to simulate a single-element response of the wood subjected to tension and compression under the parallel and the perpendicular material directions. Comparing with the exact solution and numerical simulations results using LS-DYNA, it demonstrates the accuracy and the efficiency of the proposed simulation method.

Keywords: LS-DYNA, wood structure, single-element simulations, MAT_143

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Engin Metin Kaplan, Kemal Yaman

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In this study, the crash of a medium heavy vehicle onto a designed Road blocker (vehicle barrier) is studied numerically. Structural integrity of the Road blocker is studied by nonlinear dynamic methods under the loading conditions which are defined in the standards. NASTRAN® and LS-DYNA® which are commercial software are used to solve the problem. Outer geometry determination, alignment of the inner part and material properties of the road blocker are studied linearly to yield design parameters. Best design parameters are determined to achieve the most structurally optimized road blocker. Strain and stress values of the vehicle barrier are obtained by solving the partial differential equations.

Keywords: vehicle barrier, truck collision, road blocker, crash analysis

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Authors: M. Bouinoun, M. Bouhadef

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The present study is concerned with the problem of determining the shape of the free surface flow in a hydraulic channel which has an uneven bottom. For the mathematical formulation of the problem, the fluid of the two-dimensional irrotational steady flow in water is assumed inviscid and incompressible. The solutions of the nonlinear problem are obtained by using the usual conformal mapping theory and Hilbert’s technique. An experimental study, for comparing the obtained results, has been conducted in a hydraulic channel (subcritical regime and supercritical regime).

Keywords: free-surface flow, experiments, numerical method, uneven bottom, supercritical regime, subcritical regime

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Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

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In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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Authors: Jorge Prada, Christina Cordes, Carsten Harms, Walter Lang

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The development of microfluidic-based biosensors over the last years has shown an increasing employ of thermoplastic polymers as constitutive material. Their low-cost production, high replication fidelity, biocompatibility and optical-mechanical properties are sought after for the implementation of disposable albeit functional lab-on-chip solutions. Among the range of thermoplastic materials on use, the Cyclo-Olefin Copolymer (COC) stands out due to its optical transparency, which makes it a frequent choice as manufacturing material for fluorescence-based biosensors. Moreover, several processing techniques to complete a closed COC microfluidic biosensor have been discussed in the literature. The reported techniques differ however in their implementation, and therefore potentially add more or less complexity when using it in a mass production process. This work introduces and reports results on the application of a purely thermal bonding process between COC substrates, which were produced by the hot-embossing process, and COC foils containing screen-printed circuits. The proposed procedure takes advantage of the transition temperature difference between two COC grades foils to accomplish the sealing of the microfluidic channels. Patterned heat injection to the COC foil through the COC substrate is applied, resulting in consistent channel geometry uniformity. Measurements on bond strength and bursting pressure are shown, suggesting that this purely thermal bonding process potentially renders a technique which can be easily adapted into the thermoplastic microfluidic chip production workflow, while enables a low-cost as well as high-quality COC biosensor manufacturing process.

Keywords: biosensor, cyclo-olefin copolymer, hot embossing, thermal bonding, thermoplastics

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Authors: Somia Bouzid, Messaoud Ramdani

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The success of any diagnosis strategy critically depends on the sensors measuring process variables. This paper presents a detection and diagnosis sensor faults method based on a Bottleneck Neural Network (BNN). The BNN approach is used as a statistical process control tool for drinking water distribution (DWD) systems to detect and isolate the sensor faults. Variable reconstruction approach is very useful for sensor fault isolation, this method is validated in simulation on a nonlinear system: actual drinking water distribution system. Several results are presented.

Keywords: fault detection, localization, PCA, NLPCA, auto-associative neural network

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Hassan Al Salman, Ahmed Al Ghafli

Abstract:

In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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Authors: Archil Motsonelidze, Vitaly Dvalishvili

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Existing roller compacted concrete (RCC) dams indicate that the layer-by-layer construction method gives considerable economies as compared with the conventional methods. RCC dams have also gained acceptance in the regions of high seismic activity. Earthquake resistance analysis of RCC gravity dams based on nonlinear finite element technique is presented. An elastic-plastic approach is used to describe the material of a dam while it is under static conditions (period of construction). Seismic force, as an acceleration equivalent to that produced by a real earthquake, is supposed to act when the dam is completed. The materials of the dam and foundation may be nonhomogeneous and anisotropic. The “dam-foundation” system is idealized as a plain strain problem.

Keywords: finite element method, layer-by-layer construction, RCC dams, strength analysis

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: Semayat Fanta, P.M. Mohite, C.S. Upadhyay

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Damage meso-model for laminates is one of the most widely applicable approaches for the analysis of damage induced in laminated fiber-reinforced polymeric composites. Damage meso-model for laminates has been developed over the last three decades by many researchers in experimental, theoretical, and analytical methods that have been carried out in micromechanics as well as meso-mechanics analysis approaches. It has been fundamentally developed based on the micromechanical description that aims to predict the damage initiation and evolution until the failure of structure in various loading conditions. The current damage meso-model for laminates aimed to act as a bridge between micromechanics and macro-mechanics of the laminated composite structure. This model considers two meso-constituents for the analysis of damage in ply and interface that imparted from low-velocity impact. The damages considered in this study include fiber breakage, matrix cracking, and diffused damage of the lamina, and delamination of the interface. The damage initiation and evolution in laminae can be modeled in terms of damaged strain energy density using damage parameters and the thermodynamic irreversible forces. Interface damage can be modeled with a new concept of spherical micro-void in the resin-rich zone of interface material. The damage evolution is controlled by the damage parameter (d) and the radius of micro-void (r) from the point of damage nucleation to its saturation. The constitutive martial model for meso-constituents is defined in a user material subroutine VUMAT and implemented in ABAQUS/Explicit finite element modeling tool. The model predicts the damages in the meso-constituents level very accurately and is considered the most effective technique of modeling low-velocity impact simulation for laminated composite structures.

Keywords: mesomodel, laminate, low-energy impact, micromechanics

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Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: M. Bassoui, M. Ferfra, M. Chrayagne

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This paper presents a qualitative modeling for the nonlinear B-H curve of the saturable magnetic materials for a transformer with shunts used in the power supply for the magnetron. This power supply is composed of a single phase leakage flux transformer supplying a cell composed of a capacitor and a diode, which double the voltage and stabilize the current, and a single magnetron at the output of the cell. A procedure consisting of a fuzzy clustering method and a rule processing algorithm is then employed for processing the constructed fuzzy modeling rules to extract the qualitative properties of the curve.

Keywords: B(H) curve, fuzzy clustering, magnetron, power supply

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Authors: Fatemeh Shahi, Mehdi Sharifian, Laia Shahrassai, Elham Eskandari A.

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A new mechanism is reported here for magnetic field generation in laser-plasma interaction by means of nonlinear ponderomotive force. The plasma considered here is unmagnetized inhomogeneous plasma with an exponentially decreasing profile. A damped periodic magnetic field with a relatively lower frequency is obtained using the ponderomotive force exerted on plasma electrons. Finally, with an electric field and by using Faraday’s law, the magnetic field profile in the plasma has been obtained. Because of the negative exponential density profile, the generated magnetic field is relatively slowly oscillating and damped through the plasma.

Keywords: magnetic field generation, laser-plasma interaction, ponderomotive force, inhomogeneous plasma

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Authors: Leila Graini

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In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

Keywords: all-optical function, 2R optical regeneration, self-similar broadening, Mamyshev regenerator

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Authors: Andre S. de Lima, Alfredo R. de Faria, Jose J. R. Faria

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Accurate prediction of thermal stresses is particularly important for laminated composite structures, as large temperature changes may occur during fabrication and field application. The normal transverse deformation plays an important role in the prediction of such stresses, especially for problems involving thick laminated plates subjected to uniform temperature loads. Bearing this in mind, the present study aims to investigate the thermo-mechanical behavior of laminated composite structures using a new beam element based on global-local superposition, accounting for through-the-thickness effects. The element formulation is based on a global-local superposition in the thickness direction, utilizing a cubic global displacement field in combination with a linear layerwise local displacement distribution, which assures zig-zag behavior of the stresses and displacements. By enforcing interlaminar stress (normal and shear) and displacement continuity, as well as free conditions at the upper and lower surfaces, the number of degrees of freedom in the model is maintained independently of the number of layers. Moreover, the proposed formulation allows for the determination of transverse shear and normal stresses directly from the constitutive equations, without the need of post-processing. Numerical results obtained with the beam element were compared to analytical solutions, as well as results obtained with commercial finite elements, rendering satisfactory results for a range of length-to-thickness ratios. The results confirm the need for an element with through-the-thickness capabilities and indicate that the present formulation is a promising alternative to such analysis.

Keywords: composite beam element, global-local superposition, laminated composite structures, thermal stresses

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Authors: Alaoua Bouaicha, Fahim Kahlouche, Abdelhamid Benouali

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Many embankment dams have suffered failures during earthquakes due to the increase of pore water pressure under seismic loading. After analyzing of the behavior of embankment dams under severe earthquakes, major advances have been attained in the understanding of the seismic action on dams. The present study concerns numerical analysis of the seismic response of earth dams. The procedure uses a nonlinear stress-strain relation incorporated into the code FLAC2D based on the finite difference method. This analysis provides the variation of the pore water pressure and horizontal displacement.

Keywords: Earthquake, Numerical Analysis, FLAC2D, Displacement, Embankment Dam, Pore Water Pressure

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Siwar Fadhel, Imen Bahri, Man Zhang

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The switched reluctance machine (SRM) has undeniable qualities in terms of low cost and mechanical robustness. However, its highly nonlinear character and its uncertain parameters justify the development of complicated controls. In this paper, authors present the design of a robust H-infinity current controller for an 8/6 SRM with taking into account the nonlinearity of the SRM and with rejection of disturbances. The electromagnetic torque is indirectly regulated through the current controller. To show the performances of this control, a robustness analysis is performed by comparing the H-infinity and PI controller simulation results. This comparison demonstrates better performances for the presented controller. The effectiveness and robustness of the presented controller are also demonstrated by experimental tests.

Keywords: current regulation, experimentation, robust H-infinity control, switched reluctance machine

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Authors: Matthew C. Best

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Linear Multi-Input Multi-Output (MIMO) dynamic models can be identified, with no a priori knowledge of model structure or order, using a new Generalised Identifying Filter (GIF). Based on an Extended Kalman Filter, the new filter identifies the model iteratively, in a continuous modal canonical form, using only input and output time histories. The filter’s self-propagating state error covariance matrix allows easy determination of convergence and conditioning, and by progressively increasing model order, the best fitting reduced-order model can be identified. The method is shown to be resistant to noise and can easily be extended to identification of smoothly nonlinear systems.

Keywords: system identification, Kalman filter, linear model, MIMO, model order reduction

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Authors: Sajeda Elbashabsheh, Kamel Al-Khaled

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This paper applies a modified Laplace Adomian decomposition method to solve the time-fractional JaulentMiodek system. The method produce convergent series solutions with easily compatible components. This paper considers the Caputo fractional derivative. The effectiveness and applicability of the method are demonstrated by comparing its results with those of prior studies. Results are presented in tables and figures. These solutions might be imperative and significant for the explanation of some practical physical phenomena. All computations and figures in the work are done using MATHEMATICA. The numerical results demonstrate that the current methods are effective, reliable, and simple to i implement for nonlinear fractional partial differential equations.

Keywords: approximate solutions, Jaulent-Miodek system, Adomian decomposition method, solitons

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Authors: S. Sathiyamoorthi, P. Srinivasan, K. Suganya Devi

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Arylidene derivatives are the subclass of chalcone derivatives. Chalcone derivatives are studied widely for the past decade because of its nonlinearity. To seek new organic group of crystals which suit for fabrication of optical devices, three-member organic arylidene crystals were synthesized by using Claisen–Schmidt condensation reaction. Good quality crystals were grown by slow evaporation method. Functional groups were identified by FT-IR and FT-Raman spectrum. Optical transparency and optical band gap were determined by UV-Vis-IR studies. Thermal stability and melting point were calculated using TGA and DSC. Variation of dielectric loss and dielectric constant with frequency were calculated by dielectric measurement.

Keywords: DSC and TGA studies, nonlinear optic studies, Fourier Transform Infrared Spectroscopy, UV-vis-NIR spectra

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Authors: Maria Bercea, Monica Diana Olteanu

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Investigation of polymer systems able to change inside of the body into networks represent an attractive approach, especially when there is a minimally invasive and patient friendly administration. Pharmaceutical formulations based on Pluronic F127 [poly (oxyethylene) (PEO) blocks (70%) and poly(oxypropylene) (PPO) blocks (30%)] present an excellent potential as drug delivery systems. The use of Pluronic F127 alone as gel-forming solution is limited by some characteristics, such as poor mechanical properties, short residence time, high permeability, etc. Investigation of the interactions between the natural and synthetic polymers and surfactants in solution is a subject of great interest from both scientific and practical point of view. As for example, formulations based on Pluronics and chitosan could be used to obtain dual phase transition hydrogels responsive to temperature and pH changes. In this study, different materials were prepared by using poly(vinyl alcohol), chitosan solutions mixed with aqueous solutions of Pluronic F127. The rheological properties of different formulations were investigated in temperature sweep experiments as well as at a constant temperature of 37oC for exploring in-situ gel formation in the human body conditions. In addition, some viscometric investigations were carried out in order to understand the interactions which determine the complex behaviour of these systems. Correlation between the thermodynamic and rheological parameters and phase separation phenomena observed for the investigated systems allowed the dissemination the constitutive response of polymeric materials at different external stimuli, such as temperature and pH. The rheological investigation demonstrated that the viscoelastic moduli of the hydrogels can be tuned depending on concentration of different components as well as pH and temperature conditions and cumulative contributions can be obtained.

Keywords: hydrogel, polymer mixture, stimuli responsive, biomedical applications

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