Search results for: Discrete boundary value problem
4456 A Numerical Algorithm for Positive Solutions of Concave and Convex Elliptic Equation on R2
Authors: Hailong Zhu, Zhaoxiang Li
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In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.
Keywords: positive solutions, concave-convex, sub-super solution method, pseudo arclength method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13104455 Solving the Set Covering Problem Using the Binary Cat Swarm Optimization Metaheuristic
Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin
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In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.Keywords: Binary cat swarm optimization, set covering problem, metaheuristic, binarization methods.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23204454 Tsunami Inundation Modeling in a Boundary Fitted Curvilinear Grid Model Using the Method of Lines Technique
Authors: M. Ashaque Meah, M. Shah Noor, M Asif Arefin, Md. Fazlul Karim
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A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4th order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundary technique is applied instead of fixed sea side wall or fixed coastal boundary to ensure the movement of the coastal boundary. The extent of intrusion of water and associated tsunami propagation are simulated for the 2004 Indian Ocean tsunami along the west coast of Peninsular Malaysia and southern Thailand. The simulated results are compared with the results obtained from a finite difference model and the data available in the USGS website. All simulations show better approximation than earlier research and also show excellent agreement with the observed data.
Keywords: Open boundary condition, moving boundary condition, boundary-fitted curvilinear grids, far field tsunami, Shallow Water Equations, tsunami source, Indonesian tsunami of 2004.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8524453 Experimental Simulation of Soil Boundary Condition for Dynamic Studies
Authors: Omar.S. Qaftan, T. T. Sabbagh
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This paper studies the free-field response by adopting a flexible membrane container as soil boundary for experimental shaking table tests. The influence of the soil container boundary on the soil behaviour and the dynamic soil properties under seismic effect were examined. A flexible container with 1/50 scale factor was adopted in the experimental tests, including construction, instrumentation, and determination of the results of dynamic tests on a shaking table. Horizontal face displacements and accelerations were analysed to determine the influence of the container boundary on the performance of the soil. The outputs results show that the flexible boundary container allows more displacement and larger accelerations. The soil in a rigid wall container cannot deform as similar as the soil in the real field does. Therefore, the response of flexible container tested is believed to be more reliable for soil boundary than that in the rigid container.Keywords: Soil, boundary, seismic, earthquake, ground motion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10904452 High Accuracy Eigensolutions in Elasticity for Boundary Integral Equations by Nyström Method
Authors: Pan Cheng, Jin Huang, Guang Zeng
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Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36354451 A Parametric Study of an Inverse Electrostatics Problem (IESP) Using Simulated Annealing, Hooke & Jeeves and Sequential Quadratic Programming in Conjunction with Finite Element and Boundary Element Methods
Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis
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The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.
Keywords: Elastostatic, inverse problem, optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18674450 An Accurate Computation of Block Hybrid Method for Solving Stiff Ordinary Differential Equations
Authors: A. M. Sagir
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In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14724449 Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method
Authors: M. A. Ghorbani, M. Pasbani Khiavi
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In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23004448 Natural Convection Boundary Layer Flow of a Viscoelastic Fluid on Solid Sphere with Newtonian Heating
Authors: A.R.M. Kasim, N.F. Mohammad, Aurangzaib, S. Sharidan
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The present paper considers the steady free convection boundary layer flow of a viscoelastic fluid on solid sphere with Newtonian heating. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. Thus, the augmentation an extra boundary condition is needed to perform the numerical computational. The governing boundary layer equations are first transformed into non-dimensional form by using special dimensionless group and then solved by using an implicit finite difference scheme. The results are displayed graphically to illustrate the influence of viscoelastic K and Prandtl Number Pr parameters on skin friction, heat transfer, velocity profiles and temperature profiles. Present results are compared with the published papers and are found to concur very well.Keywords: boundary layer flow, Newtonian heating, sphere, viscoelastic fluid.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23924447 Thermosolutal MHD Mixed Marangoni Convective Boundary Layers in the Presence of Suction or Injection
Authors: Noraini Ahmad, Seripah Awang Kechil, Norma Mohd Basir
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The steady coupled dissipative layers, called Marangoni mixed convection boundary layers, in the presence of a magnetic field and solute concentration that are formed along the surface of two immiscible fluids with uniform suction or injection effects is examined. The similarity boundary layer equations are solved numerically using the Runge-Kutta Fehlberg with shooting technique. The Marangoni, buoyancy and external pressure gradient effects that are generated in mixed convection boundary layer flow are assessed. The velocity, temperature and concentration boundary layers thickness decrease with the increase of the magnetic field strength and the injection to suction. For buoyancy-opposed flow, the Marangoni mixed convection parameter enhances the velocity boundary layer but decreases the temperature and concentration boundary layers. However, for the buoyancy-assisted flow, the Marangoni mixed convection parameter decelerates the velocity but increases the temperature and concentration boundary layers.Keywords: Magnetic field, mixed Marangoni convection, similarity boundary layers, solute concentration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18704446 Experimental and Numerical Investigation of Air Ejector with Diffuser with Boundary Layer Suction
Authors: Vaclav Dvorak
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The article deals with experimental and numerical investigation of axi-symmetric subsonic air to air ejector with diffuser adapted for boundary layer suction. The diffuser, which is placed behind the mixing chamber of the ejector, has high divergence angle and therefore low efficiency. To increase the efficiency, the diffuser is equipped with slot enabling boundary layer suction. The effect of boundary layer suction on flow in ejector, static pressure distribution on the mixing chamber wall and characteristic were measured and studied numerically. Both diffuser and ejector efficiency were evaluated. The diffuser efficiency was increased, however, the efficiency of ejector itself remained low.Keywords: Air ejector, boundary layer suction, CFD, diffuser.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28014445 An Efficient Hamiltonian for Discrete Fractional Fourier Transform
Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma
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Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15204444 The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method
Authors: Caihong Su
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Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.Keywords: Boundary layer, e-N method, PSE, Transition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14984443 A Hybrid Approach Using Particle Swarm Optimization and Simulated Annealing for N-queen Problem
Authors: Vahid Mohammadi Saffarzadeh, Pourya Jafarzadeh, Masoud Mazloom
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This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems.
Keywords: PSO, SA, N-queen, CSP
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16744442 Stability Analysis of Neural Networks with Leakage, Discrete and Distributed Delays
Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong
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This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.
Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16114441 Comparative Study of Fault Identification and Classification on EHV Lines Using Discrete Wavelet Transform and Fourier Transform Based ANN
Authors: K.Gayathri, N. Kumarappan
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An appropriate method for fault identification and classification on extra high voltage transmission line using discrete wavelet transform is proposed in this paper. The sharp variations of the generated short circuit transient signals which are recorded at the sending end of the transmission line are adopted to identify the fault. The threshold values involve fault classification and these are done on the basis of the multiresolution analysis. A comparative study of the performance is also presented for Discrete Fourier Transform (DFT) based Artificial Neural Network (ANN) and Discrete Wavelet Transform (DWT). The results prove that the proposed method is an effective and efficient one in obtaining the accurate result within short duration of time by using Daubechies 4 and 9. Simulation of the power system is done using MATLAB.
Keywords: EHV transmission line, Fault identification and classification, Discrete wavelet transform, Multiresolution analysis, Artificial neural network
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24364440 Stability Criteria for Uncertainty Markovian Jumping Parameters of BAM Neural Networks with Leakage and Discrete Delays
Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong
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In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.
Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 51304439 A Further Improvement on the Resurrected Core-Spreading Vortex Method
Authors: M-J. Huang, C-J. Huang, L-C. Chen
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In a previously developed fast vortex method, the diffusion of the vortex sheet induced at the solid wall by the no-slip boundary conditions was modeled according to the approximation solution of Koumoutsakos and converted into discrete blobs in the vicinity of the wall. This scheme had been successfully applied to a simulation of the flow induced with an impulsively initiated circular cylinder. In this work, further modifications on this vortex method are attempted, including replacing the approximation solution by the boundary-element-method solution, incorporating a new algorithm for handling the over-weak vortex blobs, and diffusing the vortex sheet circulation in a new way suitable for high-curvature solid bodies. The accuracy is thus largely improved. The predictions of lift and drag coefficients for a uniform flow past a NASA airfoil agree well with the existing literature.Keywords: Resurrected core-spreading vortex method, Boundaryelement method, Vortex sheet, Over-weak vortex blobs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14054438 Bridging Stress Modeling of Composite Materials Reinforced by Fibers Using Discrete Element Method
Authors: Chong Wang, Kellem M. Soares, Luis E. Kosteski
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The problem of toughening in brittle materials reinforced by fibers is complex, involving all of the mechanical properties of fibers, matrix and the fiber/matrix interface, as well as the geometry of the fiber. Development of new numerical methods appropriate to toughening simulation and analysis is necessary. In this work, we have performed simulations and analysis of toughening in brittle matrix reinforced by randomly distributed fibers by means of the discrete elements method. At first, we put forward a mechanical model of toughening contributed by random fibers. Then with a numerical program, we investigated the stress, damage and bridging force in the composite material when a crack appeared in the brittle matrix. From the results obtained, we conclude that: (i) fibers of high strength and low elasticity modulus are beneficial to toughening; (ii) fibers of relatively high elastic modulus compared to the matrix may result in substantial matrix damage due to spalling effect; (iii) employment of high-strength synthetic fibers is a good option for toughening. We expect that the combination of the discrete element method (DEM) with the finite element method (FEM) can increase the versatility and efficiency of the software developed. The present work can guide the design of ceramic composites of high performance through the optimization of the parameters.
Keywords: Bridging stress, discrete element method, fiber reinforced composites, toughening.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18884437 A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations
Authors: A. M. Sagir
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In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14704436 Variational Iteration Method for the Solution of Boundary Value Problems
Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.
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In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.
Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20894435 Natural and Mixed Convection Heat Transfer Cooling of Discrete Heat Sources Placed Near the Bottom on a PCB
Authors: Tapano Kumar Hotta, S P Venkateshan
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Steady state experiments have been conducted for natural and mixed convection heat transfer, from five different sized protruding discrete heat sources, placed at the bottom position on a PCB and mounted on a vertical channel. The characteristic length ( Lh ) of heat sources vary from 0.005 to 0.011 m. The study has been done for different range of Reynolds number and modified Grashof number. From the experiment, the surface temperature distribution and the Nusselt number of discrete heat sources have been obtained and the effects of Reynold number and Richardson number on them have been discussed. The objective is to find the rate of heat dissipation from heat sources, by placing them at the bottom position on a PCB and to compare both modes of cooling of heat sources.Keywords: Discrete heat source, mixed convection, natural convection, vertical channel
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20514434 Numerical Simulations of Acoustic Imaging in Hydrodynamic Tunnel with Model Adaptation and Boundary Layer Noise Reduction
Authors: Sylvain Amailland, Jean-Hugh Thomas, Charles Pézerat, Romuald Boucheron, Jean-Claude Pascal
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The noise requirements for naval and research vessels have seen an increasing demand for quieter ships in order to fulfil current regulations and to reduce the effects on marine life. Hence, new methods dedicated to the characterization of propeller noise, which is the main source of noise in the far-field, are needed. The study of cavitating propellers in closed-section is interesting for analyzing hydrodynamic performance but could involve significant difficulties for hydroacoustic study, especially due to reverberation and boundary layer noise in the tunnel. The aim of this paper is to present a numerical methodology for the identification of hydroacoustic sources on marine propellers using hydrophone arrays in a large hydrodynamic tunnel. The main difficulties are linked to the reverberation of the tunnel and the boundary layer noise that strongly reduce the signal-to-noise ratio. In this paper it is proposed to estimate the reflection coefficients using an inverse method and some reference transfer functions measured in the tunnel. This approach allows to reduce the uncertainties of the propagation model used in the inverse problem. In order to reduce the boundary layer noise, a cleaning algorithm taking advantage of the low rank and sparse structure of the cross-spectrum matrices of the acoustic and the boundary layer noise is presented. This approach allows to recover the acoustic signal even well under the boundary layer noise. The improvement brought by this method is visible on acoustic maps resulting from beamforming and DAMAS algorithms.Keywords: Acoustic imaging, boundary layer noise denoising, inverse problems, model adaptation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9614433 The Error Analysis of An Upwind Difference Approximation for a Singularly Perturbed Problem
Authors: Jiming Yang
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An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.
Keywords: Singularly perturbed, upwind difference, uniform convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13884432 Existence and Uniqueness of Periodic Solution for a Discrete-time SIR Epidemic Model with Time Delays and Impulses
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In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.
Keywords: Discrete-time SIR epidemic model, time delay, nonlinear incidence rate, impulse.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16404431 A Laplace Transform Dual-Reciprocity Boundary Element Method for Axisymmetric Elastodynamic Problems
Authors: B. I. Yun
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A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16614430 Comparison Results of Two-point Fuzzy Boundary Value Problems
Authors: Hsuan-Ku Liu
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This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.
Keywords: Fuzzy derivative, lateral type of H-derivative, fuzzy differential equations, fuzzy boundary value problems, boundary value problems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15204429 Analytical Solution of the Boundary Value Problem of Delaminated Doubly-Curved Composite Shells
Authors: András Szekrényes
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Delamination is one of the major failure modes in laminated composite structures. Delamination tips are mostly captured by spatial numerical models in order to predict crack growth. This paper presents some mechanical models of delaminated composite shells based on shallow shell theories. The mechanical fields are based on a third-order displacement field in terms of the through-thickness coordinate of the laminated shell. The undelaminated and delaminated parts are captured by separate models and the continuity and boundary conditions are also formulated in a general way providing a large size boundary value problem. The system of differential equations is solved by the state space method for an elliptic delaminated shell having simply supported edges. The comparison of the proposed and a numerical model indicates that the primary indicator of the model is the deflection, the secondary is the widthwise distribution of the energy release rate. The model is promising and suitable to determine accurately the J-integral distribution along the delamination front. Based on the proposed model it is also possible to develop finite elements which are able to replace the computationally expensive spatial models of delaminated structures.
Keywords: J-integral, Lévy method, third-order shell theory, state space solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5944428 Robust BIBO Stabilization Analysis for Discrete-time Uncertain System
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.
Keywords: Robust BIBO stabilization, delay-dependent stabilization, discrete-time system, time delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15804427 Modeling and Simulation of Flow Shop Scheduling Problem through Petri Net Tools
Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez
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The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.
Keywords: Flow-shop scheduling problem, makespan, Petri nets, state equation.
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