Search results for: boundary integral method

Authors: F. Waffo Tchuimmo, G. S. Kwandio Dongoua, C. U. Yves Mbono Samba, O. Dafounansou, L. Nana

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The strength criterion is an important condition of great interest to guarantee the stability of the structural elements. The present work is based on the study of the free vibration of Euler’s Bernoulli column of equal strength in compression while considering its own weight and the axial load in compression and tension subjected to symmetrical boundary conditions. We use the differential quadrature method to investigate the first fifth naturals frequencies parameters of the column according to the different forms of geometrical sections. The results of this work give help in making a judicious choice of type of cross-section and a better boundary condition to guarantee good stability of this type of column in civil constructions.

Keywords: free vibration, equal strength, self-weight, tip force, differential quadrature method

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Authors: Abdulhakeem Yusuf, Yomi Monday Aiyesimi, Mohammed Jiya

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The failure in an ordinary heat transfer fluid to meet up with today’s industrial cooling rate has resulted in the development of high thermal conductivity fluid which nanofluids belongs. In this work, the problem of unsteady one dimensional laminar flow of an incompressible fluid within a parallel wall is considered with one wall assumed to be wavy. The model is presented in its rectangular coordinate system and incorporates the effects of thermophoresis and Brownian motion. The local similarity solutions were also obtained which depends on Soret number, Dufour number, Biot number, Lewis number, and heat generation parameter. The analytical solution is obtained in a closed form via the Adomian decomposition method. It was found that the method has a good agreement with the numerical method, and it is also established that the heat generation parameter has to be kept low so that heat energy are easily evacuated from the system.

Keywords: Adomian decomposition method, Biot number, Dufour number, nanofluid

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Authors: N. Chayaopas, W. Assawinchaichote

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In order to maximize energy capturing from wind energy, controlling the doubly fed induction generator to have optimal power from the wind, generator speed and output electrical power control in wind energy system have a great importance due to the nonlinear behavior of wind velocities. In this paper purposes the design of a control scheme is developed for power control of wind energy system via H∞ fuzzy integral controller. Firstly, the nonlinear system is represented in term of a TS fuzzy control design via linear matrix inequality approach to find the optimal controller to have an H∞ performance are derived. The proposed control method extract the maximum energy from the wind and overcome the nonlinearity and disturbances problems of wind energy system which give good tracking performance and high efficiency power output of the DFIG.

Keywords: doubly fed induction generator, H-infinity fuzzy integral control, linear matrix inequality, wind energy system

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Authors: Lawrence A. Farinola

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Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

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Authors: Elyas Shivanian

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In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in doubly connected domains. It is obtained the unknown data on the inner boundary of the domain while overspecified boundary data are imposed on the outer boundary of the domain by using the SMRPI. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high order convergence rate. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and it is revealed the SMRPI is more accurate and stable by adding strong perturbations.

Keywords: cauchy problem, doubly connected domain, radial basis function, shape function

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Authors: Somnath Karmakar, S. Chakraverty

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This work investigates the vibration of nonhomogeneous Timoshenko nanobeam resting on the Winkler-Pasternak foundation. Eringen’s nonlocal theory has been used to investigate small-scale effects. The Differential Quadrature method is used to obtain the frequency parameters with various classical boundary conditions. The nonhomogeneous beam model has been considered, where Young’s modulus and density of the beam material vary linearly and quadratically. Convergence of frequency parameters is also discussed. The influence of mechanical properties and scaling parameters on vibration frequencies are investigated for different boundary conditions.

Keywords: Timoshenko beam, Eringen's nonlocal theory, differential quadrature method, nonhomogeneous nanobeam

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Authors: Mark Watson, J.-F. Bousquet, Adam Forget

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A magnetic induction based underwater communication link is evaluated using an analytical model and a custom Finite-Difference Time-Domain (FDTD) simulation tool. The analytical model is based on the Sommerfeld integral, and a full-wave simulation tool evaluates Maxwell’s equations using the FDTD method in cylindrical coordinates. The analytical model and FDTD simulation tool are then compared and used to predict the system performance for various transmitter depths and optimum frequencies of operation. To this end, the system bandwidth, signal to noise ratio, and the magnitude of the induced voltage are used to estimate the expected channel capacity. The models show that in seawater, a relatively low-power and small coils may be capable of obtaining a throughput of 40 to 300 kbps, for the case where a transmitter is at depths of 1 to 3 m and a receiver is at a height of 1 m.

Keywords: magnetic induction, FDTD, underwater communication, Sommerfeld

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Hossain Samani, Mohammad Ehteram

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In this paper, we consider finite volume method (FVM) in water hammer. We will simulate these techniques on a looped network with complex boundary conditions. After comparing methods, we see the FVM method as the best method. We compare the results of FVM with experimental data. Finite volume using staggered grid is applied for solving water hammer equations.

Keywords: hydraulic transient, water hammer, interpolation, non-liner interpolation

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Authors: Ch. Ramreddy, P. Naveen, D. Srinivasacharya

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The objective of the present study is to investigate the effect of nonlinear temperature and concentration on the mixed convective flow of micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of convective boundary condition. In order to analyze all the essential features, the transformed nonlinear conservation equations are worked out numerically by spectral method. By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the coupling number and inclination of angle tend to decrease the skin friction, mass transfer rate and the reverse change is there in wall couple stress and heat transfer rate. The nominal effect on the wall couple stress and skin friction is encountered whereas the significant effect on the local heat and mass transfer rates are found for high enough values of Biot number.

Keywords: convective boundary condition, micropolar fluid, non-darcy porous medium, non-linear convection, spectral method

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Authors: H. Niranjan, S. Sivasankaran

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Heat and mass transfer near a steady stagnation point boundary layer flow of viscous incompressible fluid through porous media investigates along a vertical plate is thoroughly studied under the presence of magneto hydrodynamic (MHD) effects. The fluid flow is steady, laminar, incompressible and in two-dimensional. The nonlinear differential coupled parabolic partial differential equations of continuity, momentum, energy and specie diffusion are converted into the non-similar boundary layer equations using similarity transformation, which are then solved numerically using the Runge-Kutta method along with shooting method. The effects of the conjugate heat transfer parameter, the porous medium parameter, the permeability parameter, the mixed convection parameter, the magnetic parameter, and the thermal radiation on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature. The various parameters on local skin friction, heat and mass transfer rates are presented in tabular form.

Keywords: MHD, porous medium, slip, convective boundary condition, stagnation point

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Authors: Junling Li, Fang Meng, Yichun Zhang

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Image saliency detection has been long studied, while several challenging problems are still unsolved, such as detecting saliency inaccurately in complex scenes or suppressing salient objects in the image borders. In this paper, we propose a new saliency detection algorithm in order to solving these problems. We represent the image as a graph with superixels as nodes. By considering appearance similarity between the boundary and the background, the proposed method chooses non-saliency boundary nodes as background priors to construct the background probability model. The probability that each node belongs to the model is computed, which measures its similarity with backgrounds. Thus we can calculate saliency by the transformed probability as a metric. We compare our algorithm with ten-state-of-the-art salient detection methods on the public database. Experimental results show that our simple and effective approach can attack those challenging problems that had been baffling in image saliency detection.

Keywords: visual saliency, background probability, boundary knowledge, background priors

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Authors: Eduard Marusic-Paloka

Abstract:

The Darcy-Weisbach formula is used to compute the pressure drop of the fluid in the pipe, due to the friction against the wall. Because of its simplicity, the Darcy-Weisbach formula became widely accepted by engineers and is used for laminar as well as the turbulent flows through pipes, once the method to compute the mysterious friction coefficient was derived. Particularly in the second half of the 20th century. Formula is empiric, and our goal is to derive it from the basic conservation law, via rigorous asymptotic analysis. We consider the case of the laminar flow but with significant Reynolds number. In case of the perfectly smooth pipe, the situation is trivial, as the Navier-Stokes system can be solved explicitly via the Poiseuille formula leading to the friction coefficient in the form 64/Re. For the rough pipe, the situation is more complicated and some effects of the roughness appear in the friction coefficient. We start from the Navier-Stokes system in the pipe with periodically corrugated wall and derive an asymptotic expansion for the pressure and for the velocity. We use the homogenization techniques and the boundary layer analysis. The approximation derived by formal analysis is then justified by rigorous error estimate in the norm of the appropriate Sobolev space, using the energy formulation and classical a priori estimates for the Navier-Stokes system. Our method leads to the formula for the friction coefficient. The formula involves resolution of the appropriate boundary layer problems, namely the boundary value problems for the Stokes system in an infinite band, that needs to be done numerically. However, theoretical analysis characterising their nature can be done without solving them.

Keywords: Darcy-Weisbach law, pipe flow, rough boundary, Navier law

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Authors: Shai Sarussi

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Let S be an integral domain which is not a field, let F be its field of fractions, and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R ∩ F = S and F R = A. A topological space whose set of open sets is closed under arbitrary intersections is called an Alexandroff space. Inspired by the well-known Zariski-Riemann space and the Zariski topology on the set of prime ideals of a commutative ring, we define a topology on the set of all S-nice subalgebras of A. Consequently, we get an interplay between Algebra and topology, that gives us a better understanding of the S-nice subalgebras of A. It is shown that every irreducible subset of S-nice subalgebras of A has a supremum; and a characterization of the irreducible components is given, in terms of maximal S-nice subalgebras of A.

Keywords: Alexandroff topology, integral domains, Zariski-Riemann space, S-nice subalgebras

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Authors: M. S. Gadala, Khaled Ahmed, Elasadig Mahdi

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In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

Keywords: inverse analysis, function specification, neural net works, particle swarm, run-out table

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Chinsuk Hong

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This paper investigates the characteristics of wall pressure fluctuations in naturally developing boundary layer flows on axisymmetric bodies experimentally. The axisymmetric body has a modified ellipsoidal blunt nose. Flush-mounted microphones are used to measure the wall pressure fluctuations in the boundary layer flow over the body. The measurements are performed in a low noise wind tunnel. It is found that the correlation between the flow regime and the characteristics of the pressure fluctuations is distinct. The process from small fluctuation in laminar flow to large fluctuation in turbulent flow is investigated. Tollmien-Schlichting wave (T-S wave) is found to generate and develop in transition. Because of the T-S wave, the wall pressure fluctuations in the transition region are higher than those in the turbulent boundary layer.

Keywords: wall pressure fluctuation, boundary layer flow, transition, turbulent flow, axisymmetric body, flow noise

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Authors: Ibrahim Cicek, Melike Nikbay

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Electrically propelled vehicles, either road or aerial vehicles are studied on contemporarily for their robust maneuvers and cost-efficient transport operations. The main power generating systems of such vehicles electrified by selecting proper components and assembled as e-powertrain. Generally, e-powertrain components selected considering the target performance requirements. Since the main component of propulsion is the drive unit, e-motor control system is subjected to achieve the performance targets. In this paper, the optimization of e-motor control parameters studied by Integral Squared Method (ISE). The overall aim is to minimize power consumption of such vehicles depending on mission profile and maintaining smooth maneuvers for passenger comfort. The sought-after values of control parameters are computed using the Optimal Control Theory. The system is modeled as a closed-loop linear control system with calibratable parameters.

Keywords: optimization, e-powertrain, optimal control, electric vehicles

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

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This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: convection flow, similarity, numerical analysis, spectral method, Williamson nanofluid, internal heat generation

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Authors: Sumei Cai, Hong Li

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Either during water or gas injection into reservoir, in order to understand the areal flow pressure distribution underground, associated bounding deformation is prevalently monitored by ground or downhole tiltmeters. In this paper, an inverse solution to elastic response of far field displacements induced by reservoir pressure change due to flow injection was studied. Furthermore, the fundamental theory on inverse solution to elastic problem as well as its spatial smoothing approach is presented. Taking advantage of source code development based on Boundary Element Method, numerical analysis on the monitoring data of ground surface displacements to further understand the behavior of reservoir process was developed. Numerical examples were also conducted to verify the effectiveness.

Keywords: remote displacement, inverse problem, boundary element method, BEM, reservoir process

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Authors: Prodromos E. Atlamazoglou

Abstract:

The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.

Keywords: hyperthermia, integral equations, insulated antennas, method of symmetrical components

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Po-Chun Wang, Yan-Ru Lai, Sophia I. C. Lin, Alvin W. Y. Su

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The Generative Theory of Tonal Music (GTTM) provides systematic approaches to recognizing local boundaries of music. The rules have been implemented in some automated melody segmentation algorithms. Besides, there are also deep learning methods with GTTM features applied to boundary detection tasks. However, these studies might face constraints such as a lack of or inconsistent label data. The GTTM database is currently the most widely used GTTM database, which includes manually labeled GTTM rules and local boundaries. Even so, we found some problems with these labels. They are sometimes discrepancies with GTTM rules. In addition, since it is labeled at different times by multiple musicians, they are not within the same scope in some cases. Therefore, in this paper, we examine this database with musicians from the aspect of classical music and relabel the scores. The relabeled database - GTTM Database v2.0 - will be released for academic research usage. Despite the experimental and statistical results showing that the relabeled database is more consistent, the improvement in boundary detection is not substantial. It seems that we need more clues than GTTM rules for boundary detection in the future.

Keywords: dataset, GTTM, local boundary, neural network

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Authors: Tsoi Kim Ming, Yu King Pong

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Background: With powered wheelchair, patients can travel more easily and conveniently. However, some patients suffer from other difficulties, such as visual impairment, cognitive disorder, or psychological issues, which make them unable to control powered wheelchair safely. Purpose: Therefore, those patients are required to complete a comprehensive driving training by therapists on confined area, which simulates narrow paths in daily live. During the training, therapists will give series of driving instruction to patients, which may be unaware of patients crossing out the boundary of area. To facilitate the training, it is needed to develop a device to provide warning to patients during training Method: We adopt LIDAR for distance sensing started from center of confined area. Then, we program the LIDAR with linear geometry to remember each side of the area. The LIDAR will sense the location of wheelchair continuously. Once the wheelchair is driven out of the boundary, audio alert will be given to patient. Result: Patients can pay their attention to the particular driving situation followed by audio alert during driving training, which can learn how to avoid out of boundary in similar situation next time. Conclusion: Instead of only instructed by therapist, the LIDAR can facilitate the powered wheelchair training by patients actively pay their attention to driving situation. After training, they are able to control the powered wheelchair safely when facing difficult and narrow path in real life.

Keywords: PWC, training, rehab, AT

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Authors: Korosh Khorshidi, Mohammad Khodadadi

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In this paper, exact close form solution for out of plate free flexural vibration of moderately thick rectangular nanoplates are presented based on nonlocal modified trigonometric shear deformation theory, with assumptions of the Levy's type boundary conditions, for the first time. The aim of this study is to evaluate the effect of small-scale parameters on the frequency parameters of the moderately thick rectangular nano-plates. To describe the effects of small-scale parameters on vibrations of rectangular nanoplates, the Eringen theory is used. The Levy's type boundary conditions are combination of six different boundary conditions; specifically, two opposite edges are simply supported and any of the other two edges can be simply supported, clamped or free. Governing equations of motion and boundary conditions of the plate are derived by using the Hamilton’s principle. The present analytical solution can be obtained with any required accuracy and can be used as benchmark. Numerical results are presented to illustrate the effectiveness of the proposed method compared to other methods reported in the literature. Finally, the effect of boundary conditions, aspect ratios, small scale parameter and thickness ratios on nondimensional natural frequency parameters and frequency ratios are examined and discussed in detail.

Keywords: exact solution, nonlocal modified sinusoidal shear deformation theory, out of plane vibration, moderately thick rectangular plate

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Authors: Haoui Rabah

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The aim of this work is to analyze a viscous flow around the axisymmetric blunt body taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier-Stokes equations is realized by using the finite volume method to determine the flow parameters and detached shock position. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, CFL coefficient and mesh size level are selected to ensure numerical convergence. The effect of the mesh size is significant on the shear stress and velocity profile. The best solution is obtained with using a very fine grid. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: supersonic flow, viscous flow, finite volume, blunt body

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Authors: R. Bensaada, M. Almansba, M. Ould Ouali, R. Ferhoum, N. E. Hannachi

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The aim of this work is to simulate the ductile fracture of SEN specimens in aluminium alloy. The assessment of fracture toughness is performed with the calculation of Jc (the critical value of J-Integral) through the resistance curves. The study is done using finite element code calculation ABAQUSTM including an elastic plastic with damage model of material’s behaviour. The procedure involves specimens of four different thicknesses and four ligament sizes for every thickness. The material of study is an aluminium alloy 6061-T6 for which the necessary parameters to complete the study are given. We found the same results for the same specimen’s thickness and for different ligament sizes when the fracture criterion is evaluated.

Keywords: j-integral, critical-j, damage, fracture toughness

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Authors: Haw-Long Lee, Win-Jin Chang, Yu-Ching Yang

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In this study, we use the atomic-scale finite element method to investigate the vibrational behavior of the armchair- and zigzag-structured nanoporous graphene layers with different size under the SFSF and CFFF boundary conditions. The fundamental frequencies computed for the graphene layers without pore are compared with the results of previous studies. We observe very good correspondence of our results with that of the other studies in all the considered cases. For the armchair- and zigzag-structured nanoporous graphene layers under the SFSF and CFFF boundary conditions, the frequencies decrease as the size of the nanopore increase. When the positions of the pore are symmetric with respect to the center of the graphene, the frequency of the zigzag pore graphene is higher than that of the armchair one.

Keywords: atomic-scale finite element method, graphene, nanoporous, natural frequency

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Authors: S. Kida

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We consider the flow of an incompressible viscous fluid in a precessing sphere whose spin and precession axes are orthogonal to each other. The flow is characterized by two non-dimensional parameters, the Reynolds number Re and the Poincare number Po. For which values of (Re, Po) will the flow approach a steady state from an arbitrary initial condition? To answer it we are searching the instability boundary of the steady states in the whole (Re, Po) plane. Here, we focus the rapidly rotating and weakly precessing limit, i.e., Re >> 1 and Po << 1. The steady flow was obtained by the asymptotic expansion for small ε=Po Re¹/² << 1. The flow exhibits nearly a solid-body rotation in the whole sphere except for a thin boundary layer which develops over the sphere surface. The thickness of this boundary layer is of O(δ), where δ=Re⁻¹/², except where two circular critical bands of thickness of O(δ⁴/⁵) and of width of O(δ²/⁵) which are located away from the spin axis by about 60°. We perform the linear stability analysis of the steady flow. We assume that the disturbances are localized in the critical bands and make an expansion analysis in terms of ε to derive the eigenvalue problem for the growth rate of the disturbance, which is solved numerically. As the solution, we obtain an asymptote of the stability boundary as Po=28.36Re⁻⁰.⁸. This agrees excellently with the corresponding laboratory experiments and numerical simulations. One of the most popular instability mechanisms so far is the parametric instability, which turns out, however, not to give the correct stability boundary. The present instability is different from the parametric instability.

Keywords: boundary layer, critical band, instability, precessing sphere

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