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Ming-chang Wu - One of the best experts on this subject based on the ideXlab platform.
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Effect of Natural Boundary Condition and the neutral surface of nonlinear type on the upper-bound solution to upset forging of rings using a variational approach
Mechanics of Materials, 2008Co-Authors: Ming-chang WuAbstract:Abstract The purpose of this work is to investigate the effect of Natural Boundary Condition and the type of neutral surface on the upper-bound solutions using a variational approach. To this end, the neutral surface of the upset ring was considered a function of polynomials of various orders during deformation process, and then an upper-bound forming energy equation was formulated in terms of the function as well as the velocity field derived from the theory of stream function. Since the velocity field had been expressed in terms of an implicit stream function before the upper-bound forming energy equation J was established, a variational approach was fulfilled to determine an upper-bound solution by extremizing J. As a result, a set of Boundary Conditions was derived mathematically. To determine the upper-bound solution, the derived Boundary Conditions, which include the so-called Natural Boundary Conditions and kinematically Boundary Conditions, were imposed in an optimization procedure. Such a method we have proposed to determine the solution is particularly termed the variational upper-bound (VUB) method in order to distinguish it from the traditional upper-bound (UB) method, which usually ignores the Natural Boundary Condition perceptibly unobtainable. The Natural Boundary Condition can be physically interpreted as to constrain plastic flow of the upset ring at frictional interfaces. However, in order to investigate the effect of the type of neutral surface on upper-bound solutions, a polynomial that may result in the neutral surface of nonlinear type was proposed. By comparing with some experimental results, it is found that the VUB method has considerably improved on the UB method in predicting the calibration curves, the bulged profiles of upset ring and disks, and the forming energy. The result presented in this work also demonstrates that the effect of the Natural Boundary Condition is much more pronounced than that of the type of neutral surface used on improving the upper-bound solution. While keeping the same number of free parameters left for the purpose of minimization procedure, the VUB method is permitted to establish an approximate solution of higher order than the UB method, because it additionally satisfies the Natural Boundary Condition derived in this work. The finite element solution determined using MARC, a commercial software package, is also presented in this work for discussion.
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Effect of Natural Boundary Conditions on the upper-bound analysis of upset forging of ring and disks
Materials & Design, 2006Co-Authors: Ming-chang WuAbstract:The purpose of this investigation is to discuss the effect of Natural Boundary Conditions derived using the method of variational calculus for upset forging of rings. In order to derive the Natural Boundary Condition, an assumed admissible function with unknown constants is replaced by an arbitrary function. Rather than minimizing the unknown constants in the assumed function, the arbitrary function is found using variational calculus, and the Natural Boundary Condition is derived as a consequence. The upper-bound solutions, with and without imposing the Natural Boundary Condition, as well as finite element solutions were compared and discussed. The finite element solutions were determined using the commercial software package MARC. All solutions were experimentally verified using the experimental result of the calibration curve from ring tests. They were then discussed, by comparing with experimental bulged profiles as well as experimental forming load. From the result, we can clearly indicate that the Natural Boundary Condition, which constrains plastic flow of the upsetting ring on the contact interface, significantly affects the upper-bound solution not only in predicting the bulge profile of the upset ring, but also in calculating the total forming load. The variational upper-bound solution, which accounts for the Natural Boundary Condition, has shown to present a significant improvement on the traditional upper-bound solution in general.
Tomáš Neustupa - One of the best experts on this subject based on the ideXlab platform.
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A mathematical model of a steady flow through the Kaplan turbine – The existence of a weak solution in the case of an arbitrarily large inflow
2017Co-Authors: Tomáš NeustupaAbstract:The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding Boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called “artificial” or “Natural” Boundary Condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.
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Weak Formulation of the Problem of Modelling the Steady Flow of a Viscous Incompressible Liquid Through a Rotating Radial Blade Machine
Numerical Mathematics and Advanced Applications 2011, 2012Co-Authors: Tomáš NeustupaAbstract:The paper presents the mathematical model of a two dimensional steady viscous incompressible flow through a rotating radial blade machine. The flow is described and studied in the rotating frame. The paper provides the classical and weak formulation of the corresponding Boundary value problem. The Boundary Condition on the outflow is the so called “Natural” Boundary Condition, with the additional nonlinear term proposed by Bruneau and Fabrie (Math Model Numer Anal 30(7):815–840, 1996), and a new term arising from the rotation of the machine. The existence of a weak solution is proved.
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The analysis of stationary viscous incompressible flow through a rotating radial blade machine, existence of a weak solution
Applied Mathematics and Computation, 2012Co-Authors: Tomáš NeustupaAbstract:Abstract The paper deals with the analysis of the mathematical model of the two dimensional stationary viscous incompressible flow through a rotating radial blade machine. The flow is described and studied in the rotating frame. The paper provides the classical and weak formulation of the corresponding Boundary value problem. The Boundary Condition on the outflow is the so called “Natural” Boundary Condition, with the nonlinear term proposed by Bruneau and Fabrie (1996) [1] , and also modified by a term arising from the rotation of the machine. The existence of a weak solution is proved.
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On existence and uniqueness of the solution of stationary flow in a profile cascade with Natural Boundary Condition involving Bernoulli's pressure on the outflow
2012Co-Authors: Tomáš NeustupaAbstract:The paper is concerned with the theoretical analysis of the model of incompressible, viscous, stationary flow through a plane cascade of profiles. We study the existence and uniqueness of the weak solution in the case of linear Boundary Condition of the "do-nothing" type. (Let us recall that this is not possible for the well known basic Natural "do-nothing" Boundary Condition).
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On non-stationary viscous incompressible flow through a cascade of profiles
Mathematical Methods in the Applied Sciences, 2006Co-Authors: Miloslav Feistauer, Tomáš NeustupaAbstract:The paper deals with theoretical analysis of non-stationary incompressible flow through a cascade of profiles. The initial-Boundary value problem for the Navier–Stokes system is formulated in a domain representing the exterior to an infinite row of profiles, periodically spaced in one direction. Then the problem is reformulated in a bounded domain of the form of one space period and completed by the Dirichlet Boundary Condition on the inlet and the profile, a suitable Natural Boundary Condition on the outlet and periodic Boundary Conditions on artificial cuts. We present a weak formulation and prove the existence of a weak solution. Copyright © 2006 John Wiley & Sons, Ltd.
Wei-ching Yeh - One of the best experts on this subject based on the ideXlab platform.
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A variational upper-bound method for analysis of upset forging of rings
Journal of Materials Processing Technology, 2005Co-Authors: Wei-ching YehAbstract:Abstract In this investigation, a variational upper-bound (VUB) method is employed. It is the method that determines an upper-bound solution using variational calculus. By using the method, the Natural Boundary Condition, which was ignored in the traditional upper-bound (UB) method, can be theoretically derived for the stream function assumed to be arbitrary in prior. The VUB method has shown to be applicable to the problem of upset forgings of ring, and it presents an improvement on the UB method in general. From the result, we can clearly indicate that the Natural Boundary Condition, which constrains plastic flow of the upsetting ring on the contact interface, significantly affects the upper-bound solution not only in predicting the bulge profile of the upset ring, but also in calculating the total forming energy rate. Theoretical predictions obtained using the VUB, the UB and the FEM methods were compared and discussed. Some experimental results were employed for verification of the theories as well.
Wenwu Cao - One of the best experts on this subject based on the ideXlab platform.
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Theoretical study on the influence of surface imperfections on the properties of ferroelectric thin films in first‐order ferroelectric systems
physica status solidi (b), 2006Co-Authors: Shan Lin, Wenwu CaoAbstract:A generalized Ginzburg–Landau–Devonshire (GLD) theory is used to study the properties of ferroelectric thin films sandwiched between two metal electrodes with a first-order phase transition. By taking into account the effect of the imperfect surface layer and a Natural Boundary Condition, the temperature and film-thickness dependence of the spontaneous polarization and the dielectric susceptibility are calculated. The depolarization field makes the polarization distribution more uniform. In addition, an asymmetric hysteresis loop can be obtained due to the existence of asymmetrical imperfect surface layers. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Generalized continuum theory for ferroelectric thin films
Physical Review B, 2002Co-Authors: Wenwu CaoAbstract:A generalized Ginzburg-Landau-Devonshire free energy has been used to describe the influence of imperfect surface layers or interface layers in ferroelectric thin films. The Natural Boundary Condition has been employed insolving the polarization profile, which can reflect a more realistic situation compared to the previous treatments of the same problem using the so-called extrapolation length. We show that the unscreened portion of the depolarization field makes the polarization distribution more uniform while reducing the amplitude of the effective polarization. The less perfect layer can lower the effective phase-transition temperature. We also used the model to study the effect of asymmetric Boundary Conditions, which will cause a shift of the hysteresis loop from the center point, similar to the effect of a bias field.
K.e Barrett - One of the best experts on this subject based on the ideXlab platform.
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Variational principle for two-dimensional high Hartmann number flow
International Journal of Engineering Science, 2001Co-Authors: K.e BarrettAbstract:A variational principle for the stream function-vorticity form of the linearised two-dimensional MHD equations which incorporates the no-slip Condition as a Natural Boundary Condition has been used to solve a range of problems. Finite element discretisations leading to sparse non-symmetric linear systems have been solved by a corrected version of a standard non-symmetric frontal solver. The numerical solutions obtained for flows over an unbounded cylinder at the larger Hartmann numbers agree with recently obtained theoretical asymptotic estimates. Other calculations for bounded flows in channels with or without obstructions are also in agreement with previous results obtained by matched asymptotic expansion methods.