The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Hasan Kurtaran - One of the best experts on this subject based on the ideXlab platform.
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large displacement static and transient analysis of functionally graded deep curved beams with generalized differential Quadrature Method
Composite Structures, 2015Co-Authors: Hasan KurtaranAbstract:Abstract In this article, large displacement static and transient behavior of moderately thick deep functionally graded curved beams with constant curvature are investigated using generalized differential Quadrature Method. Equilibrium equations for static and dynamic responses are obtained using the virtual work principle. Spatial derivatives in the equilibrium equations are expressed with the generalized differential Quadrature Method. Large displacements are taken into account using Green–Lagrange nonlinear strain–displacement relations that are derived from elasticity theory equations. Transverse shear effect is considered through the first-order shear deformation theory. Static and dynamic equilibrium equations are solved using Newton and Newmark Methods respectively. Several curved beam problems with different level of deepness is solved with the proposed Method. Effect of functionally graded material properties on the behavior of curved beam is investigated using various ceramic and metal combinations such as Zirconia/Aluminum, Alumina/Aluminum, Zirconia/Monel, Silicon Nitride/Steel and Alumina/Steel materials in analyses.
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geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential Quadrature Method
Composite Structures, 2015Co-Authors: Hasan KurtaranAbstract:Abstract This article focuses on geometrically nonlinear transient analysis of thick deep laminated composite curved beams with generalized differential Quadrature Method. Generalized differential Quadrature Method is coupled with the weak form of the equation of motion. Virtual work principle is used to derive the equation of motion. Spatial derivatives in the equation of motion are expressed with generalized differential Quadrature Method. Geometric nonlinearity is considered through Green–Lagrange nonlinear strain–displacement relations that are derived using elasticity theory equations. First-order shear deformation theory is used to consider the transverse shear effect. Time integration of the equation of motion is carried out using Newmark average acceleration Method. Several problems from the literature are solved with the proposed Method and results are compared.
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geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells with generalized differential Quadrature Method
Composite Structures, 2015Co-Authors: Hasan KurtaranAbstract:Abstract In this article, geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells is performed using generalized differential Quadrature Method. First-order shear deformation theory of doubly curved shells is used to consider transverse shear effect and Von-Karman nonlinear strain–displacement relationships are used to consider geometric nonlinearity due to large displacements. Virtual work principle is used to derive the equation of motion. Partial derivatives in the equation of motion is expressed with generalized differential Quadrature Method and time integration is carried out using Newmark average acceleration Method. Several laminated composite plate, cylindrical and spherical panel problems from the literature are solved with the proposed Method. Transient responses are compared with those obtained with other Methods in the literature.
Daniel E Rosner - One of the best experts on this subject based on the ideXlab platform.
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bivariate extension of the Quadrature Method of moments for modeling simultaneous coagulation and sintering of particle populations
Journal of Colloid and Interface Science, 2001Co-Authors: Douglas L Wright, Robert Mcgraw, Daniel E RosnerAbstract:Abstract We extendthe application of moment Methods to multivariate suspended particle population problems—those for which size alone is insufficient to specify the state of a particle in the population. Specifically, a bivariate extension of the Quadrature Method of moments (QMOM) (R. McGraw, Aerosol Sci. Technol. 27, 255 (1997)) is presented for efficiently modeling the dynamics of a population of inorganic nanoparticles undergoing simultaneous coagulation and particle sintering. Continuum regime calculations are presented for the Koch–Friedlander–Tandon–Rosner model, which includes coagulation by Brownian diffusion (evaluated for particle fractal dimensions, Df, in the range 1.8–3) and simultaneous sintering of the resulting aggregates (P. Tandon and D. E. Rosner, J. Colloid Interface Sci.213, 273 (1999)). For evaluation purposes, and to demonstrate the computational efficiency of the bivariate QMOM, benchmark calculations are carried out using a high-resolution discrete Method to evolve the particle distribution function n(ν, a) for short to intermediate times (where ν and a are particle volume and surface area, respectively). Time evolution of a selected set of 36 low-order mixed moments is obtained by integration of the full bivariate distribution and compared with the corresponding moments obtained directly using two different extensions of the QMOM. With the more extensive treatment, errors of less than 1% are obtained over substantial aerosol evolution, while requiring only a few minutes (rather than days) of CPU time. Longer time QMOM simulations lend support to the earlier finding of a self-preserving limit for the dimensionless joint (ν, a) particle distribution function under simultaneous coagulation and sintering (Tandon and Rosner, 1999; D. E. Rosner and S. Yu, AIChE J., 47 (2001)). We demonstrate that, even in the bivariate case, it is possible to use the QMOM to rapidly model the approach to asymptotic behavior, allowing an immediate assessment of when previously established asymptotic results can be applied to dynamical situations of current/future interest.
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bivariate extension of the Quadrature Method of moments for modeling simultaneous coagulation and sintering of particle populations
Journal of Colloid and Interface Science, 2001Co-Authors: Douglas L Wright, Robert Mcgraw, Daniel E RosnerAbstract:We extendthe application of moment Methods to multivariate suspended particle population problems-those for which size alone is insufficient to specify the state of a particle in the population. Specifically, a bivariate extension of the Quadrature Method of moments (QMOM) (R. McGraw, Aerosol Sci. Technol. 27, 255 (1997)) is presented for efficiently modeling the dynamics of a population of inorganic nanoparticles undergoing simultaneous coagulation and particle sintering. Continuum regime calculations are presented for the Koch-Friedlander-Tandon-Rosner model, which includes coagulation by Brownian diffusion (evaluated for particle fractal dimensions, D(f), in the range 1.8-3) and simultaneous sintering of the resulting aggregates (P. Tandon and D. E. Rosner, J. Colloid Interface Sci. 213, 273 (1999)). For evaluation purposes, and to demonstrate the computational efficiency of the bivariate QMOM, benchmark calculations are carried out using a high-resolution discrete Method to evolve the particle distribution function n(nu, a) for short to intermediate times (where nu and a are particle volume and surface area, respectively). Time evolution of a selected set of 36 low-order mixed moments is obtained by integration of the full bivariate distribution and compared with the corresponding moments obtained directly using two different extensions of the QMOM. With the more extensive treatment, errors of less than 1% are obtained over substantial aerosol evolution, while requiring only a few minutes (rather than days) of CPU time. Longer time QMOM simulations lend support to the earlier finding of a self-preserving limit for the dimensionless joint (nu, a) particle distribution function under simultaneous coagulation and sintering (Tandon and Rosner, 1999; D. E. Rosner and S. Yu, AIChE J., 47 (2001)). We demonstrate that, even in the bivariate case, it is possible to use the QMOM to rapidly model the approach to asymptotic behavior, allowing an immediate assessment of when previously established asymptotic results can be applied to dynamical situations of current/future interest. Copyright 2001 Academic Press.
Rodney O Fox - One of the best experts on this subject based on the ideXlab platform.
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an extended Quadrature Method of moments for population balance equations
Journal of Aerosol Science, 2012Co-Authors: Cansheng Yuan, Rodney O Fox, Frederique LaurentAbstract:Population balance equations (PBE) for a number density function (NDF) arise in many applications of aerosol technology. Thus, there has been considerable interest in the development of numerical Methods to find solutions to PBE, especially in the context of spatially inhomogeneous systems where moment realizability becomes a significant issue. Quadrature-based moment Methods (QBMM) are an important class of Methods for which the accuracy of the solution can be improved in a controlled manner by increasing the number of Quadrature nodes. However, when a large number of nodes is required to achieve the desired accuracy, the moment-inversion problem can become ill-conditioned. Moreover, oftentimes pointwise values of the NDF are required, but are unavailable with existing QBMM. In this work, a new generation of QBMM is introduced that provides an explicit form for the NDF. This extended Quadrature Method of moments (EQMOM) approximates the NDF by a sum of non-negative weight functions, which allows unclosed source terms to be computed with great accuracy by increasing the number of Quadrature nodes independent of the number of transported moments. Here, we use EQMOM to solve a spatially homogeneous PBE with aggregation, breakage, condensation, and evaporation terms, and compare the results with analytical solutions whenever possible. However, by employing realizable finite-volume Methods, the extension of EQMOM to spatially inhomogeneous systems is straightforward.
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conditional Quadrature Method of moments for kinetic equations
Journal of Computational Physics, 2011Co-Authors: Cansheng Yuan, Rodney O FoxAbstract:Kinetic equations arise in a wide variety of physical systems and efficient numerical Methods are needed for their solution. Moment Methods are an important class of approximate models derived from kinetic equations, but require closure to truncate the moment set. In Quadrature-based moment Methods (QBMM), closure is achieved by inverting a finite set of moments to reconstruct a point distribution from which all unclosed moments (e.g. spatial fluxes) can be related to the finite moment set. In this work, a novel moment-inversion algorithm, based on 1-D adaptive Quadrature of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative Quadrature weights). This conditional Quadrature Method of moments (CQMOM) can be used to compute exact N-point Quadratures for multi-valued solutions (also known as the multi-variate truncated moment problem), and provides optimal approximations of continuous distributions. In order to control numerical errors arising in volume averaging and spatial transport, an adaptive 1-D Quadrature algorithm is formulated for use with CQMOM. The use of adaptive CQMOM in the context of QBMM for the solution of kinetic equations is illustrated by applying it to problems involving particle trajectory crossing (i.e. collision-less systems), elastic and inelastic particle-particle collisions, and external forces (i.e. fluid drag).
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numerical simulation of spray coalescence in an eulerian framework direct Quadrature Method of moments and multi fluid Method
Journal of Computational Physics, 2008Co-Authors: Rodney O Fox, Frederique Laurent, Marc MassotAbstract:The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct Quadrature Method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct Quadrature Method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid Method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each Method, thus giving criteria for their use as well as for their respective efficiency.
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solution of population balance equations using the direct Quadrature Method of moments
Journal of Aerosol Science, 2005Co-Authors: Daniele Marchisio, Rodney O FoxAbstract:The implementation of a population balance equation (PBE) in computational fluid dynamics (CFD) represents a crucial element in the simulation of multiphase flows. Some of the available Methods, such as classes Methods (CM) and Monte Carlo (MC) Methods, are computationally expensive and simulation of real cases of practical interest requires intractable CPU times. On the other hand, other Methods such as the Method of moments (MOM) are computationally affordable but have proven to be inaccurate for a number of cases. In recent work a new closure, the Quadrature Method of moments (QMOM), has been introduced, applied and validated. In our earlier work, QMOM was shown to be an efficient and accurate Method for tracking the moments of the particle size distribution (PSD) in a CFD simulation. However, QMOM presents two main disadvantages: (i) if applied to multi-variate distributions it loses simplicity and efficiency, and (ii) by tracking only the moments of the PSD, it does not represent realistically polydisperse systems with strong coupling between the internal coordinates and phase velocities. In order to address these issues, in this work the direct Quadrature Method of moments (DQMOM) is formulated, validated, and tested. DQMOM is based on the idea of tracking directly the variables appearing in the Quadrature approximation, rather than tracking the moments of the PSD. Nevertheless, for monovariate cases we show that QMOM and DQMOM yield identical results. In addition, we show how it is possible to extend the DQMOM to multivariate cases and some of relevant theoretical and numerical issues are discussed. These issues are discussed in the present work for homogeneous and one-dimensional flows. References to recent CFD applications of DQMOM to multiphase flows are provided as further proof of the utility of the Method.
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Quadrature Method of moments for population balance equations
Aiche Journal, 2003Co-Authors: Daniele Marchisio, Rodney O Fox, Jesse T Pikturna, Dennis R Vigil, Antonello BarresiAbstract:Although use of computational fluid dynamics (CFD) for simulating precipitation (and particulate systems in general) is becoming a standard approach, a number of issues still need to be addressed. One major problem is the computational expense of coupling a standard discretized population balance (DPB) with a CFD code, as this approach requires the solution of an intractably large number of transport equations. In this work the Quadrature Method of moments (QMOM) is tested for size-dependent growth and aggregation. The QMOM is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel. Moreover, model predictions are compared with a DPB to compare accuracy, computational time, and the number of scalars involved. Analysis of the relative performance of various Methods for treating aggregation provides readers with useful information about the range of application and possible limitations.
Robert Mcgraw - One of the best experts on this subject based on the ideXlab platform.
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bivariate extension of the Quadrature Method of moments for modeling simultaneous coagulation and sintering of particle populations
Journal of Colloid and Interface Science, 2001Co-Authors: Douglas L Wright, Robert Mcgraw, Daniel E RosnerAbstract:We extendthe application of moment Methods to multivariate suspended particle population problems-those for which size alone is insufficient to specify the state of a particle in the population. Specifically, a bivariate extension of the Quadrature Method of moments (QMOM) (R. McGraw, Aerosol Sci. Technol. 27, 255 (1997)) is presented for efficiently modeling the dynamics of a population of inorganic nanoparticles undergoing simultaneous coagulation and particle sintering. Continuum regime calculations are presented for the Koch-Friedlander-Tandon-Rosner model, which includes coagulation by Brownian diffusion (evaluated for particle fractal dimensions, D(f), in the range 1.8-3) and simultaneous sintering of the resulting aggregates (P. Tandon and D. E. Rosner, J. Colloid Interface Sci. 213, 273 (1999)). For evaluation purposes, and to demonstrate the computational efficiency of the bivariate QMOM, benchmark calculations are carried out using a high-resolution discrete Method to evolve the particle distribution function n(nu, a) for short to intermediate times (where nu and a are particle volume and surface area, respectively). Time evolution of a selected set of 36 low-order mixed moments is obtained by integration of the full bivariate distribution and compared with the corresponding moments obtained directly using two different extensions of the QMOM. With the more extensive treatment, errors of less than 1% are obtained over substantial aerosol evolution, while requiring only a few minutes (rather than days) of CPU time. Longer time QMOM simulations lend support to the earlier finding of a self-preserving limit for the dimensionless joint (nu, a) particle distribution function under simultaneous coagulation and sintering (Tandon and Rosner, 1999; D. E. Rosner and S. Yu, AIChE J., 47 (2001)). We demonstrate that, even in the bivariate case, it is possible to use the QMOM to rapidly model the approach to asymptotic behavior, allowing an immediate assessment of when previously established asymptotic results can be applied to dynamical situations of current/future interest. Copyright 2001 Academic Press.
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bivariate extension of the Quadrature Method of moments for modeling simultaneous coagulation and sintering of particle populations
Journal of Colloid and Interface Science, 2001Co-Authors: Douglas L Wright, Robert Mcgraw, Daniel E RosnerAbstract:Abstract We extendthe application of moment Methods to multivariate suspended particle population problems—those for which size alone is insufficient to specify the state of a particle in the population. Specifically, a bivariate extension of the Quadrature Method of moments (QMOM) (R. McGraw, Aerosol Sci. Technol. 27, 255 (1997)) is presented for efficiently modeling the dynamics of a population of inorganic nanoparticles undergoing simultaneous coagulation and particle sintering. Continuum regime calculations are presented for the Koch–Friedlander–Tandon–Rosner model, which includes coagulation by Brownian diffusion (evaluated for particle fractal dimensions, Df, in the range 1.8–3) and simultaneous sintering of the resulting aggregates (P. Tandon and D. E. Rosner, J. Colloid Interface Sci.213, 273 (1999)). For evaluation purposes, and to demonstrate the computational efficiency of the bivariate QMOM, benchmark calculations are carried out using a high-resolution discrete Method to evolve the particle distribution function n(ν, a) for short to intermediate times (where ν and a are particle volume and surface area, respectively). Time evolution of a selected set of 36 low-order mixed moments is obtained by integration of the full bivariate distribution and compared with the corresponding moments obtained directly using two different extensions of the QMOM. With the more extensive treatment, errors of less than 1% are obtained over substantial aerosol evolution, while requiring only a few minutes (rather than days) of CPU time. Longer time QMOM simulations lend support to the earlier finding of a self-preserving limit for the dimensionless joint (ν, a) particle distribution function under simultaneous coagulation and sintering (Tandon and Rosner, 1999; D. E. Rosner and S. Yu, AIChE J., 47 (2001)). We demonstrate that, even in the bivariate case, it is possible to use the QMOM to rapidly model the approach to asymptotic behavior, allowing an immediate assessment of when previously established asymptotic results can be applied to dynamical situations of current/future interest.
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description of aerosol dynamics by the Quadrature Method of moments
Aerosol Science and Technology, 1997Co-Authors: Robert McgrawAbstract:The Method of moments (MOM) may be used to determine the evolution of the lower-order moments of an unknown aerosol distribution. Previous applications of the Method have been limited by the requirement that the equations governing the evolution of the lower-order moments be in closed form. Here a new approach, the Quadrature Method of moments (QMOM), is described. The dynamical equations for moment evolution are replaced by a Quadrature-based approximate set that satisfies closure under a much broader range of conditions without requiring that the size distribution or growth law maintain any special mathematical form. The conventional MOM is recovered as a special case of the QMOM under those conditions, e.g., free-molecular growth, for which conventional closure is satisfied. The QMOM is illustrated for the growth of sulfuric acid-water aerosols and simulations of diffusion-controlled cloud droplet growth are presented.
M H Yas - One of the best experts on this subject based on the ideXlab platform.
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free vibration analysis of functionally graded annular plates by state space based differential Quadrature Method and comparative modeling by ann
Composites Part B-engineering, 2012Co-Authors: A Jodaei, Mostafa Jalal, M H YasAbstract:Abstract This paper deals with three-dimensional analysis of functionally graded annular plates through using state-space based differential Quadrature Method (SSDQM) and comparative behavior modeling by artificial neural network (ANN) for different boundary conditions. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space Method in thickness direction and one-dimensional differential Quadrature Method in radial direction is used to obtain the vibration frequencies. The state variables include a combination of three displacement parameters and three stress parameters. Numerical results are given to demonstrate the convergency and accuracy of the present Method. Once the semi-analytical Method is validated, an optimal ANN is selected, trained and tested by the obtained numerical results. In addition to the quantitative input parameters, support type is also considered as a qualitative input in NN modeling. Eventually the results of SSDQM and ANN are compared and the influence of thickness of the annular plate, material property graded index and circumferential wave number on the non-dimensional natural frequency of annular functionally graded material (FGM) plates with different boundary conditions are investigated. The results show that ANN can acceptably model the behavior of FG annular plates with different boundary conditions.
