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Variational base and solution strategies for non-linear force-based beam finite elements

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2012年第3期47卷 54-64页

作者： Saritas, Afsin Soydas, Ozan Middle E Tech Univ Dept Civil Engn TR-06800 Ankara Turkey

This paper presents the variational bases for the non-linear force-based beam elements. The element state determination of these elements is obtained exactly from a two-field functional with independent stress and strain fields. The variational base of the non-linear force-based beam elements implemented in a general purpose displacement-based finite element program requires the inclusion of independent displacement field in the formulation. For this purpose, a three-field functional is considered with independent displacement, stress, and strain fields. Various local and global solution strategies come out from the mixed formulation of the beam element, and these are shown to yield the algorithms presented for non-linear force formulation beam elements in literature;thus removing any doubts on their variational bases. The presented numerical examples demonstrate the accuracy and robustness of the solution algorithms adapted for mixed formulation elements over popularly used displacement-based beam finite elements even for large structural systems. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Mixed methods Finite element Element state determination solution algorithm Force formulation Flexibility method

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Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2014年 145卷 121-146页

作者： Coelho, Pedro J. Univ Lisbon Inst Super Tecn Dept Mech Engn LAETAIDMEC P-1049001 Lisbon Portugal

Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Discrete ordinates method Finite volume method Spatial and angular discretization solution accuracy solution algorithm Parallelization strategies

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Ideal adsorbed solution theory solved with direct search minimisation

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COMPUTERS & CHEMICAL ENGINEERING 2014年 71卷 235-240页

作者： Santori, Giulio Luberti, Mauro Ahn, Hyungwoong Univ Edinburgh Sch Engn Inst Mat & Proc Edinburgh EH9 3JL Midlothian Scotland

The ideal adsorbed solution theory (IAST) is the most widespread theory for multicomponent adsorption interpretation. It postulates the existence of an adsorbed phase which behaves as a Raoult ideal solution. The theory results in a system of nonlinear algebraic equations which are solved to know the composition of the adsorbed mixture at equilibrium. In this paper an investigation on an alternative method for the IAST equations solution is proposed which is based on the minimisation of an objective function representing the iso-spreading pressure condition. This approach to the solution of the IAST equations reduces in some cases the computational effort and mitigates the issues of the currently adopted approaches (inversion of functions and initial guess). For binary systems, direct search minimisation approach is faster than the classic IAST equations solution approach up to 19.0 (Dual Langmuir isotherm) and 22.7 times (Toth isotherm). In ternary systems, this difference decreases to 10.4 (O'Brien and Myers isotherm) times. Compared to FASTIAS approach, direct search minimisation is up to 4.2 times slower in ternary systems. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Ideal adsorbed solution theory Adsorption equilibria Adsorption thermodynamics solution algorithm

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Anisotropic solution-adaptive for turbulent viscous Cartesian grid method flow simulation

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AIAA JOURNAL 2002年第10期40卷 1969-1978页

作者： Wang, ZJ Chen, RF Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA ETA Inc Troy MI 48083 USA

An anisotropic viscous Cartesian grid method based on a 2(N) tree data structure is developed. The method is capable of handling complex geometries automatically. In addition, viscous boundary layers can be computed with high resolution, using automatically projected high aspect ratio viscous layer grids. Compared with a widely used Octree data structure, the 2(N) tree data structure supports anisotropic grid adaptations in any of the coordinate directions. Therefore, key flow features such as shock waves, wakes, and vortices can be captured in a very efficient manner. To handle the adaptive viscous Cartesian grid, an implicit, second-order, finite volume flow solver supporting arbitrary grids has been developed. A linearity-preserving least-squares solution reconstruction algorithm is used to achieve second-order accuracy. Furthermore, several directional adaptation criteria are developed and tested, The overall grid generation, flow simulation, and grid adaptation methodology is then demonstrated for a variety of flow problems, including a case of supersonic turbulent flow over a high-angle-of-attack missile configuration.

关键词： Transonic Flow solution algorithm Boundary Layer High Aspect Ratio Angle of Attack Shock Waves Vortex Structure Unstructured Grid Turbulence Models Ogive Cylinder

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Formulation and solution method of bounded path size stochastic user equilibrium models - consistently addressing route overlap and unrealistic routes

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2024年第2期20卷

作者： Duncan, Lawrence Christopher Watling, David Paul Connors, Richard Dominic Rasmussen, Thomas Kjaer Nielsen, Otto Anker Tech Univ Denmark Dept Technol Management & Econ Lyngby Denmark Univ Leeds Inst Transport Studies Leeds England Univ Luxembourg Fac Sci Technol & Med Esch Sur Alzette Luxembourg Tech Univ Denmark Dept Technol Management & Econ Bygningstorvet 116B DK-2800 Lyngby Denmark

Bounded Path Size (BPS) route choice models (Duncan et al, 2021) offer a theoretically consistent and practical approach to dealing with both route overlap and unrealistic routes. It captures correlations between overlapping routes by including correction terms within the probability relations, and has a consistent criterion for assigning zero probabilities to unrealistic routes while eliminating their path size contributions. The present paper establishes Stochastic User Equilibrium (SUE) conditions for BPS models, where the choice sets of realistic routes are equilibrated along with the route flows. solution existence/uniqueness are addressed. A generic solution algorithm is proposed, where realistic route choice sets are equilibrated from a pre-generated approximated universal set of routes. Numerical experiments on the Sioux Falls and Winnipeg networks show that BPS SUE models can be solved in feasible computation times compared to nonbounded versions, while providing potential for significantly improved robustness to the adopted master route choice set.

关键词： Bounded path size stochastic user equilibrium solution algorithm fixed-point convergence equilibrated choice sets

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Exact solution for nonlinear thermal diffusion and its use for verification

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2002年第3期16卷 366-372页

作者： McMasters, RL Zhou, ZF Dowding, KJ Somerton, C Beck, JV Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA Sandia Natl Labs Validat & Uncertainty Quantificat Prod Dept 9133 Tech Staff Albuquerque NM 87185 USA Michigan State Univ Dept Math E Lansing MI 48824 USA

An analytical solution is provided to the nonlinear diffusion equation, with the thermal conductivity given as a linear function of temperature. The derivation of the solution, and implications of it, are presented. The boundary and initial conditions associated with the solution provide applicability to specific cases. The solution is useful for verifying numerical (computer) solutions to thermal diffusion with temperature-dependent thermal conductivity. The (nonlinear) analytical solution is compared to a numerical solution from a finite element code to verify the accuracy of the code and to establish the order of convergence for the spatial discretization error.

关键词： Thermal Diffusion Thermal Conductivity Thermal Properties Fourier Number Convection Conduction Computer Programs Green's Function solution algorithm Thermal Analysis

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solution-ADAPTIVE STRUCTURED-UNSTRUCTURED GRID METHOD FOR UNSTEADY TURBOMACHINERY ANALYSIS .1. METHODOLOGY

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JOURNAL OF PROPULSION AND POWER 1994年第4期10卷 576-584页

作者： MATHUR, SR MADAVAN, NK RAJAGOPALAN, RG NASA AMES RES CTRMCAT INSTMOFFETT FIELDCA 94035

A solution-adaptive method for the time-accurate analysis of two-dimensional flows in multistage turbomachinery is presented. The method employs a hybrid structured-unstructured zonal grid topology in conjunction with appropriate modeling equations and solution techniques in each zone, thus combining the advantages of both structured and unstructured grid methods. The viscous flow region in the immediate vicinity of the airfoils is resolved on structured 0-type grids, while the rest of the domain is discretized using an unstructured mesh of triangular cells. In the inner regions, the Navier-Stokes equations are solved using an implicit, third-order accurate, upwind-biased scheme. The use of both central difference and upwind schemes is explored for the solution of the Euler equations in the outer regions. An efficient and robust grid adaptation strategy, including both grid refinement and coarsening capabilities, is developed for the unstructured grid regions. Methodologies for the accurate, conservative transfer of information at the interface between the structured and unstructured domains, as well as that between two unstructured grids in relative motion, are also developed. For generality, three-dimensional effects of stream-tube contraction are modeled. The numerical methodology is presented in detail in the present article (Part 1). Results obtained using this method and comparisons of these results with experimental data and earlier structured-grid based methods are presented in a companion article (Part II).

关键词： Unstructured Grid Turbomachinery Configurations Computational Fluid Dynamics Primitive Variable Unsteady Flows Navier Stokes Equations Adaptive Structures solution algorithm Runge Kutta Integration Static Pressure

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Numerical solution to Vinti's Problem

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2015年第9期38卷 1757-1764页

作者： Wiesel, William E. US Air Force Inst Technol Dept Aeronaut & Astronaut Astronaut Engn 2950 Hobson Way Wright Patterson AFB OH 45433 USA

A practical, calculable solution to Vinti's problem is offered. Vinti's problem describes the motion of a satellite orbiting an oblate planet, including the point mass and oblateness J2 terms and differing from the actual geopotential only at the higher harmonics. Vinti's original solution is extended to cover motion over a rotating Earth. An eccentric-anomaly-like transform removes the singularities in the elliptic integrals, rendering them accessible to numerical calculation. The prediction problem requires the simultaneous solution of two Kepler's equations. Reduction to canonical action angle variables can also be accomplished via numerical techniques. This new realization of Vinti's solution is free of series expansions that limit accuracy and uses only simple well-understood numerical techniques. Possible use of Vinti's solution for further efforts is discussed.

关键词： Saturn Eccentric Anomaly Kepler's Equation Earth Satellites Newton Raphson Method Right Ascension Perigee solution algorithm Orbital Elements Earth Core

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Parallel overset-grid Euler solution of generic wing pylon and finned store

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JOURNAL OF AIRCRAFT 2005年第5期42卷 1337-1339页

作者： Tarhan, E Kavsaoglu, MS Turkish Aircraft Ind Inc TUSAS Technol Dev Dept TR-06520 Ankara Turkey Istanbul Tech Univ Dept Aeronaut Engn TR-34469 Istanbul Turkey

SINCE the 1980s, after Steger et al. solved two- and three-dimensionalmultibody configurations, overset (chimera) grid systems became very popular because of theiradvantages in easing the grid generation. Later in 1994, Kao et al. used overset grids in order toperform grid adaptation in the flow regions where higher gradients exist. Tuncer preferred to useoverset grids for unsteady Navier-Stokes solutions of sinusoidally pitching airfoil. Cho et *** the generic wing/pylon/finned store (WPFS) configuration as a steady three-dimensionalproblem by using the overset grids. Later Lee et al. used overset grid system for the solution of astore release problem. Furthermore, Hoist also developed a new search algorithm for locating thedonor cells associated with the overset grid system used in the solution of wing-fuselage geometryby full potential equations. In the present work, a three-dimensional finite differencing scheme,multiblock structured Euler and thin-layer Navier-Stokes solver is modified in order to enhanceoverset grid capability and to run in a parallel-computing environment. A wing-store configurationand Eglin WPFS configuration are selected as the test cases for the validation purposes.

关键词： Message Passing Interface Pressure Coefficient Search algorithm Angle of Attack Parallel Computing Environment Navier Stokes Equations Freestream Mach Number solution algorithm Wind Tunnel Tests Pitching Airfoil

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Multiparameter solution Methods for Semistructured Aeroelastic Flutter Problems

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AIAA JOURNAL 2017年第10期55卷 3530-3538页

作者： Pons, Arion Gutschmidt, Stefanie Univ Cambridge Dept Engn Cambridge CB2 1PZ England Univ Canterbury Dept Mech Engn Christchurch 8041 New Zealand

This paper presents several new methods for the solution of aeroelastic flutter problems with a partial polynomial structure: problems consisting of a mix of polynomial and more complex nonlinear components. The focus is particularly on systems that use Theodorsen aerodynamics: for such systems, four new solution algorithms are devised. Two of these are direct but yield approximate results, and two are iterative. These algorithms are tested on an example system, and their computational characteristics are investigated and discussed. Three of them are suitable for practical implementation;the fourth is too computationally intensive to be of great practical use. Extensions and improvements to these algorithms, and the overall methods used, are also discussed.

关键词： Aerodynamic Coefficients solution algorithm Aeroelastic Stability Taylor Series Damping Coefficient Black Box MATLAB Angle of Attack Aircraft Flight Dynamics Newton's Method

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