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On the robustness and efficiency of integration algorithms for a 3D finite strain phenomenological SMA constitutive model

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2011年第1期85卷 107-134页

作者： Arghavani, J. Auricchio, F. Naghdabadi, R. Reali, A. Sharif Univ Technol Dept Mech Engn Tehran 111559567 Iran Univ Pavia Dipartimento Meccan Strutturale I-27100 Pavia Italy IUSS Ctr Adv Numer Simulat CeSNA Pavia Italy European Ctr Training & Res Earthquake Engn EUCEN Pavia Italy Sharif Univ Technol Inst Nanosci & Technol Tehran 111559567 Iran

Most devices based on shape memory alloys experience large rotations and moderate or finite strains. This motivates the development of finite-strain constitutive models together with the appropriate computational counterparts. To this end, in the present paper a three-dimensional finite-strain phenomenological constitutive model is investigated and a robust and efficient integration algorithm is proposed. Properly defining the variables, extensively used regularization schemes are avoided and a nucleation-completion criterion is defined. Moreover, introducing a logarithmic mapping, a new form of time-discrete equations is proposed. The solution algorithm as well as a suitable initial guess for the resultant nonlinear equations are also deeply discussed. Extensive numerical tests are performed to show robustness as well as efficiency of the proposed integration algorithm. Implementation of the integration algorithm within a user-defined subroutine UMAT in the commercial nonlinear finite element software ABAQUS/Standard makes also possible the solution of a variety of boundary value problems. The obtained results show the efficiency and robustness of the proposed approach and confirm the improved efficiency (in terms of solution CPU time) when a nucleation-completion criterion is used instead of regularization schemes, as well as when a logarithmic mapping is used for the time-discrete evolution equation instead of an exponential mapping. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： shape memory alloys finite strain solution algorithm logarithmic mapping exponential mapping UMAT

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A route-based solution algorithm for dynamic user equilibrium assignments

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2007年第10期41卷 1094-1113页

作者： Han, Sangjin UCL Ctr Transport Studies London WC1E 6BT England

The aim of this study is to establish a method to calculate good quality user equilibrium assignments under time varying conditions. For this purpose, it introduces a dynamic network loading method that can maintain correct flow propagation as well as flow conservation, and it shows a novel route-based solution algorithm. This novel algorithm turns out to be convenient and logically plausible compared to the conventional [Frank, M., Wolfe, P., 1956. An algorithm for quadratic programming. Naval Research Logistics Quarterly 3, 95-110] algorithm, because the former does not require evaluation of an objective function and it finds solutions maintaining correct flow propagation in the time-varying network conditions. The application of novel dynamic network loading method and solution algorithm to test networks shows that we can find high quality dynamic user equilibrium assignment. This is illustrated in an example network using the deterministic queuing model for a link performance function and associating costs and flows in a predictive way in discrete time. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： dynamic user equilibrium assignment solution algorithm flow propagation deterministic queuing model discrete time

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Unstructured-Grid Third-Order Finite Volume Discretization Using a Multistep Quadratic Data-Reconstruction Method

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AIAA JOURNAL 2010年第4期48卷 808-817页

作者： Caraeni, D. Hill, D. C. ANSYS Inc Lebanon NH 03766 USA

Finite volume discretizations on unstructured grids that are more than second-order-accurate have not yet gained wide acceptance. This is due to the high computational cost and memory requirements of the proposed schemes and the technical difficulties in achieving a high-order-accurate solution. It is especially true when considering flows in complex geometries. In this paper, a third-order cell-centered finite volume discretization is detailed that is based on quadratic data recovery, which is computationally efficient and has optimal memory requirements. The density-based flow-solver discretization and solution algorithm are described briefly, followed by a detailed presentation of the least-squares-based multistep quadratic data-reconstruction methodology proposed here. The paper is concluded with numerical examples to verify the accuracy and numerical efficiency of this high-order finite volume discretization.

关键词： Unstructured Grid solution algorithm Finite Volume Scheme Angle of Attack Mach Number Riemann Problem Turbulent Flow Primitive Variable Singular Value Decomposition Computing

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Equivalent nonlinear potential systems: Review of previous assumptions

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PROBABILISTIC ENGINEERING MECHANICS 2010年第1期25卷 142-152页

作者： Floris, Claudio Politecn Milan Dept Struct Engn I-20133 Milan Italy

Few exact solutions for the response of stochastic dynamical systems are available. Thus, the methods of the equivalent linearization and of the equivalent nonlinear system are often used. While the former yields a Gaussian response to a Gaussian excitation, the latter gives a non-Gaussian response, which is nearer to the exact unknown response of a nonlinear system. Among the equivalent nonlinear system methods the one based on the replacement of the actual dynamic system by means of a potential system is promising, Cavaleri and Di Paola (2000) 1411, as it leads to a fixed procedure differently from other methods. The procedure is developed under the assumption that the ratio of the moments E[Lambda(j)(X) over dot(2) and E [Lambda(j+1)] is a constant alpha not depending on j, A being the mechanical energy of the oscillator and (X) over dot its velocity. This relationship is demonstrated only for the so called Robert's oscillator, that is an oscillator with restoring force g(X) = omega(0) sgn(X) . |X|(nu), but in the above mentioned reference it is argued that it is valid in general. In this paper, numerical analyses are presented to ascertain its validity in order to apply the method to systems with different restoring forces. It is found that in some cases it is true, some others are doubtful, while there are cases in which alpha clearly depends on j. The effects of considering alpha constant when it is not are ascertained for a Duffing oscillator with linear plus cubic damping. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Stochastic dynamics Nonlinear systems Equivalent nonlinear system Potential systems solution algorithm

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Numerical Study of Fluid Flow and Heat Transfer Behaviors in a Physical Model Similar in Shape to an Actual Glass Melting Furnace and Its Experimental Verification

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MATERIALS TRANSACTIONS 2010年第10期51卷 1964-1972页

作者： Yen, Chien-Chih Hwang, Weng-Sing Natl Cheng Kung Univ Dept Mat Sci & Engn Tainan 70101 Taiwan

In this study a three dimensional numerical model based on the SOLA VOF method which Incorporates a Quasi two Phase method to consider the gas bubbling phenomena was developed to investigate the fluid flow and heat transfer behaviors in a glass melting furnace A reduced physical model with heating electrodes and air bubbling devices was also constructed to validate the numerical model The reduced physical model was made of an acrylic tank similar in shape to an actual glass melting furnace but reduced to one tenth in size The gas flow rate was determined at 6 67 x 10(-7) Nm(3)/s by the similarity conversions The electrode temperatures were set between 298 K to 373 K The flow trajectories of tracer particles and temperature field were measured to validate the accuracy and reliability of the numerical model The results show that the temperature and trajectories of tracer particles predicted by the numerical model were consistent with experimental observations/measurements from the physical model [doi 10 2320/matertrans M2010215]

关键词： numerical model glass melting furnace solution algorithm volume of fluid marker and cell (MAC) physical model gas bubbling electrode heating

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Generalized Nash Equilibrium Problems

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ANNALS OF OPERATIONS RESEARCH 2010年第1期175卷 177-211页

作者： Facchinei, Francisco Kanzow, Christian Univ Roma La Sapienza Dept Comp & Syst Sci A Ruberti Via Ariosto 25 I-00185 Rome Italy Univ Wurzburg Inst Math D-97074 Wurzburg Germany

The Generalized Nash Equilibrium Problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main prop... 详细信息

关键词： Nash Equilibrium Problem Pseudo game Social equilibrium Coupled constraints Existence Stability solution algorithm

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Efficient solution algorithms for thermomechanical contact problems based on a domain/boundary decomposition method

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INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2009年第6期44卷 610-622页

作者： Shin, Eui Sup Kim, Yong Uhn Jung, Sung Nam Chonbuk Natl Univ Dept Aerosp Engn Jeonju 561756 South Korea Konkuk Univ Dept Aerosp Engn Seoul 143701 South Korea

An efficient domain/boundary decomposition method is presented for fully coupled thermomechanical problems with contact boundaries. The whole domain is regarded as a union of subdomains, an interface, and contact interfaces. Penalized variational formulations are performed to connect the interface or contact interfaces with the neighboring subdomains that satisfy continuity constraints on the displacement and temperature fields. As a result, non-linear finite element computations due to the contact boundaries can be localized within a few subdomains or contact interfaces. Therefore, the computational efficiency can be enhanced considerably by devising suitable solution algorithms. A variety of numerical examples were tested to confirm the important features of the new algorithms presented. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Thermomechanical contact Domain/boundary decomposition Penalty method Finite element solution algorithm

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Enhanced-interval linear programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期199卷 323-333页

作者： Zhou, Feng Huang, Gordon H. Chen, Guo-Xian Guo, Huai-Cheng Peking Univ Coll Environm Sci & Engn Beijing 100871 Peoples R China Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada Peking Univ LMAM Beijing 100871 Peoples R China Peking Univ CCSE Sch Math Sci Beijing 100871 Peoples R China

An enhanced-interval linear programming (EILP) model and its solution algorithm have been developed that incorporate enhanced-interval uncertainty (e.g., A(+/-), B-+/- and C-+/-) in a linear optimization framework. As a new extension of linear programming, the EILP model has the following advantages. Its solution space is absolutely feasible compared to that of interval linear programming (ILP), which helps to achieve insight into the expected-value-oriented trade-off between system benefits and risks of constraint violations. The degree of uncertainty of its enhanced-interval objective function (EIOF) would be lower than that of ILP model when the solution space is absolutely feasible, and the EIOF's expected value could be used as a criterion for generating the appropriate alternatives, which help decision-makers obtain non-extreme decisions. Moreover, because it can be decomposed into two submodels. EILP's computational requirement is lower than that of stochastic and fuzzy LP models. The results of a numeric example further indicated the feasibility and effectiveness of EILP model. In addition, El nonlinear programming models, hybrid stochastic or fuzzy EILP models as well as risk-based trade-off analysis for El uncertainty within decision process can be further developed to improve its applicability. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Linear programming Optimization Uncertainty Feasibility solution algorithm Risk-based decision making

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Quaternion Analysis Tools for Engineering and Scientific Applications

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第2期32卷 686-693页

作者： Turner, James D. Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA

QUATERNION algebra has found a number of applications for engineering and scientific problems, including fluid mechanics [1], quantum mechanics [2,3], robotics [4,5], and spacecraft attitude control [5,6]. Unfortunate... 详细信息

关键词： Gaussian Elimination FORTRAN Computing Newton's Method Spacecraft Attitude Lyapunov Equation Search algorithm Numerical algorithms solution algorithm Fluid Mechanics

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Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2009年第5期49卷 748-761页

作者： Bulgakov, V. K. Strigunov, V. V. Pacific Ocean State Univ Khabarovsk 680035 Russia

The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.

关键词： optimal control optimal trajectories Pontryagin maximum principle boundary value problem integral curves solution algorithm numerical study

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