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ALTERNATIVE APPROACH TO THE SOLUTION OF LAMBERT PROBLEM

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1992年第4期15卷 1003-1009页

作者： NELSON, SL ZARCHAN, P Charles Stark Draper Laboratory Inc. Cambridge Massachusetts 02139

A method for solving the two-point, two-body orbital transfer boundary-value problem, commonly referred to as Lambert's problem, is presented. Previous algorithms have depended heavily on the geometric properties of conic sections to obtain an iterative solution. An alternative approach is offered, making use of velocity and time functions of the flyout angle that have been derived directly from the equations of motion. A procedure is presented that rapidly iterates directly on the flyout angle until the desired initial velocity vector can be obtained.

关键词： Lambert's Problem Earth Hyperbolic Trajectories Orbital Transfer Iterative Solution Apollo Guidance Computer Boundary Value Problems Spacecraft Navigation numerical algorithms Missile Guidance

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An iterative predictor-corrector approach for modeling static and kinetic friction in interactive simulations

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GRAPHICAL MODELS 2015年 82卷 29-42页

作者： Arikatla, Venkata S. De, Suvranu Rensselaer Polytech Inst Dept Mech Aerosp & Nucl Engn Ctr Modeling Simulat & Imaging Med 1108th St Troy NY 12180 USA

In this paper we propose a novel iterative predictor-corrector (IPC) approach to model static and kinetic friction during interactions with deformable objects. The proposed IPC method works within the purview of the implicit mixed linear complementarity problem (MLCP) formulation of collision response. In IPC, first the potential directions of frictional force are determined at each contact point by leveraging the monotonic convergence of an iterative MLCP solver. All the contacts are then categorized into either static or kinetic frictional states. Linear projection constraints (LPCs) are used to enforce 'stiction' for contacts in static friction. We propose a modified iterative constraint anticipation (MICA) approach that can resolve the LKs while simultaneously solving the MLCP. Our method can handle arbitrary models including asymmetric and anisotropic friction models. IPC requires low memory and is highly tunable. Multiple example problems are solved to demonstrate the method. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Finite element Simulation numerical algorithms

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A general approach to waveform relaxation solutions of nonlinear differential-algebraic equations: The continuous-time and discrete-time cases

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2004年第9期51卷 1770-1780页

作者： Jiang, YL Xi An Jiao Tong Univ Inst Informat & Syst Sci Sch Sci Xian 710049 Peoples R China

For a general class of nonlinear differential-algebraic equations of index one, we develop and unify a convergence theory on waveform relaxation (WR). Convergence conditions are achieved for the cases of continuous-time and discrete-time WR approximations. Most of known convergence results in this field can be easily derived from the new theory established here.

关键词： continuous-time and discrete-time waveform relaxation (WR) iterations convergence conditions circuit simulation differential-algebraic equations (DAEs) numerical algorithms WR

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Framework for capacity credit assessment of electrical energy storage and demand response

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第9期10卷 2267-2276页

作者： Zhou, Yutian Mancarella, Pierluigi Mutale, Joseph Univ Manchester Sch Elect & Elect Engn Elect Energy & Power Syst Grp Manchester M13 9PL Lancs England

The use of electrical energy storage (EES) and demand response (DR) to support system capacity is attracting increasing attention. However, little work has been done to investigate the capability of EES/DR to displace generation while providing prescribed levels of system reliability. In this context, this study extends the generation-oriented concept of capacity credit (CC) to EES/DR, with the aim of assessing their contribution to adequacy of supply. A comprehensive framework and relevant numerical algorithms are proposed for the evaluation of EES/DR CC, with different traditional' generation-oriented CC metrics being extended and a new CC metric defined to formally quantify the capability of EES/DR to displace conventional generation for different applications (system expansion, reliability increase etc.). In particular, specific technology-agnostic models have been developed to illustrate the implications of energy capacity, power ratings, and efficiency of EES, as well as payback characteristics and customer flexibility (that often also depend on different forms of storage available to customers) of DR. Case studies are performed on the IEEE RTS to demonstrate how the different characteristics of EES/DR can impact on their CC. The framework developed can thus support the important debates on the role of EES/DR for smart grid planning and market development.

关键词： energy storage numerical analysis smart power grids power markets reliability capacity credit assessment electrical energy storage demand response EES DR generation-oriented concept capacity credit CC metric system reliability numerical algorithms specific technology-agnostic models energy capacity power ratings payback characteristics customer flexibility IEEE RTS smart grid planning market development

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An atomistically informed kinetic Monte Carlo model for predicting solid solution strengthening of body-centered cubic alloys

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INTERNATIONAL JOURNAL OF PLASTICITY 2019年 122卷 319-337页

作者： Shinzato, Shuhei Wakeda, Masato Ogata, Shigenobu Osaka Univ Grad Sch Engn Sci Dept Mech Sci & Bioengn 1-3 Machikaneyama Toyonaka Osaka 5608531 Japan NIMS 1-2-1 Sengen Tsukuba Ibaraki 3050047 Japan Kyoto Univ Ctr Element Strategy Initiat Struct Mat ESISM Sakyo Ku Kyoto 6068501 Japan

In order to predict solid solution strengthening in body-centered cubic dilute substitutional alloys, we developed an atomistically informed kinetic Monte Carlo (kMC) model for screw dislocation motion, which is a major determinant of the yield strength of the BCC alloys. The kMC model only requires parameters obtainable using atomic simulations. The parameters in the developed kMC model were actually determined for Fe Si dilute alloys using atomistically derived activation energies of kink-pair nucleation and kink migration as well as their stress dependencies. The activation energies were computed using the nudged elastic band method with developed interatomic potentials based on first-principles density functional theory. Eventually, the critical resolved shear stress (CRSS), activation volume of the dislocation glide, and their temperature and solute concentration dependencies were directly obtained by two dimensional kMC dislocation glide simulations. Our kMC model qualitatively reproduced the trends of experimentally observed temperature and concentration dependencies of CRSS, and thus it can naturally describe solid solution strengthening, and softening without any empirical information. In addition, the limitations of the two dimensional model, including single slip and lack of non-Schmid effect, are discussed, which results in quantitative difference with the experimental CRSS.

关键词： Dislocations Metallic material numerical algorithms Strengthening mechanisms

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Uniqueness of a class of nonlinear electrostatic field problems

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IEE PROCEEDINGS-SCIENCE MEASUREMENT AND TECHNOLOGY 1999年第4期146卷 175-181页

作者： de Hoop, AT Lager, IE Delft Univ Technol Fac Informat Technol & Syst Lab Electromagnet Res NL-2628 CD Delft Netherlands Delft Univ Technol Fac Informat Technol & Syst Int Res Ctr Telecommun Transmiss & Radar NL-2628 CD Delft Netherlands

The uniqueness properties of a class of nonlinear electrostatic field problems are investigated. The study was motivated by the development of numerical algorithms to analyse the performance of nonlinear semiconducting electron devices. Here, existence and uniqueness of the solution are prerequisites for the numerical results to have any meaning at all.

关键词： Mathematical analysis Function theory, analysis 3D Euclidean space nonlinear semiconducting electron device nonlinear electrostatic field problems Electrostatics, magnetostatics semiconductor device models constitutive operators classical field theory electric fields uniqueness properties numerical algorithms electric potential performance analysis interface boundary conditions Classical field theory Semiconductor device modelling, equivalent circuits, design and testing partial differential equations Electrostatics

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REDUCED-ORDER COMPENSATION - LINEAR-QUADRATIC REDUCTION VERSUS OPTIMAL PROJECTION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1988年第4期11卷 328-335页

作者： GREELEY, SW HYLAND, DC Harris Corp. Melbourne FL

Six methods for design of reduced-order compensation are compared using an example problem. The methods considered comprise five linear-quadratic reduction techniques, reviewed in a recent paper by Liu and Anderson, and the Optimal Projection theory as implemented via a simple homotopy solution algorithm. Design results obtained by the different methods for 42 different design cases are compared with respect to closed-loop stability and transient response characteristics. Of the linear-quadratic reduction procedures, two are found to offer distinctly superior performance. However, only the Optimal Projection method provided stable designs in all cases. Further details are given on the performance of the numerical algorithm for solving the optimal projection equations and the corresponding design results. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Closed Loop System Solution Algorithm Optimal Projection Equations numerical algorithms Riccati Equations Topological Degree Theory Iterative Solution Computing

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Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第6期47卷 1219-1238页

作者： Sarma, G Zacharia, T Oak Ridge Natl Lab Oak Ridge TN 37831 USA

An integration scheme is presented for modeling the texture evolution and stress-strain response of elasto-viscoplastic polycrystalline materials. Single crystal kinematics based on a multiplicative decomposition of the deformation gradient is used to obtain an evolution equation for the crystal elastic deformation gradient. An implicit scheme to integrate this equation is presented which is stable and efficient. The reorientation of the crystal as well as the elastic strain can then be obtained from a polar decomposition of the elastic deformation gradient. numerical studies are presented using material parameters for aluminum (FCC crystals) and zircaloy (HCP crystals) to demonstrate the general nature of the model. Predictions of the model are also compared with those obtained using a rigid-viscoplastic polycrystal model which neglects the elastic response. Retaining the elastic response makes the model useful for large deformation analyses where both anisotropy due to texture as well as elastic effects such as springback and residual stresses are important. (C) 1999 Elsevier Science Ltd, All rights reserved.

关键词： constitutive behavior crystal plasticity elastic-viscoplastic material polycrystalline material numerical algorithms

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High-Fidelity Flexibility-Based Component Mode Synthesis Method with Interface Degrees of Freedom Reduction

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AIAA JOURNAL 2016年第11期54卷 3619-3631页

作者： Kim, Jin-Gyun Markovic, Damijan Korea Inst Machinery & Mat Mech Syst Safety Res Div 156 Gajeongbuk Ro Daejeon 34103 South Korea Nucl Engn Basic Design Dept Elect France Dept Mech Engn 12-14 Ave Dutrievoz F-69628 Villeurbanne France

The partitioned structural equations of motion via the method of localized Lagrange multipliers (PALM) consist of internal and interface variables. The model reduction achieved based on PALM is called flexibility-based component mode synthesis (F-CMS), and it thus far has concentrated on reducing the internal degrees of freedom (DOFs) or reducing the internal and interface DOFs at once. In this work, well-defined three-level reduction formulations of the F-CMS method are proposed for better precision: internal DOFs, the localized Lagrange multipliers, and the interface boundary displacement. The proposed formulations include three different reduction techniques for the interface boundary displacement for better computational efficiency. numerical experiments indicate that the proposed formulations can substantially reduce the overall reduced-order models further without compromising the accuracy, thus achieving a substantial additional reduction of computational cost compared with the previous works. In addition, the performance of a novel error estimator in the overall reduction levels is tested.

关键词： Degrees of Freedom Lagrange Multipliers Finite Element Modeling Poisson's Ratio Structural Modeling Material Properties Structural System Structural Dynamics numerical algorithms Parallel Computing

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A multiscale method for dislocation nucleation and seamlessly passing scale boundaries

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INTERNATIONAL JOURNAL OF PLASTICITY 2011年第12期27卷 2103-2124页

作者： Fan, Jinghong Stewart, Ross J. Zeng, Xiangguo Alfred Univ Kazuo Inamori Sch Engn Alfred NY 14802 USA Shichuan Univ Dept Engn Mech Chengdu 610065 Peoples R China

In the concurrent multiscale analysis, it is difficult to have truly seamless transition between the atomistic and continuum scale. This situation is even worse when defects pass through the boundary between different scales. For example, there is a lack of effective methods to handle the dislocation passing through scale boundaries which is important to investigate plasticity at the nanoscale. In this paper, the generalized particle (GP) method proposed by the first author is further developed so that a seamless transition and dislocation passing between different scales can be realized. Specifically, the linkage between different scales is through material neighbor-link cells (NLC) with scale duality. This indicates that material elements can be high-scale particles through a lumping process and can also be atoms via decomposition depending on the needs of the simulation. At the interface, the information transfer from bottom scale-up or from top scale-down is through the particles or atoms in the NLC. They are with the same material structure, all possess nonlocal constitutive behavior;thus, the smooth transition at the interface between different scales can be attained and validated to avoid non-physical responses. To save degrees of freedom, atoms are lumped together into a generalized particle in the domain in which the deformation gradient is near homogeneous. On the other hand, when defects such as dislocations in the atomistic domain are near the particle domain, the particles along dislocation propagation path and its surrounding region will be decomposed into atoms so dislocations can freely pass through the scale boundary and propagate inside the model just as it propagates in the deformed atomistic crystal structure. The method is verified first for seamless transition of variables at the scale boundary by a one-dimensional model and then verified for dislocation nucleation and propagation passing through scale boundaries in two cases, one is near the f

关键词： Dislocations Constitutive behavior numerical algorithms Metallic material

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