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Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database

INTERNATIONAL JOURNAL OF PLASTICITY 2018年 103卷 168-187页

作者： Gupta, Akash Ben Bettaieb, Mohamed Abed-Meraim, Farid Kalidindi, Surya R. Tata Res Dev & Design Ctr Tam Consultancy Serv TCS Res Pune 411013 Maharashtra India Georgia Inst Technol Woodruff Sch Mech Engn Atlanta GA 30332 USA Arts & Metiers Paris Tech CNRS Lab Etud Microstruct & Mecan Mat LEM3 UMR 7239 4 Rue Augustin Presnel F-57078 Metz 3 France Univ Lorraine Lab Excellence Design Alloy Met Low mAss Struct D Lorraine France CNRS Georgia Tech UMI 2958 2-3 Rue Marconi F-57070 Metz France

The present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak-Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).

关键词： Crystal plasticity Viscoplastic material numerical algorithms Localized necking Spectral method

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Optimal strategies for the control of a train

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AUTOMATICA 1996年第4期32卷 519-532页

作者： Howlett, P Scheduling and Control Group Centre for Industrial and Applied Mathematics University of South Australia The Levels 5095 Australia

This paper describes a method for the calculation of optimal control strategies in an important engineering application. A train travels from one station to the next along a track with non-constant gradient. The journey must be completed within a given time, and it is desirable to minimise the fuel consumption. We assume that only certain discrete throttle settings are possible and that each setting determines a constant rate of fuel supply. This assumption is based on the control mechanism for a typical diesel-electric locomotive. For each fixed finite sequence of control settings, we show that fuel consumption is minimised only if the settings are changed when certain key equations are satisfied. The strategy determined by these equations is called a strategy of optimal type. Several realistic examples are given with the results of associated numerical calculations. The examples demonstrate the profound effect of even a small gradient on a strategy of optimal type. We show that a strategy of optimal type with alternate phases of coast and maximum power can be used to approximate the idealised minimum cost strategy.

关键词： train control optimal control discrete control optimal switching numerical algorithms

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REAL STRUCTURED SINGULAR-VALUE SYNTHESIS USING THE SCALED POPOV CRITERION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1995年第6期18卷 1244-1252页

作者： SPARKS, AG BERNSTEIN, DS University of Michigan Ann Arbor Michigan 48109-2118

The scaled Popov criterion is used to derive an upper bound for the worst-case H-2 norm over a set of linear, time-invariant, norm-bounded, block-structured parameter perturbations. This upper bound provides the basis for a robust controller synthesis procedure that minimizes the upper bound and guarantees asymptotic stability of the closed-loop system for ail real parameter perturbations in the specified set. numerical examples demonstrate the tradeoff between achievable H-2 performance and guaranteed robustness to real parameter perturbations as web as the reduction in conservatism due to the scaling matrix. Controllers designed for flexible structures using this technique are shown to have similarities to maximum entropy controllers designed for the same examples.

关键词： Popov Criterion Observability Gramian Entropy Flexible Structures White Noise Linear Quadratic Gaussian numerical algorithms Riccati Equations Aerospace Engineering numerical Optimization

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Discrete element simulation of shock wave propagation in polycrystalline copper

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2007年第3期55卷 589-614页

作者： Case, Simon Horie, Yasuyuki Atom Weapons Establishment Reading RG7 4PR Berks England USA Res Lab Eglin AFB FL USA

The implementation of the characteristic of compressive plasticity into the Discrete Element Code, DM2, while maintaining its quasi-molecular scheme, is described. The code is used to simulate the shock compression of polycrystalline copper at 3.35 and 11.0 GPa. The model polycrystal has a normal distribution of grain sizes, with mean diameter 14 pm, and three distinct grain orientations are permitted with respect to the shock direction;< 100 >, < 110 >, and < 111 >. Particle velocity dispersion (PVD) is present in the shock-induced flow, attaining its maximum magnitude at the plastic wave rise. PVD normalised to the average particle velocity of Delta u(y)/(u) over bar (P) = 0.05 and Delta u(y)/(u) over bar (P) = 0.087 are yielded for the 3.35 and 11.0 GPa shocks, respectively, and are of the same order as those seen in the experiment. Non-planar elastic and plastic wave fronts are present, the distribution in shock front position increasing with propagation distance. The rate of increase of the spread in shock front positions is found to be significantly smaller than that seen in probabilistic calculations on nickel polycrystals, and this difference is attributed, in the main, to grain interaction. Reflections at free surfaces yield a region of tension near to the target free surface. Due to the dispersive nature of the shock particle velocity and the non-planarity of the shock front, the tensile pressure is distributed. This may have implications for the spall strength, which are discussed. Simulations reveal a transient shear stress distribution behind the shock front. Such a distribution agrees with that put forward by Lipkin and Asay to explain the quasi-elastic reloading phenomenon. Simulation of reloading shocks show that the shear stress distribution can give rise to quasi-elastic reloading on the grain scale. Crown Copyright (c) 2006 Published by Elsevier Ltd. All rights reserved.

关键词： shock waves polycrystalline material numerical algorithms microstructures elastic-plastic material

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The distributed dislocation method applied to the analysis of elastoplastic strain concentrations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第5期47卷 1007-1026页

作者： Blomerus, PM Hills, DA Kelly, PA Univ Oxford Dept Engn Sci Oxford OX1 3PJ England

Conventionally, the use of continuous distributions of dislocations to model plasticity has been confined to the analysis of crack tip plasticity using linear arrays of dislocations, within the framework of plane analysis. By expanding this technique into a distribution of dislocation over an area, a method is developed to model the plasticity at stress raising feat;res such as notches or holes under plane strain conditions. The method explicitly takes account of the boundary conditions by using a dislocation solution which accounts for the presence of the stress-raise itself. Other free boundaries may be modelled more approximately using boundary elements which also correctly include the presence of the stress raiser. The dislocations are distributed over finite sized cells, and the solutions found for the strain fields compare favourably with both finite element and bounding Neuber and Glinka results. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： dislocations stress concentrations elastic-plastic material numerical algorithms

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Periodic solutions for spinning asymmetric rigid bodies with constant principal-axis torque

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2000年第5期23卷 781-788页

作者： Gick, RA Williams, MH Longuski, JM Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA

We analyze the motion of a spinning asymmetric rigid body subject to constant torque along one of the principal axes. Periodic solutions for the angular velocity vector and the corresponding kinematic parameters are given in terms of Fourier series expansions. Three semi-analytic solution methods are presented: one-period integration, Newton's method, and a perturbation method. These are compared for computational efficiency with a given error bound. The solutions apply to arbitrarily large attitude motions. When multiple period solutions are desired, these methods always prove more efficient than straightforward numerical integration. The techniques may be applied to onboard computations, maneuver analysis, and maneuver optimization.

关键词： numerical Integration Perturbation Method Euler Equations Thrust to Weight Ratio Spacecraft Maneuvers numerical algorithms Computing Three Degrees of Freedom Kinetic Energy Space Program

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Analytical Solutions to Two-Impulse Nondrifting Transfer Problems for Rendezvous in Elliptical Orbits

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2014年第3期37卷 775-788页

作者： Peters, Thomas V. Noomen, Ron Colmenarejo, Pablo GMV ES-28760 Madrid Spain

This paper develops the analytical solution to the nondrifting transfer problem for rendezvous in elliptical orbits. The transfer algorithm generates a nondrifting, passively safe trajectory between two spacecraft states by finding the appropriate maneuvers and transfer time. The nondrifting solution is derived first for Cartesian state vectors, which is useful for transferring to a terminal approach point that is defined in terms of such a Cartesian state vector. Next, the transfer problem is solved in terms of differential orbital elements. This second solution lends itself well to perform close-range rendezvous in elliptical orbits.

关键词： Orbit Determination Geostationary Transfer Orbit Orbital Period Orbit Rendezvous Automated Transfer Vehicle Flight Path Angle Kepler's Equation Propellant numerical algorithms Satellites

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Estimation of multiple heat sources in two-dimensional heat conduction problems

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2005年第3期19卷 388-394页

作者： Yang, CY Natl Kaohsiung Univ Appl Sci Dept Mold & Die Engn Kaohsiung 807 Taiwan

There have been some recent restrictions in the estimation of location and strength in inverse problems. One of the restrictions is that the problem is limited to the fixed number of heat sources. In other words, the moving sources cannot coincide in the moving path. Therefore, it is necessary to develop a method to estimate the location and the strength of various numbers of moving heat sources. A numerical algorithm combined with simplex method is proposed to determine the problem sequentially. A special feature of this method is that no prior knowledge of the number, the location, and the strength of the heat sources is necessary and that no sensitivity analysis is needed in the algorithm. Two examples are used to demonstrate the characteristics of the proposed method. The examples enable the investigation of the multiple moving sources with some coincided paths that lead to the number of sources varied with respect to the temporal coordinate. The numerical results show that the proposed method is an accurate and efficient method to determine the location and the strength of multiple moving sources in the inverse heat conduction problem.

关键词： Transient Heat Conduction Inverse Problems Dirac Delta Function numerical algorithms Finite Element Modeling Temperature Fields Conjugate Gradient Method Heat Transfer Coefficients Thermal Conductivity Finite Difference Method

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Inverse Design of Airfoil Using a Deep Convolutional Neural Network

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AIAA JOURNAL 2019年第3期57卷 993-1003页

作者： Sekar, Vinothkumar Zhang, Mengqi Shu, Chang Khoo, Boo Cheong Natl Univ Singapore Dept Mech Engn 9 Engn Dr 1 Singapore 117575 Singapore

This paper proposes an approach to perform the inverse design of airfoils using deep convolutional neural networks (CNNs). The conventional approaches are based on the solution of differential equations, which are either difficult to solve or take a tedious procedure to obtain the solution. As shown in this paper, the deep learning technique can be used effectively to obtain the airfoil shape from the coefficient of pressure distribution. More specifically, the CNN is applied due to its ability to handle any airfoil geometry without the need for complex parametrization. In the training phase, the pressure coefficient distribution is fed as input to the CNN to obtain a prediction model for the airfoil shape. In the testing phase, a new pressure coefficient distribution is given to the CNN model, generating an airfoil shape that is very close to the associated airfoil with an L2 error of less than 2% for most of the cases. An extensive investigation of the effects of various hyperparameters in the CNN architectures is performed. The results show that the CNN method is very efficient in terms of computational time and shows a competitive prediction accuracy. It thus constitutes an attractive new method in the inverse design of airfoils, especially when existing data can be readily exploited.

关键词： Airfoil Databases Deep Convolutional Neural Network Pressure Coefficient Airfoil Geometry Machine Learning Angle of Attack Aerodynamic Shape Optimization numerical algorithms Computational Fluid Dynamics Flow Conditions

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The connected-moments polynomial approach for Hamiltonian eigenvalues calculation and its application to the one-particle systems

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2008年第2期108卷 272-278页

作者： Bartashevich, Igor FESU Dept Phys St Petersburg 197378 Russia

The new connected-moments polynomial approach (CMP) is developed for evaluation of Hamiltonian eigenvalues. It is based on properties of specially designed polynomial and does not use any basis set and variational procedure. Like all the methods based on hamiltonain moments knowledge, the CMP is conceptually simple but is less tedious and is usually convergent even for very "crude" trial functions. This method is applicable not only to the ground state energy calculation but also to the excited states. The formalism is presented in two modifications: non-local (integral) and local (integral-free) ones. An accuracy of both versions is illustrated by numerical examples of Hamiltonian eigenvalues calculations for harmonic and anharmonic oscillators. (C) 2007 Wiley Periodicals, Inc.

关键词： connected-moments polynomial Hamiltonian moments one-dimensional Schrodinger equation numerical algorithms

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