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A 3-D model for void evolution in viscous materials under large compressive deformation

INTERNATIONAL JOURNAL OF PLASTICITY 2015年 74卷 192-212页

作者： Feng, Chao Cui, Zhenshan Shanghai Jiao Tong Univ Inst Forming Technol & Equipment Shanghai 200030 Peoples R China

The paper presents a study on the evolution of dilute ellipsoidal voids in power-law viscous materials under triaxial loading condition. Firstly, referring to the work of Eshelby (1957), a semi-analytical expression is deduced to evaluate the deformation of ellipsoidal void in linear viscous material. Then, for the non-linear viscous materials, the concept of mesoscopic representative volume element (RVE), is applied to study the voids deformation under different stress states, and a rigid visco-plastic finite element (FE) procedure is applied to solve the RVE model. For the condition of stress triaxiality ranging from -1 to +1, it is found that the voids deformation behaves similarly in both linear and non-linear viscous materials. Due to this fact, the framework of the expression of void deformation in linear viscous material is inferred to describe the void evolution in nonlinear viscous materials, while the parameters of the expression are re-evaluated for the specific materials. The results show that the void shapes and loading conditions take important roles in the void evolution. Therefore, for an ellipsoidal void, the void radius strain rate is expressed as a function of the void shape index, the macroscopic stress and strain-rate. Meanwhile, the void volume strain rate is obtained as a function of the void radius strain rate. This void evolution model is integrated into FE code and applied to study the void closure problem in the metal forming process. The FE simulation provides the evolution of macroscopic stress, strain and strain-rate, and then the model is used to calculate the changes of void shape and volume in each step of the deformation history. It can be found that the results predicted by this model agree well with the analytical solution, experiment measurements and numerical simulations with embedded void shapes, which demonstrates that this method can be appropriately used to predict the void evolution during the large compressive deformation

关键词： Voids and inclusions Viscoplastic material numerical algorithms Representative volume element

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A PERSPECTIVE OF THEORETICAL AND APPLIED COMPUTATIONAL FLUID-DYNAMICS

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AIAA JOURNAL 1985年第3期23卷 328-341页

作者： KUTLER, P NASA Ames Research Center Moffett Field California

This paper discusses the advantages and disadvantages that underlie the growth of computational fluid dynamics (CFD) and its increasing role in the design of new flight vehicles. CFD tools are important because they reduce the amount of experimental development work from what would have been required without their use. There are both primary and secondary pacing items that must and are being addressed by the CFD research community. They include (1) three-dimensional grid generation, (2) turbulence modeling, (3) algorithm development, and (4) computer mainframe design advances. The secondary pacing items include (1) algorithm development, (2) complex geometry definition, and (3) input and output data processing. Most of this paper is devoted to a discussion of these pacing items. In addition, user demands on computational tools for simulations are also discussed.

关键词： Applied Computational Fluid Dynamics Software Development Ames Research Center Aerospace Engineering Reynolds Averaged Navier Stokes Aerodynamic Flowfield Scientific Computing Navier Stokes Solver Turbulence Models numerical algorithms

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A physically-based constitutive model for bcc crystals with application to polycrystalline tantalum

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1998年第6期46卷 1009-1038页

作者： Nemat-Nasser, S Okinaka, T Ni, LQ Univ Calif San Diego Dept Appl Mech & Engn Sci Ctr Excellence Adv Mat La Jolla CA 92093 USA

Based on the results of an extensive series of systematic experiments on commercially pure tantalum (bcc crystals), a physically-based, rate-and temperature-dependent constitutive model is proposed for bcc single crystals and is applied to simulate the experimental results, using the Taylor averaging method. The model calculation is based on a new efficient algorithm for the numerical solution of the finite deformation of bcc single crystals, involving up to 48 potentially active slip systems. The accuracy and efficiency of the proposed algorithm are checked through comparison with the results of the conventional explicit Euler time-integration scheme, using a very large number of timesteps. The model effectively simulates a large body of experimental data, over a broad range of strain rates (10(-3) x 10(4)/s), and temperatures (77 to 1300 K), with strains exceeding 1000%, using very few adjustable parameters whose values are fixed at the outset for a given material. All other involved constitutive parameters are estimated based on the crystal structure and the physics of plastic flow. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： constitutive behavior crystal plasticity polycrystalline material numerical algorithms bcc crystal

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Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory Optimization Problems

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2020年第4期43卷 645-655页

作者： Ozaki, Naoya Campagnola, Stefano Funase, Ryu Japan Aerosp Explorat Agcy Dept Spacecraft Engn Sagamihara Kanagawa 2525210 Japan CALTECH Jet Prop Lab Outer Planet Mission Anal Group 4800 Oak Grove Dr Pasadena CA 91109 USA Univ Tokyo Dept Aeronaut & Astronaut Bunkyo Ku 7-3-1 Hongo Tokyo 1138656 Japan

Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. This problem is among the most complex in control theory, and no practically applicable method to low-thrust trajectory optimization problems has been proposed to date. This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. The proposed algorithm uses the unscented transform to convert a stochastic optimal control problem into a deterministic problem, which is then solved by trajectory optimization methods such as differential dynamic programming. Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution.

关键词： Hamilton Jacobi Bellman (HJB) Equations Linear Time Invariant System Monte Carlo Simulation Space Missions Nonlinear Systems Cumulative Distribution Function numerical algorithms numerical Optimization Earth Control Algorithm

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Close-approach trajectories in the elliptic restricted problem

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1997年第4期20卷 797-802页

作者： Prado, AFBD Instituto Nacional de Pesquisas Espaciais Sao Paulo Jose dos Campos Sao Paulo 12227-010 Brazil

The swing-by maneuver uses a close approach with a celestial body to modify the velocity, energy, and angular momentum of a spacecraft's orbit. The swing-by trajectories are studied and classified under the model given by the elliptic restricted three-body problem. Several simulations are made to show the effects of the eccentricity of the primaries in this maneuver. The position of the secondary in its orbit (specified by its true anomaly) also has effects on the results, and they are quantified. To show the results, the orbit of the spacecraft is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct, and hyperbolic retrograde. Then the modification in the orbit of the spacecraft due to the close approach is shown in plots that specify from which group the spacecraft's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters vary is performed, and the influence of each of them is shown and explained. The results presented can also be used to find optimal sets of parameters for several types of problems, such as finding an escape orbit that has minimum velocity at periapsis and other related problems.

关键词： Periapsis Giant Planet numerical Integration Patched Conic Approximation numerical Simulation Celestial Mechanics numerical algorithms Spacecraft Orbits Runge Kutta Methods Keplerian Orbit

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ACCELERATED CONVERGENCE TO STEADY-STATE BY GRADUAL FAR-FIELD DAMPING

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AIAA JOURNAL 1992年第5期30卷 1220-1227页

作者： KARNI, S University of Michigan Ann Arbor Michigan 48109

Reflections from artificial boundaries inhibit convergence of transient solutions to their steady limit. Far-field damping operators to suppress such reflections are presented for general first-order hyperbolic systems, and particular reference is made to the compressible Euler equations. The damping operator has the following properties: 1) no reflections are generated due to the introduction of the damping terms and 2) different wave systems may be damped at different rates. Feature 1 is imperative for successful damping and enables the attenuation of waves over relatively short length scales. Feature 2 enables the damping operator to act selectively on the outgoing waves alone, leaving the incoming waves unharmed. This property is desirable in genuine time-dependent problems where consistent information should be allowed to propagate from the artificial boundaries into the domain. Results for compressible Euler flows past airfoils show the potential of far-field damping in substantially accelerating convergence, particularly in fully subsonic problems.

关键词： Bernoulli's Equation Freestream Conditions Compressible Flow Damping Coefficient numerical algorithms Symmetric Airfoil numerical Stability Specific Enthalpy Damping Matrix Specific Heat

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Teaching a generative model: Mathematical formulation and solution framework

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 130卷 119-126页

作者： Wang, Honggang Zhang, Bo Univ La Verne Dept Appl Business Sci & Econ Coll Business & Publ Management La Verne CA 91750 USA IBM Thomas J Watson Res Ctr Yorktown Hts NY USA

We develop the mathematical formulation for teaching generative models to a learner whose learning processes and cognitive behaviors may be analytically intractable, but can be simulated by numerical processes. The model considers the learner's bias (prior knowledge) or memory process by using stochastic models. We also present an optimization framework for solving the involved non-convex, stochastic optimization problems associated with machine teaching. The algorithm design and the conditions and analysis are discussed for local convergence properties of the proposed optimization algorithms. In the paper, we discuss a number of example cases to illustrate the algorithmic ideas and demonstrate their efficiency.

关键词： Statistical learning Machine teaching Data driven optimization Computer simulation numerical algorithms

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PARALLEL algorithms FOR INITIAL-VALUE PROBLEMS - PARALLEL SHOOTING

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PARALLEL COMPUTING 1992年第6期18卷 661-673页

作者： KHALAF, BMS HUTCHINSON, D UNIV LEEDS SCH COMP STUDIESDIV COMP SCILEEDS LS2 9JTW YORKSHIREENGLAND

The purpose of this paper is to consider the implementation of the parallel shooting for solving IVPs using a multiprocessor computing system. The paper shows the significance of these methods and demonstrates their e... 详细信息

关键词： PARALLEL COMPUTING INITIAL VALUE PROBLEMS numerical algorithms

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Fatigue crack-growth behavior of materials in viscous fluid environments

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第9期47卷 1843-1871页

作者： Yi, KS Cox, BN Dauskardt, RH Stanford Univ Dept Mat Sci & Engn Stanford CA 94305 USA Rockwell Int Sci Ctr Thousand Oaks CA 91360 USA

The potent effect of the hydrodynamic pressure developed in the wake of a crack growing under cyclic loads in a viscous fluid environment is considered. While existing semi-analytical solutions provide an estimate of the hydrodynamic pressure effect, they are inherently restricted by the assumption of specific crack opening profiles. To correct this limitation and to extend the study to a complete range of materials and fluid environments, a fully consistent numerical approach was developed. A self-consistent fracture mechanics solution procedure is derived initially for atomistically sharp cracks in brittle materials, and then extended to include the effect of crack tip blunting in more ductile materials. Three important dimensionless parameters are identified through which effects of various physical properties on crack-growth behavior can be examined. These include specimen geometry, material properties, fluid viscosity and cyclic loading conditions. General plots are constructed spanning wide ranges of these dimensionless parameters so that the hydrodynamic pressure contribution to crack-growth rates can easily be estimated for a complete range of materials, fluid environments and loading parameters. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： fracture fluid crack mechanics cyclic loading numerical algorithms

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AN ORTHOGONAL RESIDUAL PROCEDURE FOR NONLINEAR FINITE-ELEMENT EQUATIONS

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INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 1995年第5期38卷 823-839页

作者： KRENK, S Department of Building Technology and Structural Engineering University of Aalborg Aalborg Denmark

A general and robust solution procedure for non-linear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state. The method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector. The orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters. Passage of load and displacement limit points is discussed as well as the relation to line search, minimum residual, and are-length methods. The method is illustrated by two examples.

关键词： numerical algorithms PATH FOLLOWING TECHNIQUE NONLINEAR EQUATIONS NONLINEAR FINITE ELEMENTS

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