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Reconfiguration of Three-Craft Coulomb Formation Based on Patched-Conic-Section Trajectories

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2016年第3期39卷 474-486页

作者： Xu, Yinan Wang, Shuquan Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA Chinese Acad Sci Technol & Engn Ctr Space Utilizat Key Lab Space Utilizat Beijing 100094 Peoples R China

This paper investigates the nonequilibrium fixed-shape three-craft Coulomb formation reconfiguration problem. Being aware that using the feedback-control approach might result in the chattering of the charges due to the nonequilibrium nature of the system dynamics, this paper proposes a trajectory planning approach to accomplish the reconfiguration. Entire maneuver trajectories are divided into multiple phases. During each phase, only two of the three craft are charged. In this way, the relative trajectory of the charged spacecraft during a certain phase is a conic section. Entire trajectories are composed of patched conics and/or straight lines. The procedures determining the three-phase maneuver strategy are developed, including a preadjusting phase and two transition phases. numerical simulations demonstrate the effectiveness of the algorithm and the elegance of the charge histories.

关键词： Feedback Control numerical Simulation Specific Angular Momentum Secant Method Earth Kepler's Equation Formation Flying Ion Engines numerical algorithms Three Degrees of Freedom

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Computing the Homology of Semialgebraic Sets. II: General Formulas

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2021年第5期21卷 1279-1316页

作者： Buergisser, Peter Cucker, Felipe Tonelli-Cueto, Josue Tech Univ Berlin Inst Math Berlin Germany City Univ Hong Kong Dept Math Hong Kong Peoples R China Sorbonne Univ Inria Paris Paris France Sorbonne Univ IMJ PRG OURAGAN Team Paris France

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm works in weak exponential time. This means that outside a subset of data having exponentially small measure, the cost of the algorithm is single exponential in the size of the data. This extends the work in Part I to arbitrary semialgebraic sets. All previous algorithms proposed for this problem have doubly exponential complexity.

关键词： numerical algorithms Homology groups Weak complexity Semialgebraic sets

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Limit-cycle oscillation induced by nonlinear aerodynamic forces

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AIAA JOURNAL 2002年第11期40卷 2197-2205页

作者： Dotson, KW Baker, RL Sako, BH Aerosp Corp Struct Dynam Dept Los Angeles CA 90009 USA Aerosp Corp Fluid Mech Dept Los Angeles CA 90009 USA

The aerodynamic How state on launch vehicle payload fairings and aircraft wings can change abruptly during transonic flight if the angle of attack reaches a critical value. The nonlinear pressure variation associated with a flow-state change induces transient structural responses that may converge to a limit-cycle oscillation (LCO). In this steady state, the work conducted during the flow-state changes balances the energy dissipation from structural damping. Analysis of this transonic LCO, phenomenon is often conducted using a semi-empirical, unsteady pressure variation in which the levels for the flow states are determined from steady wind-tunnel test data. The presented theory addresses the condition in which the flow-state changes occur near a quasi-steady, nonzero angle of attack. The analysis for the resulting asymmetric forcing function complements the authors' existing derivations for a symmetric forcing function at zero angle of attack. Both the asymmetric and the symmetric analyses develop closed-form equations for the structural response frequency and amplitude. These expressions show that the solution space contains a subcritical Hopf bifurcation when the critical angle of attack equals the quasi-steady angle of attack. They also show that a saddle-node bifurcation, or fold, corresponds to the critical angle of attack beyond which LCO will not occur for a given quasi-steady angle of attack.

关键词： Aerodynamic Damping Critical Angle of Attack Structural Damping Launch Vehicles Structural Response Aircraft Wings Wind Tunnel Tests numerical algorithms Free Vibrations numerical Analysis

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Shock-shape alteration caused by interaction with organized structures

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AIAA JOURNAL 2000年第6期38卷 1002-1009页

作者： Erlebacher, G Hussaini, MY Florida State Univ Dept Math & Comuputat Sci & Informat Technol Tallahassee FL 32306 USA Florida State Univ Dept Comuputat Sci & Informat Technol Tallahassee FL 32306 USA

The dynamics of shock waves interacting with organized structures such as a vortex or a temperature spot are examined. In particular, the shock structure, i.e., its shape and velocity, is investigated. Approximate scalings in some asymptotic limits are derived for the shock displacement and velocity in terms of the upstream Mach number and the amplitude of the vortex or temperature spot. Two sources of nonlinearity are identified, and their effect on the dynamics of shocks are studied. Some light is shed on the incipient stage in the formation of branch points.

关键词： Vortex Velocity Mach Numbers Rankine Hugoniot Conditions Vorticity Universal Gas Constant numerical Simulation numerical algorithms Shock Front

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Implementation and application of a temperature-dependent Chaboche model

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 75卷 121-140页

作者： Zhou, C. Chen, Z. Lee, J. W. Lee, M. G. Wagoner, R. H. S China Univ Technol Sch Mech & Automot Engn Guangzhou 510641 Guangdong Peoples R China Ohio State Univ Dept Mat Sci & Engn Columbus OH 43210 USA Pohang Univ Sci & Technol Grad Inst Ferrous Technol Pohang 790784 South Korea Korea Inst Mat Sci Mat Deformat Dept Chang Won 642831 South Korea Korea Univ Dept Mat Sci & Engn Seoul 136713 South Korea

The literature shows that shear fracture of advanced high strength steels (AHSS) is affected by strain hardening at large strain, as well as the temperature dependence of flow stress and strain hardening. The role of non-isotropic hardening, such as would be expected to be important in reverse strain paths as encountered during draw-bend testing or drawing sheet metal into forming dies, has been difficult to assess without a practical constitutive model combining temperature-dependence and non-isotropic hardening capabilities. Such a model has been developed and implemented in Abaqus Standard via the UMAT subroutine. In order to apply and test the constitutive implementation, the material model was fit using alternate parameter-identification procedures starting from compression-tension (CT) data: 1) fit directly from reverse-path, CT data, and 2) fit indirectly, by combining the direct CT data plus extrapolated data at larger strains where the extrapolation uses verified large-strain monotonic hardening character. The resulting material models were used to simulate draw-bend fracture (DBF) tests for six AHSS. The results show that the indirect method improves the predictions of shear fracture significantly, allowing accurate predictions. It was also shown that the influence of non-isotropic hardening aspects are not critical to accurate predictions as long as the high-strain strain hardening is reproduced accurately. These results suggest a practical and effective method for extending measured tensile hardening to otherwise unattainable strains based on the constant ratio (a in the H/V model) of power-law and saturation-stress strain hardening at a given temperature. The success of this approach suggests that a is a material constant (describing the fundamental strain-hardening character) that depends on temperature but is unaffected by the details of transient hardening following abrupt path changes. Furthermore, the essentially transient nature of hardening follo

关键词： Constitutive behaviour Fracture Thermomechanical processes numerical algorithms Advanced High Strength Steel (AHSS)

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Accuracy of shock capturing in two spatial dimensions

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AIAA JOURNAL 1999年第9期37卷 1072-1079页

作者： Carpenter, MH Casper, JH NASA Langley Res Ctr Aerodynam & Acoust Methods Branch Hampton VA 23681 USA Old Dominion Univ Norfolk VA 23529 USA

An assessment of the accuracy of shock-capturing schemes is made for two-dimensional steady flow around a cylindrical projectile. Both a linear fourth-order method and a nonlinear third-order method are used in this study. This study shows, contrary to conventional wisdom, that captured two-dimensional shocks are asymptotically first order, regardless of the design accuracy of the numerical method. The practical implications of this finding are discussed in the context of the efficacy of high-order numerical methods for discontinuous flows.

关键词： Projectiles Freestream Conditions Rankine Hugoniot Relation Bow Shock Roe Approximate Riemann Solver Stagnation Point numerical algorithms Shock Capturing Method Cartesian Coordinate System Spectral Algorithm

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Large elastoplasticity under static megabar pressures: Formulation and application to compression of samples in diamond anvil cells

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INTERNATIONAL JOURNAL OF PLASTICITY 2016年 84卷 33-57页

作者： Feng, Biao Levitas, Valery I. Hemley, Russell J. Iowa State Univ Dept Aerosp Engn Ames IA 50011 USA Iowa State Univ Dept Aerosp Engn Dept Mech Engn Dept Mat Sci & Engn Ames IA 50011 USA Carnegie Inst Sci Geophys Lab Washington DC 20015 USA

In high pressure research, static megabar pressures are typically produced by compression of a thin sample by two diamonds in various types of diamond anvil cells. This process is accompanied by large plastic deformation (sample thickness is reduced by a factor of 30), and finite elastic deformation of a sample and even the diamond. A thermodynamically consistent system of equations for large elastic and plastic deformation of an isotropic material obeying nonlinear elasticity and pressure dependent yield condition is formulated. The Murnaghan elasticity law and pressure-dependent J(2) plasticity are utilized. The finite-strain third-order elasticity law for cubic crystals is utilized for diamond. A computational algorithm is presented with emphasis on the stress update procedure and derivation of the consistent tangent moduli. It is implemented as a user material subroutine in the finite element code ABAQUS. Material parameters for a rhenium sample, as an example, and a diamond are calibrated based on the experimental and atomistic simulation results in the literature. The evolution of the stress and strain tensor fields in the sample and diamond is studied up to a pressure of 300 GPa. Good correspondence between numerical and experimental pressure distributions at the diamond-sample contact surface is obtained. Because there is a significant scatter of the magnitude of reported third-order single-crystal elastic moduli for diamond, their effect on strains and stresses is studied in detail. With the smaller third-order elastic moduli;the phenomenon of cupping of the diamond-sample contact surface is reproduced, which plays an important role in increasing maximum pressures for a given anvil geometry. The results provide important insight into the mechanical response in diamond anvil cells, interpretation of materials properties under extreme conditions from heterogeneous fields, and optimum design of cells for reaching the maximum static pressure in a volume suffici

关键词： Elastic-plastic material Finite strain numerical algorithms Constitutive behaviors

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The harmonic linearized Navier-Stokes equations for transition prediction in three-dimensional flows

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COMPUTERS & FLUIDS 2024年 273卷

作者： Paredes, Pedro Choudhari, Meelan Carpenter, Mark H. Li, Fei Natl Inst Aerosp Hampton VA 23666 USA NASA Langley Res Ctr Hampton VA 23681 USA

The conventional method to predict the onset of laminar -turbulent transition in convectively unstable boundary -layer flows is based on the logarithmic amplification ratio, the N -factor, of the linear instability waves. To calculate the N -factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108 even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow -resolvent analysis based on the HLNSE for discreteroughness -induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

关键词： Boundary layer stability numerical algorithms

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Modeling of slip, twinning and transformation induced plastic deformation for TWIP steel based on crystal plasticity

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INTERNATIONAL JOURNAL OF PLASTICITY 2016年 76卷 186-212页

作者： Sun, C. Y. Guo, N. Fu, M. W. Wang, S. W. Univ Sci & Technol Beijing Sch Mech Engn Beijing 100083 Peoples R China Hong Kong Polytech Univ Dept Mech Engn Kowloon Hong Kong Peoples R China

One of the most critical issues in development of micromechanics models for TWIP steel is to establish the continuum constitutive model which can accurately represent and model the characteristic plastic deformation at macro level. However, the uncertainty in describing the evolution of state variables based on crystal plasticity theory poses a great challenge in handling the complex plastic deformation with different deformation mechanisms and their complicated interactions and interplays at microscopic scale and thus becomes a non-trivial issue. Many attempts to address this issue by coupling slip and twinning or slip and transformation have been proven to be efficient via comparing and corroborating the predicted texture evolution using crystal plasticity theory with experiment. An accurate constitutive model, however, needs to be established to articulate and model the interactions of slip, twinning and transformation, which have been observed in experiment. In this paper, a micromechanics model for modeling of slip, twinning and transformation induced plasticity of twinning-induced plasticity (TWIP) steel is proposed by using the crystal plasticity approach. The model serves as a feasible approach to reflecting the micro deformation mechanisms during the plastic deformation process of TWIP crystals. The phase transformation is introduced and represented by the rate-dependent constitutive model. The algorithms for realization of the developed model are implemented in ABAQUS/Standard platform using UMAT. Furthermore, different deformation mechanisms of the microscopic plastic deformation modes of TWIP steel are analyzed based on the proposed models. The simulation results by using the developed model reveals that both twinning and transformation have an obvious effect on hardening and transformation, which cause the decrease of stress of single crystal, and the sequence of transformation and twinning rotation can be determined according to the proposed model. (C)

关键词： Phase transformation Twinning Crystal plasticity Polycrystalline material numerical algorithms

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Aeroacoustic modeling of turbulent airfoil flows

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AIAA JOURNAL 2001年第6期39卷 1057-1064页

作者： Shen, WZ Sorensen, JN Tech Univ Denmark Dept Energy Engn DK-2800 Lyngby Denmark Cent S Univ Res Ctr High Speed Trains Hunan 410075 Peoples R China

A numerical algorithm for acoustic noise generation is extended to handle turbulent Bows, The approach involves two steps comprising a viscous incompressible how part and an inviscid acoustic part. In the turbulent case, the flow is further split into a Reynolds-averaged component and a component corresponding to the turbulent small-scale fluctuations. The latter is modeled by an eddy-viscosity-based turbulence model and appears as a source term in the acoustic equations. The formulation is applied to acoustic noise generated by the Bow past a NACA 0015 airfoil at an incidence of 20 deg, First, acoustic noise generated by laminar Bow is considered as a validation of the acoustic model. The results are compared to solutions obtained using the Lighthill acoustic analogy (linearized wave equations) (Lighthill, M, J., "On Sound Generated Aerodynamically I: General Theory," Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 211,1952, pp, 563-587). The comparisons show that noise levels and frequency content are in good agreement. Next, the acoustic model is applied on a turbulent Bow in which the small-scale turbulence is modeled by a Reynolds-averaged turbulence model [Baldwin-Barth one equation model (Baldwin, B, S., and Earth, T J., "A One-Equation Turbulence Transport Model for High Reynolds Number Wall-Bounded Flows," NASA TM 102847, 1990)]. The computations show that the generated acoustic field is dominated by the Strouhal frequency and its harmonics. The acoustic noise level for the turbulent flow is of the same order as for the laminar Bow Because of the turbulence model used in the flow solver, only one frequency and its higher harmonics are seen. For capturing more frequencies, one should combine the acoustic model with large eddy simulation or direct Navier-Stokes simulation.

关键词： Freestream Velocity NACA 0015 Acoustic Noise numerical algorithms Turbulence Models Eddy Viscosity Vortex Shedding Boussinesq Approximation Large Eddy Simulation Acoustic Velocity

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