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integration WITH UNIVERSAL VARIABLES

AIAA JOURNAL 1966年第3期4卷 531-&页

作者： PITKIN, ET University of Connecticut Storrs Conn.

The universal formulation of the two-body problem is employed as a basis to derive formulas for variation of parameters integration of two sets of elements related to position and velocity at epoch. Typical behavior on low-thrust orbits is then discussed. © 1966 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： integration algorithm Nearly Circular Orbit Osculating Orbit Eccentric Anomaly Numerical integration Radial Velocity Kepler's Equation Apocenter

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Geometric integration of Quaternions

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2013年第6期36卷 1762-1767页

作者： Andrle, Michael S. Crassidis, John L. SUNY Buffalo Dept Mech & Aerosp Engn Amherst NY 14260 USA

Presented as Paper 2012-4421 at the AIAA/AAS Astrodynamics Specialists Conference, Minneapolis, MN, 13-16 August 2012

关键词： Quaternions Numerical integration Runge Kutta integration Asteroids Earth Yaw Space Situational Awareness Extended Kalman Filter integration algorithm Satellites

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PRACTICAL ERROR COEFFICIENTS IN integration OF PERIODIC ANALYTIC FUNCTIONS BY TRAPEZOIDAL RULE

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COMMUNICATIONS OF THE ACM 1968年第11期11卷 764-+页

作者： RABINOWITZ, P The Weizmann Institute of Science Rehovot Israel

Analyzes the error coefficients applicable in the integration of periodic analytic functions using the trapezoidal rule. Theoretical and practical values of error coefficients; Roundoff and truncation errors; Davis... 详细信息

关键词： integration algorithm numerical integration periodic analytic functions practical error coefficients roundoff error theoretical error coefficients trapezoidal rule truncation error

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A new integration method proposed for hyperbolic sine constitutive equation used in semi-solid forming

A new integration method proposed for hyperbolic sine consti...

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9th International Conference on Semi-Solid Processing of Alloys and Composites

作者： Zhou Jiming Qi Lehua Chen Guoding Northwestern Polytech Univ Xian 710072 Peoples R China

ISBN: (纸本)3908451264;9783908451266

This paper describes a new. integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inelastic strain rate in HSCE so that the inelastic strain rate can be solved indirectly from the Lambda. The proposed integration algorithm is based on the stress update concept and the effect of normal stress updating on the material compression is also discussed thoroughly in this paper. The investigation results show that the new algorithm can integrate the HSCE efficiently and the normal stress should keep constant as the deviatoric stress updating. An example of semi-solid extruding was given in the paper at last to illustrate the implementation of new algorithm and effect of normal stress updating on the compression of material.

关键词： constitutive equation hyperbolic sine integration algorithm semi-solid forming

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integration OF ELASTO-PLASTIC CONSTITUTIVE MODELS IN FINITE DEFORMATION: AN EXPLICIT APPROACH 13

INTEGRATION OF ELASTO-PLASTIC CONSTITUTIVE MODELS IN FINITE ...

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XIII International Conference on Computational Plasticity: Fundamentals and Applications COMPLAS 2015

作者： Monforte, Lluis Arroyo, Marcos Gens, Antonio Carbonell, Josep M. Univ Politecn Cataluna Dept Engn Terreny Jordi Girona 1-3Campus Nord UPC ES-08034 Barcelona Spain CIMNE Barcelona 08034 Spain

ISBN: (纸本)9788494424465

This paper highlights an explicit integration scheme for hyperelastic-based finite strains elasto-plastic models. One step update equations are obtained from the large deformation multiplicative elasto-plastic theory, where an exponential variation of the plastic deformation gradient is assumed. The material tangent matrix has the same formal structure as the usual small strains elasto-plastic tangent matrix. The basic algorithm to perform the stress integration, including an adaptive substepping scheme and a yield violation drift correction scheme, are also described. The accuracy and robustness of the proposal is assessed against several examples of typical geotechnical tests. Results from a convergence test suggest that, using an adaptive substepping scheme, the error of the local problem is independent of the step size.

关键词： integration algorithm finite deformation elasto-plastic constitutive models

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Multiscale friction-damage mechanics of layered rocks: theoretical formulation and numerical simulation

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Journal of Rock Mechanics and Geotechnical Engineering 2025年

作者： Lu Ren Lunyang Zhao Fujun Niu Yuanming Lai Danqing Song Qizhi Zhu Jianfu Shao South China Institution of Geotechnical Engineering School of Civil Engineering and Transportation South China University of Technology Guangzhou 510641 China State Key Laboratory of Subtropical Building and Urban Science South China University of Technology Guangzhou 510641 China School of Environmental and Geographical Sciences Shanghai Normal University Shanghai 200234 China Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering Hohai University Nanjing 210098 China University of Lille CNRS Centrale Lille LaMcube UMR9013 Lille 59000 France

Layered rocks (LR) exhibit inherent anisotropic stiffness and strength induced by oriented rough weakness planes, along with stress induced anisotropy and friction related plastic deformation occurs during loading. Furthermore, microcracks located in intact rock matrix (IRM) of LR are also critically important for friction and damage dissipation processes. In this paper, we first present a novel multiscale friction-damage (MFD) model using a two-step Mori-Tanaka homogenization scheme, with the aim of describing the multiscale friction-damage mechanics in LR. Physically, the initiation and propagation of flaws at different scales (i.e. microcracks and weakness planes) induced damage, and the plastic deformation is closely associated with frictional sliding along these flaws. In the thermodynamics framework, the macroscopic stress-strain relations, the local driving forces respectively conjuncted with flaws propagation and plastic deformation are derived. An analytical macroscopic strength criterion is subsequently deduced, which takes into account the variation of inclination angle and confining pressure. Notably, the failure mechanisms of IRM shearing and weakness planes sliding are inherent included in the criterion. As an original contribution, a new multisurface semi-implicit return mapping algorithm (MSRM) is developed to integrate the proposed MFD model. The robustness of MSRM algorithm is assessed by numerical tests with different loading steps sizes and convergence conditions. Finally, the effectiveness of the MFD model is confirmed using data from experiments under conventional triaxial compression, all main features of mechanical behaviors of LR are well captured by the proposed model, including initial anisotropy, stress-induced anisotropy and strain hardening/softening.

关键词： Layered rocks Anisotropy Multiscale modelling Friction-damage integration algorithm

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OPTIMAL OPEN MULTISTEP DISCRETIZATION FORMULAS FOR REAL-TIME SIMULATION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1993年第3期16卷 557-563页

作者： MOERDER, DD CALISE, AJ CLEMMONS, P GEORGIA INST TECHNOL SCH AEROSP ENGNATLANTAGA 30332

The performance of digital real-time simulations is considered. A figure of merit is derived that quantifies a simulation's fidelity in terms of the time-domain discrepancy between its output and that of the plant it simulates, assuming that the plant is linearizable and asymptotically stable. This performance index is then used in deriving an easily automated procedure for calculating optimal values for free parameters in plant discretizations based on a generalized form of open linear multistep integration formulas. The theory is demonstrated in simulating the rigid-body dynamics of a fully articulated helicopter rotor blade system.

关键词： Fully Articulated Rotor Rigid Body Dynamics integration algorithm Numerical integration Classical Control Theory Output Feedback Flap Angle Sampled Data Systems Numerical algorithms Damping Coefficient

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Line-search methods in general return mapping algorithms with application to porous plasticity

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2008年第10期73卷 1468-1495页

作者： Seifert, T. Schmidt, I. Fraunhofer Inst Mech Mat D-79108 Freiburg Germany

The present paper focuses on the application of line-search methods in general return mapping algorithms. Two inexact line-search methods and an exact line-search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations. As an example for the assessment of the algorithms, an elastic-plastic and an elastic-viscoplastic version of Gurson's porous plasticity model are used in simulations of the necking of a tensile bar. It is shown that larger time increments are possible and, therefore, a smaller number of increments are required when using line-search methods. The exact line-search method shows the best performance concerning the required number of increments, but takes more CPU time to complete the simulation. The application of the inexact line search methods in general lowers the number of increments along with a reduction in the CPU time, as compared with the case when no line-search is used. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： integration algorithm line-search method porous plasticity necking

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EXACTLY SOLVING THE WEIGHTED TIME FUEL OPTIMAL-CONTROL OF AN UNDAMPED HARMONIC-OSCILLATOR

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1988年第6期11卷 488-494页

作者： SOUZA, MLD Instituto de Pesquisas Espaciais Sao Jose dos campos Brazil

The exact solution presented for the weighted time/fuel optimal control of an undamped harmonic oscillator having one bounded control and any initial state is motivated by the desire to improve the final behavior of Vander Velde (1983) trajectories for large space structures' on-off control. An investigation is accordingly made of the existence, normality, and uniqueness of both the extremals and the optimal solution; numerical comparisons are then made between the approximate and exact solutions according to three criteria. (O.C.)

关键词： Harmonic Oscillator Optimal Control Fuels Large Space Structures integration algorithm Flexible Spacecrafts Closed Loop Control Fuel Consumption Computing

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Local block relaxation method for the solution of equations of gasdynamics

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AIAA JOURNAL 2000年第8期38卷 1377-1384页

作者： de Nicola, C Tognaccini, R Puoti, V Univ Naples Federico II Dipartimento Progettaz Aeronaut I-80125 Naples Italy Ctr Italiano Ric Aerospaz Dipartimento Caicoio Numer & Parallelo I-81043 Capua CE Italy

A new explicit pseudo-time-integration algorithm, termed local block relaxation, for the solution of the equations of gasdynamics in block-structured domains is proposed. The aim of the method is to reduce the computational costs in obtaining the numerical solution of complex flowfields. Attention is given to the definition of proper interface boundary conditions that ensure stability even if the smoothing of the solution is not synchronized in time among the blocks. Once stability is guaranteed, oversmoothings can be performed in a restricted number of blocks, namely, those that exhibit a slower rate of convergence. The method proposed is closely coupled with a standard multigrid cycle. A theoretical analysis of the savings in computational work is presented so that the convergence speed up can be estimated a priori. The strategy is shown to be effective in both two-dimensional and three-dimensional Navier-Stokes simulations. The present algorithm can be extended to a broad variety of numerical schemes based on explicit time integrations.

关键词： Gasdynamics Navier Stokes Calculations Courant Friedrichs Lewy integration algorithm Boundary Value Problems Computing Baldwin Lomax Turbulence Model Interprocessor Communication Numerical integration Freestream Conditions

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