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Linear Stability Analysis of Multiparameter Dynamical Systems via a numerical-Perturbation Approach

AIAA JOURNAL 2011年第9期49卷 2047-2056页

作者： Luongo, Angelo D'Annibale, Francesco Univ Aquila Dept Struct Engn I-67100 Laquila Italy

A numerical-perturbation method, based on eigenvalue sensitivity analysis, is developed that is able to build up linear stability diagrams of multiparameter dynamical systems. The algorithm furnishes the critical combinations of parameters causing multiple bifurcations of static, dynamical, or mixed types. Moreover, it determines the manifolds in the parameter space on which simple bifurcations take place. Although the method is general, it is illustrated here for codimension-2 bifurcations only, sufficient for highlighting the underlying ideas.

关键词： Perturbation Analysis Stiffness Matrices Cantilever Beam Newton's Method Damping Coefficient Bending Moment numerical algorithms Nonlinear Systems Inverse Problems Elastic Modulus

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numerical analysis and elastic-plastic deformation behavior of anisotropically damaged solids

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INTERNATIONAL JOURNAL OF PLASTICITY 2002年第9期18卷 1237-1270页

作者： Brünig, M Univ Dortmund Lehrstuhl Baumech Stat D-44221 Dortmund Germany

The present paper is concerned with the numerical modelling of the large elastic plastic deformation behavior and localization prediction of ductile metals which are sensitive to hydrostatic stress and anisotropically damaged. The model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics. The formulation relies on a multiplicative decomposition of the metric transformation tensor into elastic and damaged-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged configurations via associated metric transformations which allow for the interpretation as damage tensors. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach the constitutive framework is completed by different stress tensors, a yield criterion and a separate damage condition as well as corresponding potential functions. The evolution laws for plastic and damage strain rates are discussed in some detail. Estimates of the stress and strain histories are obtained via an explicit integration procedure which employs an inelastic (damage-plastic) predictor followed by an elastic corrector step. numerical simulations of the elastic-plastic deformation behavior of damaged solids demonstrate the efficiency of the formulation. A variety of large strain elastic-plastic-damage problems including severe localization is presented, and the influence of different model parameters on the deformation and localization prediction of ductile metals is discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： damage elastic plastic material finite strain finite element numerical algorithms

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Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2011年第11期59卷 2323-2340页

作者： Stefanov, Yu P. Chertov, M. A. Aidagulov, G. R. Myasnikov, A. V. Schlumberger Moscow Res Moscow 119285 Russia

The paper presents a numerical analysis of the inelastic deformation process in porous rocks during different stages of its development and under non-equiaxial loading. Although numerous experimental studies have already investigated many aspects of plasticity in porous rocks, numerical modeling gives valuable insight into the dynamics of the process, since experimental methods cannot extract detailed information about the specimen structure during the test and have strong limitations on the number of tests. The numerical simulations have reproduced all different modes of deformation observed in experimental studies: dilatant and compactive shear, compaction without shear, uniform deformation, and deformation with localization. However, the main emphasis is on analysis of the compaction mode of plastic deformation and compaction localization, which is characteristic for many porous rocks and can be observed in other porous materials as well. The study is largely inspired by applications in petroleum industry, i.e. surface subsidence and reservoir compaction caused by extraction of hydrocarbons and decrease of reservoir pressure. Special attention is given to the conditions, evolution, and characteristic patterns of compaction localization, which is often manifested in the form of compaction bands. Results of the study include stress-strain curves, spatial configurations and characteristics of localized zones, analysis of bifurcation of stress paths inside and outside localized zones and analysis of the influence of porous rocks properties on compaction behavior. Among other results are examples of the interplay between compaction and shear modes of deformation. To model the evolution of plastic deformation in porous rocks, a new constitutive model is formulated and implemented, with the emphasis on selection of adequate functions defining evolution of yield surface with deformation. The set of control parameters of the model is kept as short as possible;the paramete

关键词： Compaction localization Constitutive behavior Rock Dynamics numerical algorithms

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SEVERAL numerical SCHEMES FOR THE COMPUTATION OF UNSTEADY-FLOW IN PULSED LASERS

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AIAA JOURNAL 1987年第6期25卷 845-854页

作者： SRIVASTAVA, BN WALDMAN, G CRUICKSHANK, J MORAN, J AVCO SYST DIV WILMINGTON MA 01887 USA

This paper describes numerical formulation issues aimed at developing an accurate computational approach for two-dimensional acoustic studies in a typical pulsed laser system. This goal is achieved through a series of numerical algorithm studies, optimizations thereof, and improved boundary formulation techniques related to the complex laser system environment. Several model test problems are computed and successfully compared with available data/analyses to demonstrate the accuracy of the computational approach. © 1987 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Lasers Unsteady Flows numerical algorithms Mass Flow Flux Corrected Transport Conservation Equations Damping Coefficient Beam and Warming Scheme Discharge Coefficient Total Energy

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Matchsticks, scramjets, and black holes: numerical simulation faces reality

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AIAA JOURNAL 2002年第8期40卷 1481-1494页

作者： Oran, ES USN Res Lab Lab Computat Phys & Fluid Dynam Washington DC 20375 USA

The evolution of the science and art of numerical simulation of complex, complicated fluid flows has made enormous strides in the past 40 years. We have progressed from relatively simplified one-dimensional steady-state results to fully three-dimensional, time-dependent simulations including very complex physics. These advances have been driven by new computational hardware, new algorithms for solving the equations, and the real need for this technology. The broad range of applications that are possible are emphasized and some of what we can now do, what we have learned, and where we might go with this exciting technology in the future is described.

关键词： numerical Simulation Scramjet Conservation Equations Detonation High Performance Computing Vortices Torpedoes Electromagnetic Radiation MHD numerical algorithms

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An improved implicit numerical integration of a non-associated, three-invariant cap plasticity model with mixed isotropic-kinematic hardening for geomaterials

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INTERNATIONAL JOURNAL FOR numerical AND ANALYTICAL METHODS IN GEOMECHANICS 2015年第17期39卷 1853-1883页

作者： Motamedi, M. H. Foster, C. D. Univ Illinois Dept Civil & Mat Engn Chicago IL 60607 USA

The Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high-performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large-scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： three-invariant plasticity geological material strengthening and mechanisms constitutive behavior finite elements numerical algorithms

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numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization

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MATHEMATICAL PROGRAMMING 1996年第1期73卷 73-110页

作者： Conn, AR Gould, N Toint, PL IBM CORP THOMAS J WATSON RES CTR YORKTOWN HTS NY 10598 USA RUTHERFORD APPLETON LAB COMP & INFORMAT SYST DEPT CHILTON ENGLAND FAC UNIV NOTRE DAME PAIX DEPT MATH B-5000 NAMUR BELGIUM

In this paper, we describe the algorithmic options of Release A of LANCELOT, a Fortran package for large-scale nonlinear optimization, We then present the results of intensive numerical tests and discuss the relative merits of the options, The experiments described involve both academic and applied problems. Finally, we propose conclusions, both specific to LANCELOT and of more general scope.

关键词： large-scale problems nonlinear optimization numerical algorithms

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Experimental and numerical investigation of the Bridgman growth of a transparent material

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2002年第3期16卷 324-335页

作者： Simpson, JE Garimella, SV de Groh, HC Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA NASA John H Glenn Res Ctr Micrograv Sci Div Cleveland OH 44135 USA

A combined experimental and numerical study of the horizontal Bridgman growth of pure succinonitrile has been performed. The effect of convection on interface propagation and shape is quantified and discussed. Measurements were obtained both under conditions of no-growth and for a 40-mum/s growth rate. The quantities measured include interface shape and location, melt velocities, and temperature boundary conditions on the ampoule exterior. The melt velocities were measured using a new technique that employed digital cameras to image the locations of seed particles in the melt. The growth front was stable and nondendritic but was significantly distorted by the influence of convection in the melt and, for the growth case, by the moving temperature boundary conditions along the ampoule. Both two- and three-dimensional numerical simulations of the growth process were performed. Temperatures throughout the phase-change material and ampoule, as well as melt velocities, were obtained from the simulations. The predicted interface shapes and melt velocities agree well with experimental results. Two different numerical algorithms were used;the utility of each for simulating phase-change problems is discussed. This combined experimental and numerical study provides a database for the validation of phase-change numerical models, in addition to furnishing detailed information about the influence of convection on the Bridgman growth process. In ongoing work, the computer models presented are being used to simulate alloy solidification problems.

关键词： Natural Convection numerical Stability numerical Simulation Phase Change Materials numerical algorithms Thermocouples Flow Visualization Thermal Boundary Condition Isotherms Transient Conduction

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numerical BOUNDARY-CONDITION PROCEDURES FOR EULER SOLVERS

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AIAA JOURNAL 1987年第8期25卷 1054-1062页

作者： MARCUM, DL HOFFMAN, JD PURDUE UNIV CTR THERMAL SCI & PROPW LAFAYETTEIN 47907

A numerical boundary condition procedure for Euler solvers is presented. The procedure is based on a variation of the method of characteristics due to Kentzer. A second-order-accurate numerical algorithm using this procedure and the MacCormack explicit finite-difference method is presented. Results are presented for several two-dimensional and three-dimensional inviscid nozzle flowfields. Solutions obtained by the present method agree well with solutions obtained by method of characteristics algorithms and experimental data. © 1987 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Finite Difference Method numerical algorithms Static Pressure Mach Number Courant Friedrichs Lewy Stagnation Temperature Continuity Equation Two Dimensional Flow Conical Nozzles Subsonic Inlets

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Representative volume element size for elastic composites: A numerical study

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1997年第9期45卷 1449-1459页

作者： Gusev, AA Departement Werkstoffe Institut für Polymere ETH Zentrum CH-8092 Zürich Switzerland

Monte Carlo (MC) runs are employed to generate statistically independent realizations of a periodic elastic composite with a disordered unit cell made up of 8, 27, and 64 nonoverlapping identical spheres. In the limit of an infinite number of spheres in the disordered unit cell, this periodic composite obeys the Percus-Yevick hard-sphere statistics. By construction, the MC realizations studied have the same inclusion fraction. A constant-strain-tetrahedra displacement-based finite element code with an iterative solver is used to calculate the overall elastic constants of these periodic MC realizations. It appears that the scatter in the individual elastic constants already obtained with a few dozen spheres in the disordered unit cell is remarkably small and the averages obtained with varying numbers of spheres are practically stationary. (C) 1997 Elsevier Science Ltd.

关键词： microstructures constitutive behavior elastic material inhomogeneous material numerical algorithms

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