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THE OPTIMAL PROJECTION EQUATIONS FOR REDUCED-ORDER, DISCRETE-TIME MODELING, ESTIMATION, AND CONTROL

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1986年第3期9卷 288-293页

作者： BERNSTEIN, DS DAVIS, LD HYLAND, DC Harris Corporation Melbourne Florida

The optimal projection equations derived previously for reduced-order, continuous-time modeling, estimation, and control are developed for the discrete-time case. The design equations are presented in a concise, unified manner to facilitate their accessibility for the development of numerical algorithms for practical applications. As in the continuous-time case, the standard Kalman filter and linear-quadratic-Gaussian results are immediately obtained as special cases of the estimation and control results. (Author)

关键词： Optimal Projection Equations Kalman Filter numerical algorithms Closed Loop System Real Time Computing Riccati Equations White Noise Simply Supported Beams Lagrange Multipliers Cost Analysis

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Modeling of damage in unidirectional ceramic matrix composites and multi-scale experimental validation on third generation SiC/SiC minicomposites

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2014年第1期63卷 298-319页

作者： Chateau, C. Gelebart, L. Bornert, M. Crepin, J. Caldemaison, D. Sauder, C. CEA DEN DMN SRMA F-91191 Gif Sur Yvette France Univ Paris Est Lab Navier UMR 8205 CNRSENPCIFSTTAR F-77455 Marne La Vallee France Mines ParisTech Ctr Mat CNRS UMR 7633 F-91003 Evry France Ecole Polytech Solid Mech Lab CNRS UMR 7649 F-91128 Palaiseau France

The purpose of this paper is to experimentally validate a ID probabilistic model of damage evolution in unidirectional SiC/SiC composites. The key point of this approach lies in the identification and validation at both local and macroscopic scales. Thus, in addition to macroscopic tensile tests, the evolution of microscopic damage mechanisms - in the form of matrix cracks and fiber breaks - is experimentally analyzed and quantified through in-situ scanning electron microscope and computed tomography tensile tests. A complete model, including both matrix cracking and fiber breaking, is proposed on the basis of existing modeling tools separately addressing these mechanisms. It is based on matrix and fiber failure probability laws and a stress redistribution assumption in the vicinity of matrix cracks or fiber breaks. The identification of interfacial parameters is conducted to fit the experimental characterization, and shows that conventional assumptions of 1D probabilistic models can adequately describe matrix cracking at both macro- and microscopic scales. However, it is necessary to enrich them to get a proper prediction of ultimate failure and fiber break density for Hi-Nicalon type S fiber-reinforced SiC/SiC minicomposites. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Fracture mechanisms Ceramic material Fiber-reinforced composite material In-situ mechanical testing numerical algorithms

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UPDATING FINITE-ELEMENT DYNAMIC-MODELS USING AN ELEMENT-BY-ELEMENT SENSITIVITY METHODOLOGY

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AIAA JOURNAL 1993年第9期31卷 1702-1711页

作者： FARHAT, C HEMEZ, FM UNIV COLORADO CTR SPACE CONSTRUCTBOULDERCO 80309

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L2 norms of the modal dynamic residuals vis an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of ''zooming'' on the detected error locations. Several simulation examples which demonstrate the potential of the proposed methodology are discussed.

关键词： Finite Element Analysis Sensors numerical algorithms Poisson's Ratio Trusses Singular Value Decomposition Structural Element Cantilever Beam Structural Damage Lagrange Multipliers

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A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

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COMPUTERS & FLUIDS 2015年 114卷 172-192页

作者： Charest, Marc R. J. Canfield, Thomas R. Morgan, Nathaniel R. Waltz, Jacob Wohlbier, John G. Los Alamos Natl Lab Los Alamos NM 87545 USA

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linear reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： numerical algorithms Computational fluid dynamics High-order methods Compressible flows Shock hydrodynamics

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Group-based evaluation of temperature and pressure for molecular dynamics simulation with a large time step

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JOURNAL OF CHEMICAL PHYSICS 2020年第23期153卷 234115页

作者： Jung, Jaewoon Sugita, Yuji RIKEN Cluster Pioneering Res Theoret Mol Sci Lab 2-1 Hirosawa Wako Saitama 3510198 Japan RIKEN Ctr Computat Sci Computat Biophys Res Team Chuo Ku 7-1-26 Minatojima Minamimachi Kobe Hyogo 6500047 Japan RIKEN Ctr Biosyst Dynam Res Lab Biomol Funct Simulat Chuo Ku 6-7-1 Minatojima Minamimachi Kobe Hyogo 6500047 Japan

Recently, we proposed novel temperature and pressure evaluations in molecular dynamics (MD) simulations to preserve the accuracy up to the third order of a time step, delta t [J. Jung, C. Kobayashi, and Y. Sugita, J. Chem. Theory Comput. 15, 84-94 (2019);J. Jung, C. Kobayashi, and Y. Sugita, J. Chem. Phys. 148, 164109 (2018)]. These approaches allow us to extend delta t of MD simulations under an isothermal-isobaric condition up to 5 fs with a velocity Verlet integrator. Here, we further improve the isothermal-isobaric MD integration by introducing the group-based evaluations of system temperature and pressure to our previous approach. The group-based scheme increases the accuracy even using inaccurate temperature and pressure evaluations by neglecting the high-frequency vibrational motions of hydrogen atoms. It also improves the overall performance by avoiding iterations in thermostat and barostat updates and by allowing a multiple time step integration such as r-RESPA (reversible reference system propagation algorithm) with our proposed high-precision evaluations of temperature and pressure. Now, the improved integration scheme conserves physical properties of lipid bilayer systems up to delta t = 5 fs with velocity Verlet as well as delta t = 3.5 fs for fast motions in r-RESPA, respectively.

关键词： Nose-Hoover chain Rigid body dynamics Molecular dynamics algorithms and data structure numerical algorithms Lipid bilayer Velocity-Verlet time integration

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Material fields in atomistics as pull-backs of spatial distributions

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2016年 89卷 59-76页

作者： Admal, Nikhil Chandra Tadmor, Ellad B. Univ Minnesota Dept Aerosp Engn & Mech Minneapolis MN 55455 USA

The various fields defined in continuum mechanics have both a material and a spatial description that are related through the deformation mapping. In contrast, continuum fields defined for atomistic systems using the Irving-Kirkwood or Murdoch-Hardy procedures correspond to a spatial description. It is uncommon to define atomistic fields in the reference configuration due to the lack of a unique definition for the deformation mapping in atomistic systems. In this paper, we construct referential atomistic distributions as pull-backs of the spatial distributions obtained in the Murdoch-Hardy procedure with respect to a postulated deformation mapping that tracks particles. We then show that some of these referential distributions are independent of the choice of the deformation mapping and only depend on the reference and current configuration of particles. Therefore, the fields obtained from these distributions can be calculated without explicitly constructing a deformation map, and by construction they satisfy the balance equations. In particular, we obtain definitions for the first and second atomistic Piola-Kirchhoff stress tensors. We demonstrate the validity of these definitions through a numerical example involving finite deformation of a slab containing a notch under tension. An interesting feature of the atomistic first Piola-Kirchhoff stress tensor is the absence of a kinetic part, which in the atomistic Cauchy stress tensor accounts for thermal fluctuations. We show that this effect is implicitly included in the atomistic first PiolaKirchhoff stress tensor through the motion of the particles. An open source program to compute the atomistic Cauchy and first Piola-Kirchhoff stress fields called MDStressLab is available online at http://***. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Microstructures Stress relaxation Stress concentration Atomistics numerical algorithms

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Macroscopic behavior and field fluctuations in viscoplastic composites:: Second-order estimates versus full-field simulations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2006年第5期54卷 1029-1063页

作者： Idiart, MI Moulinec, H Castañeda, PP Suquet, P Univ Penn Dept Mech Engn & Appl Mech Philadelphia PA 19104 USA Ecole Polytech Mecan Solides Lab CNRS UMR 7649Dept Mecan F-91128 Palaiseau France CNRS LMA UPR 7051 F-13402 Marseille 20 France

This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris 11 318, 1417-1423], while the theoretical estimates follow from the so-called "second-order" procedure [Ponte Castaneda, P., 2002a. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I-Theory. J. Mech. Phys. Solids 50, 737-757]. Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding "second-order" estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general, the "second-order" estimates are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates. Thus, it is demonstrated that the "second-order" method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites. (c) 2005 Elsevier Lt

关键词： creep inhomogeneous material viscoplastic material homogenization numerical algorithms

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Finite deformations of metal cylinders subjected to electromagnetic fields and mechanical forces

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2005年第3期53卷 525-544页

作者： Bilyk, SR Ramesh, KT Wright, TW USA Res LabTD Weapons & Mat Res DirectorateWM AMSRDAR Aberdeen Proving Ground MD 21005 USA Johns Hopkins Univ Dept Engn Mech Baltimore MD 21218 USA

Strong electromagnetic (EM) fields coupled with mechanical loads may have a profound effect on deforming bodies. The continuum description of the plastic deformation of solids under electric fields and mechanical loads essentially involves the coupling of the field equations of continuum mechanics with Maxwell's equations. This analysis considers the effects of large EM fields on solid metal cylinders undergoing plastic deformations. Other researchers have used an electroplastic effect to explain previous EM and mechanically loaded experimental results. We examine whether it is 'necessary to invoke this controversial mechanism. First, we consider only EM loading and solve the transient EM distribution in a solid metal cylinder. This determines the EM time scales as compared to thermal diffusion time scales. Next, at the continuum level, we present the mechanical problem of quasi-static finite compressive deformations incorporating thermal expansion, strain hardening, strain rate sensitivity, thermal softening, and heat conduction. A viscoplastic model that is applicable over a wide range of strain rates (10(-4)-10(6) S-1) Characterizes the material response. Finally, we consider a metal cylinder subjected to uni-axial mechanical loading as well as high axial current pulses. The material is assumed, to be isotropic with. the plastic incompressibility constraint. The deformations are assumed to remain axisymmetric and no instabilities in the cylinder are considered. Coupled effects of Joule heating and the Lorentz force on the quasi-static deformations are examined. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： electromechanical processes strengthening and mechanisms thermomechanical finite deformation viscoplastic materials numerical algorithms

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Robust algorithms for the Solution of the Ideal Adsorbed Solution Theory Equations

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AICHE JOURNAL 2015年第3期61卷 981-991页

作者： Mangano, Enzo Friedrich, Daniel Brandani, Stefano Univ Edinburgh Sch Engn Inst Mat & Proc Scottish Carbon Capture & Storage Edinburgh EH9 3JL Midlothian Scotland

The ideal adsorbed solution (IAS) theory has been shown to predict reliably multicomponent adsorption for both gas and liquid systems. There is a lack of understanding of the conditions which guarantee convergence for various algorithms used to solve the IAS theory equations and inconsistencies are present in the reported computational effort required for the different approaches. The original nested loop and the FastIAS technique are revisited. The resulting system of equations is highly nonlinear but both methods are shown to be robust if appropriate choices are made for the starting values of the unknown variables. New initial conditions are proposed and the resulting algorithms are compared in a consistent manner with the main methods available to solve the IAS theory equations. The algorithms are extended for the first time to all nontype I isotherms. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 981-991, 2015

关键词： separations thermodynamics adsorption equilibria ideal adsorbed solution theory numerical algorithms

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A self-scaling implicit SQP method for large scale structural optimization

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INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 1996年第11期39卷 1933-1953页

作者： Huang, MW Arora, JS Optimal Design Laboratory College of Engineering The University of Iowa Iowa City IA 52242 U.S.A. [*]Optimal Design Laboratory College of Engineering The University of Iowa Iowa City IA 52242 U.S.A.

The basic idea bf an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems-small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.

关键词： structures optimization large scale structural design sequential quadratic programming self-scaling numerical algorithms algorithm evaluation test problems

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