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An evaluation of the self-determined probability-weighted moment method for estimating extreme wind speeds

JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS 2004年第3-4期92卷 219-239页

作者： Whalen, TM Savage, GT Jeong, GD Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA

For the estimation of probability distribution parameters, the method of self-determined probability-weighted moments (SD-PWM) has previously been introduced as a refinement on the original method of probability-weighted moments (PWM). Tables have been created summarizing the solution of the relevant equations for certain probability distributions, but application of these is awkward. In addition, certain associated algorithms are difficult to interpret and contain formulations that do not appear to properly enforce the definitions of self-determined probability-weighted moments. Therefore, new algorithms have been developed to both clarify and simplify the determination of SD-PWM parameter estimates. As an application of the SD-PWM algorithms, the estimation of extreme wind speeds is considered using the Gumbel and generalized extreme value (GEV) distributions. The estimation results are compared to similar results obtained via PWM, the method of moments and the maximum likelihood method. The analyses suggest SD-PWM may be a reasonable tool for analyzing the ability of a particular distribution to describe a sample. Relative to the method of moments and PWM estimates, the SD-PWM estimates compare well based on fits of the cumulative distributions. While the SD-PWM estimates exhibit increased variability relative to the method of moment (MOM) estimates, SD-PWM wind speed estimates are generally conservative relative to the MOM estimates. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： self-determined probability-weighted moments extreme wind speeds parameter estimation numerical algorithms extreme value analysis

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On electromagnetic forming processes in finitely strained solids: Theory and examples

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2009年第8期57卷 1391-1416页

作者： Thomas, J. D. Triantafyllidis, N. Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

The process of electromagnetic forming (EMF) is a high velocity manufacturing technique that uses electromagnetic (Lorentz) body forces to shape sheet metal parts. EMF holds several advantages over conventional forming techniques: speed, repeatability, one-sided tooling, and most importantly considerable ductility increase in several metals. Current modeling techniques for EMF processes are not based on coupled variational principles to simultaneously account for electromagnetic and mechanical effects. Typically, separate solutions to the electromagnetic (Maxwell) and motion (Newton) equations are combined in staggered or lock-step methods, sequentially solving the mechanical and electromagnetic problems. The present work addresses these issues by introducing a fully Coupled Lagrangian (reference configuration) least-action variational principle, involving magnetic flux and electric potentials and the displacement field as independent variables. The corresponding Euler-Lagrange equations are Maxwell's and Newton's equations in the reference configuration, which are shown to coincide with their current configuration counterparts obtained independently by a direct approach. The general theory is subsequently simplified for EMF processes by considering the eddy Current approximation. Next, an application is presented for axisymmetric EMF problems. It is shown that the proposed variational principle forms the basis of a variational integration numerical scheme that provides an efficient staggered solution algorithm. As an illustration a number of such processes are simulated, inspired by recent experiments of freely expanding uncoated and polyurea-coated aluminum tubes. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Electromechanical processes Finite strain Finite elements numerical algorithms Variational calculus

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Material parameters identification procedure for BBC2003 yield criterion and earing prediction in deep drawing

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2016年第0期115卷 552-563页

作者： Izadpanah, Sajjad Ghaderi, Seyed Hadi Gerdooei, Mandi Shahrood Univ Technol Dept Mech Engn Sheet Met Forming Res Lab Shahrood *** Iran

Formation of wavy boundaries at the open end of a drawn cup is referred to as earing. Plastic anisotropy is the main parameter contributing to formation of ears. Therefore, in order to eliminate the undesirable ears in sheet metal parts, it is essential to predict the deformation behavior of sheet metals using advanced anisotropic yield criteria. Accordingly, the objective of this article is that to use BBC2003 yield criterion, to predict earing in deep drawing of cylindrical cups from AA3105 aluminum alloy. First, a new and simple approach is introduced to calculate the eight constants of this yield function. In this approach, only the uniaxial and plane strain tension tests results, were used. Nonlinear governing equations of these constants were derived and solved by means of well-known steepest descend method. In order to investigate performance and accuracy of this method, the calculated constants were utilized to predict normalized uniaxial yield stress, anisotropy parameters and plane stress yield surface. Then, based on this yield criterion and the associated flow rule, a VUMAT subroutine was developed and employed in the commercial finite element software ABAQUS/Explicit dynamics. The simulation of drawing process was conducted for anisotropic AA3105 aluminum alloy sheet. Cup height (earing profile) and thickness distribution were obtained from experiments and corresponding numerical simulations. Comparison of these results demonstrates great potential of BBC2003 yield criterion in accurate prediction of earing. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Anisotropic material Finite elements numerical algorithms Yield condition BBC2003 yield criterion

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A spectral method solution to crystal elasto-viscoplasticity at finite strains

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INTERNATIONAL JOURNAL OF PLASTICITY 2013年 46卷 37-53页

作者： Eisenlohr, P. Diehl, M. Lebensohn, R. A. Roters, F. Max Planck Inst Eisenforsch GmbH D-40237 Dusseldorf Germany Los Alamos Natl Lab Div Mat Sci & Technol Los Alamos NM 87545 USA

A significant improvement over existing models for the prediction of the macromechanical response of structural materials can be achieved by means of a more refined treatment of the underlying micromechanics. For this, achieving the highest possible spatial resolution is advantageous, in order to capture the intricate details of complex microstructures. Spectral methods, as an efficient alternative to the widely used finite element method (FEM), have been established during the last decade and their applicability to the case of polycrystalline materials has already been demonstrated. However, until now, the existing implementations were limited to infinitesimal strain and phenomenological crystal elasto-viscoplasticity. This work presents the extension of the existing spectral formulation for polycrystals to the case of finite strains, not limited to a particular constitutive law, by considering a general material model implementation. By interfacing the exact same material model to both, the new spectral implementation as well as a FEM-based solver, a direct comparison of both numerical strategies is possible. Carrying out this comparison, and using a phenomenological constitutive law as example, we demonstrate that the spectral method solution converges much faster with mesh/grid resolution, fulfills stress equilibrium and strain compatibility much better, and is able to solve the micromechanical problem for, e.g., a 256(3) grid in comparable times as required by a 64(3) mesh of linear finite elements. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Microstructures Crystal plasticity numerical algorithms Finite elements High-resolution periodic volume element

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The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2017年 107卷 76-95页

作者： Thomas, John C. Van der Ven, Anton Univ Calif Santa Barbara Dept Mat Santa Barbara CA 93106 USA

Conventional approaches to analyzing the very large coherency strains that can occur during solid-state phase transformations are founded in linear elasticity and rely on infinitesimal strain metrics. Despite this, there are many technologically important examples where misfit strains of multi-phase mixtures are very large during their synthesis and/or application. In this paper, we present a framework for constructing strain-energy expressions and stress-strain relationships beyond the linear-elastic limit for crystalline solids. This approach utilizes group theoretical concepts to minimize both the number of free parameters in the strain-energy expression and amount of first-principles training data required to parameterize strain-energy models that are invariant to all crystal symmetries. Within this framework, the strain-energy and elastic stiffness can be described to high accuracy in terms of a set of conventional symmetry-adapted finite strain metrics that we define independent of crystal symmetry. As an illustration, we use first-principles electronic structure data to parameterize strain energy polynomials and employ them to explore the strain energy surfaces of HCP Zr and Mg, as well as several important Zr-H and Mg-Nd phases that are known to precipitate coherently within the HCP matrices of Zr and Mg. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Finite strain Elastic material Anisotropic material Constitutive behavior numerical algorithms

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DIFFERENTIAL DYNAMIC-PROGRAMMING TECHNIQUE FOR OPTIMAL-CONTROL

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OPTIMAL CONTROL APPLICATIONS & METHODS 1994年第2期15卷 77-100页

作者： LIN, TC ARORA, JS UNIV IOWA DEPT MECH ENGNDEPT CIVIL & ENVIRONM ENGN1136 ENGN BLDGIOWA CITYIA 52242 NATL CHUNGHSING UNIV DEPT AGR MACHINERY ENGNTAICHUNG 40227TAIWAN

Continuous- and discrete-time differential dynamic programming (DDP) approaches to solve general optimal control problems are described and analysed. A comparison of the two approaches shows the continuous-time approach to be more general and flexible compared with the discrete-time approach, since it is not tied to any discretization scheme. A comparison of DDP with the non-linear programming (NLP) approach is also given. Three structural control problems - a linear model of a space structure, a single degree of freedom non-linear impact absorber and a non-linear flexible beam subjected to an impulsive load - are used to numerically evaluate the continuous- and discrete-time DDP approaches. Several grid sizes are used to show that the continuous-time approach with a reasonable number of grid points is more accurate and efficient (in most cases) than the discrete-time approach. It is therefore recommended to fully develop and evaluate the technique for the optimal control of large-scale systems.

关键词： DIFFERENTIAL DYNAMIC PROGRAMMING OPTIMAL CONTROL numerical algorithms STRUCTURAL CONTROL

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New Lambert Algorithm Using the Hamilton-Jacobi-Bellman Equation

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第3期33卷 1000-1008页

作者： Bando, Mai Yamakawa, Hiroshi Kyoto Univ Kyoto 6110011 Japan

A study was conducted to demonstrate the formulation of the new Lambert Algorithm using the Hamilton-Jacobi-Bellman Equation (HJB). The two-point boundary-value problem (TPBVP) of the Hamiltonian system was treated as an optimal control problem where the Lagrangian function played a role as a performance index. The approach demonstrated in the study was based on the expansion of the value function in the Chebyshev series with unknown coefficients, considering the computational advantages of the use of Chebyshev polynomials. The differential expressions that arose in the HJB equation were expanded in Chebyshev series with the unknown coefficients. The new algorithm had the potential to provide a solution to the TPVBP using the spectral information about the gravitation potential function and was applicable to the problem under a higher-order perturbed potential function without any modification.

关键词： Hamilton Jacobi Bellman (HJB) Equations Lambert Algorithm Earth Lagrange Multipliers Kinetic Energy Boundary Value Problems Nonlinear Dynamics Nonlinear Systems Finite Difference Method numerical algorithms

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Stable GPC by dynamic programming

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SYSTEMS & CONTROL LETTERS 1998年第5期33卷 291-300页

作者： Chisci, L Rossiter, JA Rice, MJ Univ Florence Dipartimento Sistemi & Informat I-50139 Florence Italy Loughborough Univ Technol Dept Math Sci Loughborough LE11 3TU Leics England

Computationally efficient and numerically robust algorithms for stabilising predictive control are derived. In particular, a static programming (SP) algorithm which takes advantage of the structure in stable GPC and a new dynamic programming (DP) approach are developed and contrasted. Both overcome the numerical difficulties and significantly improve the computational efficiency of some earlier predictive control algorithms with guaranteed stability and moreover it is demonstrated that DP is the more efficient. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： predictive control optimal control dynamic programming numerical algorithms linear control systems

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A multilevel algorithm for solving the trust-region subproblem

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OPTIMIZATION METHODS & SOFTWARE 2009年第2期24卷 299-311页

作者： Toint, Philippe L. Tomanos, D. Weber-Mendonca, M. Univ Namur FUNDP Dept Math Namur Belgium

We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest level (corresponding to the finest discretization), but information on the problem curvature at lower levels is exploited for improved efficiency. The algorithm is inspired by the method described in [J.J. More and D.C. Sorensen, On the use of directions of negative curvature in a modified Newton method, Math. Program. 16(1) (1979), pp. 1-20], for which two different multilevel variants will be analysed. Some preliminary numerical comparisons are also presented.

关键词： nonlinear optimization trust-region subproblem numerical algorithms multilevel methods

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Multiscale modeling for the long-term behavior of laminated composite structures

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AIAA JOURNAL 2005年第8期43卷 1815-1822页

作者： Muliana, A Haj-Ali, R Texas A&M Univ Dept Mech Engn College Stn TX 77843 USA Georgia Inst Technol Sch Civil & Environm Engn Atlanta GA 30332 USA

A multiscale modeling framework for the long-term behavior of fiber-reinforced-polymeric (FRIP) laminated. composite materials and structures is presented. Each unidirectional layer is idealized as a doubly periodic array, of rectangular fibers. The authors' previously developed unit cell with four fiber and matrix subcells is used. The, constitutive models for the elastic linear fiber and nonlinear viscoelastic matrix constituents are performed at the lowest level of the micromodel. This nonlinear micromodel is integrated with both, three-dimensional and shell-based finite elements. A plane-stress constraint is added to the three-dimensional micromodel in the case where shell elements are used. Long-term experimental creep data from the literature for graphite/epoxy are used in order to characterize the material properties. The effect of material nonlinearity on the long-term, behavior of FRP composites,is also investigated. Applications are presented for long-term creep responses of a notched composite panel under surface pressure and a single lap joint under tensile loads This modeling approach is general and can include temperature, moisture, and physical aging effects.

关键词： Composite Structures Fiber Reinforced Composites Transverse Shear Material Properties Creep Test Elastic Deformation Graphite Epoxy Composites numerical algorithms Structural Analysis Elastic Properties

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