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Instability finite element analysis of fibre reinforced composite structures based on the third order theory

APPLIED COMPOSITE MATERIALS 1996年第5期3卷 301-309页

作者： Maksimovic, S AERONAUT INST YU-11133 BELGRADESERBIAYUGOSLAVIA

In this paper a refined higher-order shear deformation theory for the instability finite element analysis of fibre reinforced shell like composite structures is developed. A higher order shear deformation theory allows parabolic description of the transverse shear stresses and therefore the shear correction factors of the usual shear deformation theory are not required. The present formulation is based on a higher order shear theory in which in-plane displacements are expanded as cubic functions of the thickness coordinate. The conditions of zero transverse shear stresses on the top and bottom faces are satisfied. Laminate material is assumed to be linearly elastic, homogeneous and isotropic/orthotropic. The 4-node quadrilateral shell finite element with 8 degrees of freedom per node has been developed which eleviates most of the deficiencies associated with such types elements. The effects of the transverse shear deformation on the buckling loads are investigated. It is shown that the present theory predicts buckling loads more accurately then CTP or the first order shear deformation theory. To determine buckling loads here is used lanczos algorithm. The good agreement of the numerical and experimental results is indicative of a reliable presented shell element and procedure for practical instability analysis of the structures made of the fiber reinforced laminates.

关键词： buckling layered shells finite elements eigen problem lanczos algorithm

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FAST ESTIMATION OF PRINCIPAL EIGENSPACE USING lanczos-algorithm

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1994年第3期15卷 974-994页

作者： XU, GH KAILATH, T STANFORD UNIV INFORMAT SYST LABSTANFORDCA 94305

This paper considers the problem of finding the principal eigenspace and/or eigenpairs of M x M Hermitian matrices that can be expressed or approximated by a low-rank matrix plus a shift., i.e., A = B + sigmaI where B is a rank d Hermitian matrix and d << M. Such matrices arise in signal processing, geophysics, dynamic structure analysis, and other fields. The proposed problem can be solved by a full O(M3) eigendecomposition, or by several more efficient alternatives, e.g., the power, subspace iteration, and lanczos algorithms. This paper shows that the lanczos algorithm can exploit the inherent structure and is generally more efficient than other alternatives. More specifically, if A = B + sigmaI, the lanczos algorithm can be used to exactly determine the principal eigenspace span{B} and sigma with a finite amount of computation. If A is close to B + sigmaI, the lanczos algorithm can estimate the principal eigenvectors and eigenvalues in O(M2d) flops. It is shown that the errors in the estimates of the kth principal eigenvalue lambda(k) and eigenvector e(k) decay at the rate of epsilon2/(lambda(k) - sigma)2 and epsilon/(lambda(k) - sigma), respectively, where epsilon is a measure of the mismatch between A and B + sigmaI.

关键词： FAST EIGENDECOMPOSITION KRYLOV SUBSPACE lanczos algorithm EIGENVALUE MULTIPLICITY

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PROBABILISTIC BOUNDS ON THE EXTREMAL EIGENVALUES AND CONDITION NUMBER BY THE lanczos-algorithm

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1994年第2期15卷 672-691页

作者： KUCZYNSKI, J WOZNIAKOWSKI, H COLUMBIA UNIV INST APPL MATH NEW YORK NY 10027 USA

The authors analyze the lanczos algorithm with a random start for approximating the extremal eigenvalues of a symmetric positive definite matrix. They present some bounds on the Lebesgue measure (probability) of the sets of these starting vectors for which the lanczos algorithm gives at the kth step satisfactory approximations to the largest and smallest eigenvalues. Combining these bounds gets similar estimates for the condition number of a matrix.

关键词： EXTREME EIGENVALUES lanczos algorithm CONDITION NUMBER RANDOM START

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A SHIFTED BLOCK lanczos-algorithm FOR SOLVING SPARSE SYMMETRICAL GENERALIZED EIGENPROBLEMS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1994年第1期15卷 228-272页

作者： GRIMES, RG LEWIS, JG SIMON, HD NASA AMES RES CTRDIV NUMER AERODYNAM SIMULAT SYSTMOFFETT FIELDCA 94035

An ''industrial strength'' algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block lanczos algorithm. However, the combination of these two techniques is not trivial;there are many pitfalls awaiting the unwary implementor. The focus of this paper is on identifying those pitfalls and avoiding them, leading to a ''bomb-proof'' algorithm that can live as a black box eigensolver inside a large applications code. The code that results comprises a robust shift selection strategy and a block lanczos algorithm that is a novel combination of new techniques and extensions of old techniques.

关键词： lanczos algorithm SPARSE EIGENVALUE PROBLEMS STRUCTURAL ANALYSIS SYMMETRICAL GENERALIZED EIGENVALUE PROBLEM ORTHOGONALIZATION METHODS

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A parallel implementation of a generalized lanczos procedure for structural dynamic analysis

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INTERNATIONAL JOURNAL OF HIGH SPEED COMPUTING 1996年第2期8卷 171-204页

作者： Mackay, DR Law, KH STANFORD UNIV DEPT CIVIL ENGN STANFORD CA 94305 USA

The lanczos method has rapidly become the preferred method of solution for the generalized eigenvalue problems. The recent emergence of parallel computers has aroused much interest in the practical implementation of the lanczos algorithm on these high performance computers. This paper describes an implementation of a generalized lanczos algorithm on a distributed memory parallel computer, with specific application to structural dynamic analysis. One major cost in the parallel implementation of the generalized lanczos procedure is the factorization of the (shifted) stiffness matrix and the forward and backward solution of triangular systems. In this paper, we review a parallel sparse matrix factorization scheme and propose a strategy for inverting the principal block submatrix factors to facilitate the forward and backward solution of triangular systems on distributed memory parallel computers. We also discuss the different strategies in the implementation of mass-matrix-vector multiplication and how they are used in the implementation of the lanczos procedure. The lanczos procedure implemented includes partial and external selective reorthogonalizations. Spectral shifts are introduced when memory space is not sufficient for storing the lanczos vectors. The tradeoffs between spectral shifts and lanczos iterations are discussed. Numerical results on Intel's parallel computers, the iPSC/860 hypercube and the Paragon machines will be presented to illustrate the effectiveness and scalability of the parallel generalized lanczos procedure.

关键词： eigenvalues lanczos algorithm sparse matrices parallel matrix computation structural dynamics

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A parallel block lanczos algorithm for distributed memory architectures

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Parallel algorithms and Applications 1994年第3-4期4卷 211-221页

作者： Guarracino, Mario Rosario Perla, Francesca Dipartimento di Matematica e Applicazioni Università degli Studi di Napoli Federico II Complesso Universitario Monte Sant’Angelo Edificio T-80126 Napoli via Cinthia Italy Istituto di Statistica e Matematica Facoltà di E. T. C. I Istituto Universitario Navale di Napoli 5-80134 Napoli via A. De Gasperi Italy

In this paper we propose a block lanczos algorithm suitable for MIMD distributed memory message passing architectures. It is based on an efficient parallelization of basic linear algebra operations, such as matrix-matrix, sparse matrix-matrix, and dense QR factorization. We assume an unidirectional ring as connection topology and a block column wrap-around matrices distribution. We have chosen this approach to improve load-balancing, to eliminate the intersection of messages and to decrease communication. The parallel lanczos algorithm has been tested on a Convex Meta Series, a cluster of HP Series 9000 workstations running the PVM communication system. Results of the performance evaluation based on some classical parameters are shown. © 1994, Taylor & Francis Group, LLC. All rights reserved.

关键词： Distributed memory message passing architectures Eigenvalues problems lanczos algorithm Sparse symmetric matrices

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FAST SUBSPACE-BASED SYSTEM-IDENTIFICATION - AN INSTRUMENTAL VARIABLE APPROACH

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AUTOMATICA 1995年第6期31卷 903-905页

作者： CHO, YM KAILATH, T Information Systems Laboratory Stanford University Stanford CA 94305-4055 U.S.A.

Recently developed subspace-based system identification (4SID) techniques have opened new routes to the identification of multi-input multi-output systems. The 4SID techniques guarantee convergence, and run faster than the statistically efficient prediction error methods without much performance loss. The resulting computational load of the 4SID techniques is O(NM(2)), where N is the data length and M is the sliding window size. However, the computational burden O(NM(2)) can become prohibitively large as N and M grow large. Noting that the major bottleneck comes from the QR factorization of an M X N data matrix and that the existing 4SID techniques do not exploit the structure of the matrices arising in the identification procedure, we propose a new implementation of the existing 4SID, which reduces the computational burden to O(NM) by exploiting the displacement and low-rank structure of the matrices.

关键词： SUBSPACE SYSTEM IDENTIFICATION INSTRUMENTAL VARIABLE DISPLACEMENT STRUCTURE SCHUR algorithm lanczos algorithm

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LINEAR PREDICTION AND SINGLE-CHANNEL RECORDING

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JOURNAL OF NEUROSCIENCE METHODS 1995年第1-2期60卷 69-78页

作者： CARTER, AA OSWALD, RE CORNELL UNIV COLL VET MEDDEPT PHARMACOLITHACANY 14853

The measurement of individual single-channel events arising from the gating of ion channels provides a detailed data set from which the kinetic mechanism of a channel can be deduced. In many cases, the pattern of dwells in the open and closed states is very complex, and the kinetic mechanism and parameters are not easily determined. Assuming a Markov model for channel kinetics, the probability density function for open and closed time dwells should consist of a sum of decaying exponentials. One method of approaching the kinetic analysis of such a system is to determine the number of exponentials and the corresponding parameters which comprise the open and closed dwell time distributions. These can then be compared to the relaxations predicted from the kinetic model to determine, where possible, the kinetic constants. We report here the use of a linear technique, linear prediction/singular value decomposition, to determine the number of exponentials and the exponential parameters. Using simulated distributions and comparing with standard maximum-likelihood analysis, the singular value decomposition techniques provide advantages in some situations and are a useful adjunct to other single-channel analysis techniques.

关键词： SINGULAR VALUE DECOMPOSITION lanczos algorithm MAXIMUM-LIKELIHOOD ANALYSIS PATCH-CLAMP RECORDING

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ASYMPTOTIC WAVE-FORM EVALUATION VIA A lanczos METHOD

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APPLIED MATHEMATICS LETTERS 1994年第5期7卷 75-80页

作者： GALLIVAN, K GRIMME, E VANDOOREN, P Coordinated Science Laboratory University of Illinois at Urbana-Champaign 307 N. Mathews Urbana IL 61801 USA

In this paper we show that the two-sided lanczos procedure combined with implicit restarts, offers significant advantages over Pade approximations used typically for model reduction in circuit simulation.

关键词： DYNAMICAL SYSTEMS MODEL REDUCTION NUMERICAL METHODS PADE APPROXIMATION lanczos algorithm

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PADE APPROXIMATION OF LARGE-SCALE DYNAMIC SYSTEMS WITH lanczos METHODS

PADE APPROXIMATION OF LARGE-SCALE DYNAMIC SYSTEMS WITH LANCZ...

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33rd IEEE Conference on Decision and Control

作者： GALLIVAN, K GRIMME, E VANDOOREN, P UNIV ILLINOIS COORDINATED SCI LABURBANAIL 61801

ISBN: (纸本)0780319680

The utility of lanczos methods for the approximation of large-scale dynamical systems is considered. In particular, it is shown that the lanczos method is a technique for yielding Pade approximants which has several advantages over more traditional explicit moment matching approaches. An extension of the lanczos algorithm is developed for computing multi-point Pade approximations of descriptor systems.

关键词： DYNAMIC SYSTEM PADE APPROXIMATION lanczos algorithm MODEL REDUCTION

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