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A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

Acta Mechanica Sinica 2006年第5期22卷 479-485页

作者： Kaiping Yu Jie Zhao Department of Astronautical Science and Mechanics Harbin Institute of Technology Harbin 150001 China

A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero- stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.

关键词： Nonlinear structural dynamics numerical algorithm Stability Overshoot

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An application of DHW algorithm for the solution of inverse heat conduction problem

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 2006年第4期27卷 1264-1273页

作者： Gembarovic, J. Loeffler, M. TPRL Inc W Lafayette IN 47906 USA

A damped heat wave (DHW) algorithm is applied for the temperature distribution calculation in a solution of a linear inverse heat conduction problem (IHCP). A nonlinear least squares algorithm is used for calculation of the unknown boundary heat flux history in a one-dimensional medium. The solution is based on the assumption that the temperature measurements are available, at least, at one point of the medium over the whole time domain. Sample calculations, for a comparison between exact heat sources and estimated ones, are made to confirm the validity of the proposed method. The close agreement between the exact and estimated values calculated for both exact and noisy data shows the potential of the proposed method for finding a relatively accurate heat source distribution in a one-dimensional homogeneous finite medium. The proposed method of solving inverse heat conduction problems is very simple and easy to implement.

关键词： inverse heat conduction problem numerical algorithm temperature distribution

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Stability and finite strain of homogenized structures soft in shear: Sandwich or fiber composites, and layered bodies

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2006年第6期43卷 1571-1593页

作者： Bazant, ZP Beghini, A Northwestern Univ Evanston IL 60208 USA

The stability theories energetically associated with different finite strain measures are equivalent if the tangential moduli are transformed as a function of the stress. However, for homogenized soft-in-shear composites, they can differ greatly if the material is in small-strain and constant elastic moduli measured in small-strain tests are used. Only one theory can then be correct. The preceding variational energy analysis showed that, for sandwich columns and elastomeric bearings, respectively, the correct theories are Engesser's and Haringx's, associated with Green's and Almansi's Lagrangian strain tensors, respectively. This analysis is reviewed, along with supporting experimental and numerical results, and is then extended to arbitrary multiaxially loaded homogenized soft-in-shear orthotropic composites. It is found that, to allow the use of constant shear modulus when the material is in small strain, the correct stability theory is associated with a general Doyle-Ericksen finite strain tensor of exponent m depending on the principal stress ratio. Further it is shown that the standard updated Lagrangian algorithm for finite element analysis, which is associated with Green's Lagrangian finite strain, can give grossly incorrect results for homogenized soft-in-shear structures and needs to be generalized for arbitrary finite strain measure to allow using constant shear modulus for critical loads at small strain. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： stability finite strain buckling critical loads homogenization composites sandwich structures elastomeric bearings layered bodies finite element analysis numerical algorithm

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Determination of the relaxation modulus of a linearly viscoelastic material

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MECHANICS OF TIME-DEPENDENT MATERIALS 2006年第2期10卷 125-133页

作者： Sorvari, Joonas Malinen, Matti Univ Kuopio Dept Phys FIN-70211 Kuopio Finland

In this paper, a numerical method for computing the relaxation modulus of a linearly viscoelastic material is presented. The method is valid for relaxation tests where a constant strain rate is followed by a constant strain. The method is similar to the procedure suggested by Zapas and Phillips. Unlike Zapas-Phillips approach, this new method can be also applied for times shorter than t (1)/2, where t (1) denotes time when the maximum strain is achieved. Therefore this method is very suitable for materials that experiences fast relaxation. The method is verified with numerical simulations. Results from the simulations are compared with analytical solution and Zapas-Phillips method. Results indicate that the presented approach is suitable for estimating the relaxation modulus.

关键词： numerical algorithm relaxation test finite ramp time relaxation modulus linear viscoelasticity

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A numerical algorithm of fuzzy reliability

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2003年第3期80卷 299-307页

作者： Jiang, QM Chen, CH Nanyang Technol Univ Sch Mech & Prod Engn Singapore 639798 Singapore

In this paper, a computational model of fuzzy reliability focusing on solving the engineering problems with random general stress-fuzzy general strength is presented. The mathematical basis of this computational model is that the fuzzy probability can be computed with the computational method of conventional probability by use of a mathematical transition. Based on this computational model, a numerical algorithm is given which can be applied to compute the fuzzy reliability of mechanical components, sensors, electronic units, etc. This establishes a basis for the reliability analysis of systems consisting of components with fuzzy reliability. As an example, a case study about the fuzzy reliability analysis of a kind of sensor used in railway systems is provided to verify the logic of this algorithm. The computation results show that this algorithm fits the engineering experience. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： numerical algorithm fuzzy reliability random general stress-fuzzy general strength model

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A new algorithm for the automation of phase diagram calculation

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COMPUTATIONAL MATERIALS SCIENCE 2006年第1期35卷 61-74页

作者： Emelianenko, M Liu, ZK Du, Q Penn State Univ Dept Math University Pk PA 16803 USA Penn State Univ Dept Mat Sci & Engn University Pk PA 16803 USA

We propose a new algorithm for minimizing the Gibbs energy functional and constructing phase diagrams through utilizing geometric properties of the energy surfaces together with effective sampling techniques to improve on the starting points for the minimization. The new method possesses advantages over existing methods in terms of computational complexity and can be used to automate the calculation of phase equilibria in complex systems. numerical results for binary and ternary systems are presented. Generalizations to higher dimensions are discussed. (c) 2005 Elsevier B.V. All rights reserved.

关键词： phase diagrams stable equilibria free energy minimization automation numerical algorithm complexity

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Symmetrical components estimation through nonrecursive Newton-type numerical algorithm

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IEEE TRANSACTIONS ON POWER DELIVERY 2003年第2期18卷 359-363页

作者： Terzija, VV Markovic, D Univ Belgrade Fac Elect Engn Belgrade Serbia Elektromorava YU-12000 Pozarevac Serbia

The paper reports new software developments for symmetrical components estimation. Nonrecursive Newton-type algorithm is extended with the second stage algorithm for symmetrical components calculation from the estimated fundamental phasors of three-phase signals (arbitrary voltages or currents). The algorithm is not sensitive to power system frequency changes and to the harmonic distortion of input signals. The algorithm is tested through computer simulations and by using laboratory obtained input signals and those recorded in the real distribution network.

关键词： Newton-type algorithm nonlinear estimation numerical algorithm symmetrical components

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Navigation in non-inertial terrestrial frames using the attitude matrices

Navigation in non-inertial terrestrial frames using the atti...

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48th International Symposium ELMAR-2006 on Multimedia Signal Processing and Communications

作者： Grigorie, Teodor Lucian Sandu, Dragos George Aron, Ioan Univ Craiova Fac Elect Engn Craiova Romania Flight Test Ctr Craiova Romania Univ Politehn Bucuresti Fac Aerosp Engn Bucharest Romania

ISBN: (纸本)9789537044039

The paper presents a numerical algorithm used to establish the position of a vehicle reported to the Earth s geographical frame. The method we suggest based on the direct integration of the equation of inertial navigation, considering the vehicle's attitude as a result of the integration of the differential matriceal attitude equation. This integration is performed using a quick method, the induced commutation error being avoided with a numerical logistics which implies the usage of the data acquisition card from strop-down gyrometers in the navigation processor

关键词： inertial navigation strap-down systems attitude matrices numerical algorithm

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A new singular value decomposition algorithm suited to parallelization and preliminary results

A new singular value decomposition algorithm suited to paral...

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IASTED International Conference on Advances in Computer Science and Technology

作者： Konda, Taro Takata, Masami Iwasaki, Masashi Nakamura, Yoshimasa Kyoto Univ Dept Appl Math & Phys Grad Sch Informat Sakyo Ku Yoshida Honmachi Kyoto Japan JST PRESTO Kawaguchi Saitama Japan

ISBN: (纸本)0889865450

This paper proposes a new singular value decomposition algorithm which can be fully parallelized. I-SVD algorithm was recently proposed using the theory of integrable systems. It computes singular value decompositions much faster than standard algorithms such as QR and Divide and Conquer(D&C), and at the same accuracy level. However, we show that the parallelism of I-SVD is limited to singular vector computation only because it shows seriality in the case of singular value computation. Our concern is a fully parallelizable algorithm whose serial version is as fast and accurate as I-SVD. Compared to the original D&C, where most of the running time is consumed for vector updating during singular vector computation, our new algorithm first computes singular values by the "compact" D&C without computing singular vectors. Thus, the compact D&C is wholly faster than the original one. The corresponding singular vectors are then computed by twisted factorization. The algorithm has great parallelism because each step can be executed parallelly. Our new algorithm is numerically tested on some SVD computations. It is as fast as I-SVD and even much faster than the standard algorithms. Also, its accuracy is as good as that of the others. 505-033 in display pdf

关键词： singular value decomposition numerical algorithm numerical analysis high performance computing parallelization integrable system

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Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation

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Computational Mathematics and Mathematical Physics 2006年第4期46卷 680-690页

作者： Mikhailov, G.A. Rogazinsky, S.V. Ureva, N.M. Institute of Computational Mathematics and Mathematical Geophysics Siberian Division Russian Academy of Sciences Novosibirsk 630090 pr. Akademika Lavrent'eva 6 Russian Federation

New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number N ₀ of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is O(N ₀ ^-1 ). Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient. © MAIK "Nauka/Interperiodica" (Russia), 2006.

关键词： Monte Carlo method numerical algorithm Smoluchowski equation

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