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A weight function method for the assessment of partially closed three-dimensional plane cracks

ENGINEERING FRACTURE MECHANICS 2008年第15期75卷 4486-4500页

作者： Lopez Montenegro, Hugo Pablo Cisilino, Adrian Luis Otegui, Jose Univ Mar del Plata Inst Mat Sci & Technol INTEMA RA-7600 Mar Del Plata Argentina

The interference and physical contact between mating fracture surfaces can lead, even under the action of traction loads, to the closure of a crack. A low-cost numerical tool for the assessment of three-dimensional partially closed mode-I cracks is presented in this paper. The devised tool is based on the weight function methodology and it allows computing the geometry of the open part of the crack and the stress intensity factor along the complete crack front. The accuracy and versatility of the proposed procedure is assessed by solving a number of examples and comparing the obtained results with those available in the literature. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： fracture mechanics stress intensity factor three-dimensional cracks crack closure numerical algorithms surface cracks

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Torsion and bending periodic boundary conditions for modeling the intrinsic strength of nanowires

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2008年第11期56卷 3242-3258页

作者： Cai, Wei Fong, William Eisen, Erich Weinberger, Christopher R. Stanford Univ Dept Mech Engn Stanford CA 94305 USA

We present a unified approach for atomistic modeling of torsion and bending of nanowires that is free from artificial end effects. Torsional and bending periodic boundary conditions (t-PBC and b-PBC) are formulated by generalizing the conventional periodic boundary conditions (PBC) to cylindrical coordinates. The approach is simpler than the more general objective molecular dynamics formulation because we focus on the special cases of torsion and bending. A simple implementation of these boundary conditions is presented and correctly conserves linear and angular momenta. We also derive the virial expressions for the average torque and bending moment under these boundary conditions that are analogous to the virial expression for the average stress in PBC. The method is demonstrated by molecular dynamics simulation of Si nanowires under torsion and bending, which exhibit several modes of failure depending on their diameters. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： Elastic properties Microstructure Fracture numerical algorithms

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On the Relationship between Discrete algorithms in Computational Electromagnetics

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FREQUENZ 2008年第7-8期62卷 205-207页

作者： Hoefer, Wolfgang J. R. Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada

Peter Russer has pioneered the unified derivation of numerical algorithms in computational electromagnetics from Maxwell's equations with the general method of moments. While he focused mainly on the derivation of specific time domain algorithms, such as finite difference time domain (FDTD) and transmission line matrix (TLM) methods, he always cultivated a broad perspective of field modeling to avoid the inherent limitations of specialization. It is in this spirit that this contribution to the special issue at the occasion of Peter Russer's 65(th) birthday has been written. It demonstrates in simple terms that finite element. finite difference, finite integration and transmission line matrix (TLM) models, approaches so very different at first glance, can not only he derived from Maxwell's equations with the same general method of moments. out also lead to identical discrete field-solving algorithms when the same spatial discretization is used.

关键词： Electromagnetic fields modeling numerical algorithms finite elements finite difference time domain finite integration transmission line matrix

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A Simple Lambert Algorithm

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2008年第6期31卷 1587-1594页

作者： Avanzini, Giulio Politecn Torino Dept Aerosp Engn I-10129 Turin Italy

A classic result for the two-point boundary value problem in the framework of Keplerian motion allows the derivation of a novel parametrization of orbits passing through two arbitrary points in space. In particular, it is shown that these orbits *** unambiguously identified in terms of their eccentricity vector component in the direction perpendicular to the chord connecting the two points. The parametrization, in terms of transverse eccentricity component, lends itself to an efficient and intuitive solution algorithm for the classical Lambert problem, that is, the determination of the orbit that connects two points in space in a prescribed time. Although, from the computational point of view, the resulting numerical procedure does not provide advantages over the elegant Battin's method, its derivation is considerably less demanding from the mathematical standpoint and physically more intuitive.

关键词： Lambert Algorithm Hyperbolic Trajectories Periapsis Solution Algorithm Elliptical Transfer Orbit Boundary Value Problems numerical algorithms Kepler's Equation Jet Propulsion Laboratory Trajectory Optimization

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A method for computing the transition probability density associated with a multifactor Cox-Ingersoll-Ross model of the term structure of interest rates with no drift term

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NONLINEAR ANALYSIS-HYBRID SYSTEMS 2008年第1期2卷 144-183页

作者： Fatone, Lorella Pacelli, Graziella Recchioni, Maria Cristina Zirilli, Francesco Univ Modena & Reggio Emilia Dipartimento Matemat Pura & Appl I-41100 Modena Italy Univ Politecn Marche Dipartimento Sci Sociali D Serrani I-60121 Ancona Italy Univ Roma La Sapienza Dipartimento Matemat G Castelnuovo I-00185 Rome Italy

We consider an n-dimensional square root process and we obtain a formula involving series expansions for the associated transition probability density. The process mentioned previously can be used to model forward rates, future prices, forward prices and, as a consequence, can be used to price derivatives on these underlyings. The formula that we propose for the transition probability density has been obtained using appropriately a perturbative expansion in the correlation coefficients of the square root process, the Fourier transform and the method of characteristics to solve first-order hyperbolic partial differential equations. The computational effort needed to evaluate this formula is polynomial with respect to the dimension n of the space spanned by the square root process when the order where all the series involved in the transition probability density formula are truncated is fixed. This strategy gives an accuracy that some numerical tests show approximately constant for a wide range of values of n. Some examples of prices of financial derivatives whose evaluation involves integrals in two, twenty and one hundred dimensions (i.e. n = 2, 20, 100), that is derivatives on two, twenty and one hundred assets, where accurate results can be obtained are shown. An experiment shows that the formula derived here for the transition probability density is well suited for parallel computing. This feature makes the formula computationally very attractive to price derivatives of the LIBOR market such as caplets or swaptions since the use of parallel computing and the formula makes it possible to evaluate derivatives on several tens of underlyings in negligible times. The website http://***/recchioni/finance/w1 contains an interactive tool that helps with the understanding of this paper and a portable software library that makes it possible to the user to exploit the formula derived in this paper to evaluate the transition probability densities of its own mo

关键词： Interest rates mathematical models High dimensional parabolic partial differential equations numerical algorithms

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Mechanics of indentation of plastically graded materials - II: Experiments on nanocrystalline alloys with grain size gradients

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2008年第1期56卷 172-183页

作者： Choi, I. S. Detor, A. J. Schwaiger, R. Dao, M. Schuh, C. A. Suresh, S. MIT Dept Mat Sci & Engn Cambridge MA 02139 USA Forschungszentrum Karlsruhe Inst Mat Res 2 D-76344 Karlsruhe Germany

A systematic study of depth-sensing indentation was performed on nanocrystalline (nc) Ni-W alloys specially synthesized with controlled unidirectional gradients in plastic properties. A yield strength gradient and a roughly constant Young's modulus were achieved in the nc alloys, using electrodeposition techniques. The force vs. displacement response from instrumented indentation experiments matched very well with that predicted from the analysis of Part I of this paper. The experiments also revealed that the pile-up of the graded alloy around the indenter is noticeably higher than that for the two homogeneous reference alloys that constitute the bounding conditions for the graded material. These trends are also consistent with the predictions of the indentation analysis. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： functionally graded materials indentation and hardness mechanical testing nanostructured materials numerical algorithms

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A strong contrast homogenization formulation for multi-phase anisotropic materials

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2008年第6期56卷 2287-2297页

作者： Fullwood, David T. Adams, Brent L. Kalidindi, Surya R. Brigham Young Univ Dept Mech Engn Provo UT 84602 USA Drexel Univ Dept Mat Sci & Engn Philadelphia PA 19104 USA

Homogenization relations, linking a material's properties at the mesoscale to those at the macroscale, are fundamental tools for design and analysis of microstructure. Recent advances in this field have successfully applied spectral techniques to Kroner-type perturbation expansions for polycrystalline and composite materials to provide efficient inverse relations for materials design. These expansions have been termed 'weak-contrast' expansions due to the conditionally convergent integrals, and the reliance upon only small perturbations from the reference property. In 1955, Brown suggested a different expansion for electrical conductivity that resulted in absolutely convergent integrals. Torquato subsequently applied the method to elasticity, with good results even for high-contrast materials;thus it is commonly referred to as a 'strong contrast' expansion. The methodology has been applied to elasticity for two phases of isotropic material, generally assuming macroscopic isotropy (with noted exceptions), thus resulting in a rather elegant form of the solution. More recently, a multi-phase form of the solution was developed for conductivity. This paper builds upon this result to apply the method to elasticity of polycrystalline materials with both local and global anisotropy. New spectral formulations are subsequently developed for both the weak and strong contrast solutions. These form the basis for efficient microstructure analysis using these frameworks, and subsequently for inverse design applications. The process is taken through to demonstration of a property closure, which acts as the basis for materials design;the closure delineates the envelope of all physically realizable property combinations for the chosen properties, based on the particular homogenization relation being used. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： microstructures elastic material anisotropic material polycrystalline material numerical algorithms

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Do-it-yourself computational astronomy - Hardwares, algorithms, softwares, and sciences

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JAPANESE JOURNAL OF MATHEMATICS 2008年第1期3卷 49-92页

作者： Makino, Junichiro Natl Astron Observ Japan Ctr Computat Astrophys Tokyo Japan

We overview our GRAPE (GRAvity PipE) and GRAPE-DR project to develop dedicated computers for astrophysical N-body simulations. The basic idea of GRAPE is to attach a custom-build computer dedicated to the calculation of gravitational interaction between particles to a general-purpose programmable computer. By this hybrid architecture, we can achieve both a wide range of applications and very high peak performance. GRAPE-6, completed in 2002, achieved the peak speed of 64Tflops. The next machine, GRAPE-DR, will have the peak speed of 2 Pflops and will be completed in 2008. We discuss the physics of stellar systems, evolution of general-purpose high-performance computers, our GRAPE and GRAPE-DR projects and issues of numerical algorithms.

关键词： computational science special-purpose computer numerical algorithms

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VELOCITY CORRECTIONS TO KEPLER ENERGY AND LAPLACE INTEGRAL

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2008年第9期19卷 1411-1424页

作者： Ma, Da-Zhu Wu, Xin Liu, Fu-Yao Nanchang Univ Dept Phys Nanchang 330031 Peoples R China Shanghai Lixin Univ Commerce Shanghai 201600 Peoples R China

For each celestial body of multi-planet systems, there are two slowly varying quantities or quasi-integrals, Kepler energy and Laplace integral, which are closely associated with the orbital semimajor axis and eccentricity, respectively. To correct numerical errors of the quantities, we give an extension of Nacozy's approach and develop a new manifold correction method, where corresponding reference values of the quantities at every integration step are obtained from integral invariant relations, and only velocity corrections are used to approximately satisfy the two quasi-integrals. As a result, the scheme does enhance the quality of the integration by significantly raising the accuracy of the two elements. Especially, it is superior to the existing dual scaling method in the improvement of eccentricity in general when the adopted integrator provides a sufficient precision to the eccentricity.

关键词： Celestial mechanics numerical algorithms n-body simulations perturbed Kepler problems manifold corrections integral invariant relations

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An interpolated stochastic algorithm for quasi-linear PDEs

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MATHEMATICS OF COMPUTATION 2008年第261期77卷 125-158页

作者： Delarue, Francois Menozzi, Stephane Univ Paris 07 UFR Math F-75251 Paris 05 France

In this paper, we improve the forward-backward algorithm for quasi-linear PDEs introduced in Delarue and Menozzi (2006). The new discretization scheme takes advantage of the standing regularity properties of the true solution through an interpolation procedure. For the convergence analysis, we also exploit the optimality of the square Gaussian quantization used to approximate the conditional expectations involved. The resulting bound for the error is closely related to the Holder exponent of the second order spatial derivatives of the true solution and turns out to be more satisfactory than the one previously established.

关键词： DIFFERENTIAL-EQUATIONS numerical algorithms APPROXIMATION UNIQUENESS EXISTENCE

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