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Convergence acceleration of iterative modal reduction methods

AIAA JOURNAL 2001年第1期39卷 134-140页

作者： Kim, KO Kang, MK Inha Univ Dept Aerosp Engn Inchon 402751 South Korea

An accelerated method is presented for the iterative condensation of eigenproblems, The present study was motivated by the improved reduction system and the succession-level approximate reduction (SAR), The reduction procedures are supplemented with the secund-order approximation in the series expansion of the system transformation. The reduced equation of an equivalent system and the transformation matrix are updated in an iterative manner. In addition, systematic derivation and comparison of the equations involved in various condensations have been sought. The matrix update incorporates not only inverse iteration but also subspace transformation implicitly. The series expansion can be considered as repeated updates of the transformation matrix through inverse iteration. The solution accuracy is sensitive to the selection of the degrees of freedom, for which sequential elimination or energy method may be preferable. When a poor selection causes a sudden failure of the update method, the hybrid dynamic condensation fan be used. The method of SAR is closely related to the hybrid dynamic condensation.

关键词： Condensation Rayleigh Ritz Method Turbine Blades Transverse Vibrations Stiffness Matrices Energy Methods Structural Optimization numerical algorithms Computing Facilities Sensitivity Analysis

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Large-eddy simulation of a supersonic boundary layer using an unstructured grid

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AIAA JOURNAL 2001年第7期39卷 1288-1295页

作者： Urbin, G Knight, D Rutgers State Univ Dept Mech & Aerosp Engn Piscataway NJ 08854 USA

A Mach 3 adiabatic flat plate turbulent boundary layer is studied using large-eddy simulation (LES), The filtered compressible Navier-Stokes equations are solved on a three-dimensional unstructured grid of tetrahedral cells. A compressible extension of the rescaling-reintroducing process of Lund et al. (Lund, T., Wu, X., and Squires, K., "Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations," Journal of Compartational Physics, Vol. 140, No. 2, 1998, pp. 233-2583 is developed to generate the inflow conditions. The effect of the subgrid-scale motion is incorporated using two approaches, namely, monotone integrated LES (MILES) and the Smagorinsky subgrid-scale model. A detailed grid refinement study is performed. The statistical predictions (friction velocity, adiabatic wall temperature, mean velocity profile, normal Reynolds stress, and Reynolds shear stress) obtained from MILES are in close agreement viith experimental data and direct numerical simulation. The results indicate that the subgrid-scale effects can be adequately modeled using MILES without the need for the Smagorinsky model.

关键词： Unstructured Grid Incompressible Turbulent Boundary Layer Direct numerical Simulation Navier Stokes Equations Turbulent Prandtl Number Isotropic Turbulence Stress Distribution Free Stream Kinematic Viscosity numerical algorithms

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Continuous adjoint sensitivities for optimization with general cost functionals on unstructured meshes

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AIAA JOURNAL 2001年第1期39卷 48-55页

作者： Baysal, O Ghayour, K Old Dominion Univ Coll Engn & Technol Norfolk VA 23529 USA Old Dominion Univ Dept Aerosp Engn Norfolk VA 23529 USA

A continuous adjoint approach is developed to obtain the sensitivity derivatives for the Euler equations, The complete derivation of the costate equations and their transversality (boundary) conditions are presented. Both the state and the costate equations are second-order finite volume discretized fur unstructured meshes, and they are coupled with a constrained optimization algorithm. Also integrated into the overall methodology are a geometry parameterization method for the shape optimization, and a dynamic unstructured mesh method fur the shape evolution and the consequent volume mesh adaptations. For the proof of concept, three transonic airfoil optimization problems are presented. This method accepts general cost functionals, which are not necessarily functions of pressure only. It is also shown that a switch to the natural coordinate system in conjunction with the reduction of the governing state equation to the control surface results in sensitivity integrals that are only a function of the tangential derivatives of the state variables. This approach eliminates the need fur normal derivative computations that can be erroneous.

关键词： NACA 0012 Shape Optimization Continuity Equation numerical algorithms Sensitivity Analysis Pressure Drag numerical Optimization Material Derivatives Angle of Attack Upwind Scheme

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New approach to solution of the Falkner-Skan equation

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AIAA JOURNAL 2001年第5期39卷 965-967页

作者： Sher, I Yakhot, A Ben Gurion Univ Negev Dept Mech Engn Pearlstone Ctr Aeronaut Engn Studies IL-84105 Beer Sheva Israel

Provides information on a study which examined an approach to the general solution of laminar boundary-layer flows discovered by Falkner and Skan in 1931. numerical procedure; Results and discussion; Conclusions.

关键词： Boundary Layer Equations Strouhal Numbers Direct numerical Simulation Runge Kutta Methods Stagnation Point Boundary Value Problems Aerospace Engineering numerical algorithms numerical Analysis Radial Velocity

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The effective energy and laminated microstructures in martensitic phase transformations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2001年第4期49卷 899-925页

作者： Goldsztein, GH CALTECH Pasadena CA 91125 USA

We study the behavior of crystals that undergo martensitic transformations. On cooling, the high-temperature phase (austenite) transforms to the martensite phase changing its crystalline symmetry. The lower crystalline symmetry of the martensite gives rise to several variants of martensite. Each variant has an associated transformation strain. These variants accommodate themselves (according to the boundary conditions) forming a microstructure that minimizes the elastic energy. This minimum value of the energy is called the the effective energy. We assume that all the material is in the martensite phase (i.e. the material is at low temperatures). We show that, assuming the geometrically linear approximation, the maximum of the effective energy restricted to applied strains in the convex hull of the transformation strains is attained by an applied strain that is a convex combination of only two transformation strains. We derive a recurrence relation to compute the energy corresponding to laminated microstructures of arbitrary rank, under the assumption that the variants of martensite are linearly elastic and their elastic moduli are isotropic. We use this recurrence relation to develop an algorithm that minimizes the energy over microstructures that belong to the class of rank-v laminates. We apply our methods to the case in which the transformation is cubic to monoclinic (corresponding to TiNi). We conclude with some comments on the possible implications of our calculations on the behavior of this shape-memory alloy. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： microstructures phase transformation layered material numerical algorithms optimization

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Modeling multilayer woven fabrics

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APPLIED PHYSICS LETTERS 2001年第2期79卷 180-181页

作者： Åström, JA Mäkinen, JP Timonen, J Univ Jyvaskyla Dept Phys FIN-40351 Jyvaskyla Finland

A numerical algorithm for nonlinear elastic relaxation of a multilayer woven fabric is introduced and tested. The equilibrium solutions are compared with real samples. An excellent result is obtained in spite of two simplifications: Bending stiffness of the fibers and friction between the fibers are both neglected. The numerical simulation is very fast and cost efficient in the search for optimal fabrics. (C) 2001 American Institute of Physics.

关键词： Multilayers Elasticity Friction numerical algorithms numerical modeling

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On computing normalized-coprime factorizations of general rational matrices

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2001年第2期46卷 286-290页

作者： Oara, C Univ Polytechn Bucharest Fac Automat Control & Comp RO-73115 Bucharest Romania

This note presents a numerically reliable approach for computing the normalized-coprime factorization of an arbitrary (possibly improper) rational matrix. We consider both the cases in which the factorization is coprime and normalized with respect to either the left-half plane or the unit disk, corresponding to systems with continuous- or discrete-time evolutions. The proposed algorithm remedies the numerical drawbacks of alternative methods available thus far in the literature.

关键词： descriptor systems normalized-coprime factorization numerical algorithms rational matrices

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A model for rolling deformation with grain subdivision. Part I: The initial stage

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INTERNATIONAL JOURNAL OF PLASTICITY 2001年第4期17卷 469-489页

作者： Leffers, T Riso Natl Lab Mat Res Dept DK-4000 Roskilde Denmark

dA model is presented for plastic deformation with grain subdivision into parallel bands. The experimental reference is the subdivision into "cell blocks" observed in rolled aluminium. The model maintains intragranular strain continuity between the bands with relaxed constraints. One version of the model maintains intergranular strain continuity by imposing identical strains in all grains. Another version does not provide formal fulfilment of intergranular strain continuity, but it tries to minimize strain discontinuity by selection of the appropriate physical solutions. Part I deals with the initial stage of grain subdivision at low strain. Part II (Leffers, T. 2001. A model for rolling deformation with grain subdivision. Part II: the subsequent stage. Int. J. Plasticity 17, 491-511.) deals with the subsequent stages at higher strains and the resulting rolling texture. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： dislocations microstructures crystal plasticity metallic materials polycrystalline material numerical algorithms

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A model for rolling deformation with grain subdivision. Part II: The subsequent stage

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INTERNATIONAL JOURNAL OF PLASTICITY 2001年第4期17卷 491-511页

作者： Leffers, T Riso Natl Lab Mat Res Dept DK-4000 Roskilde Denmark

Part I of the present work dealt with the initial stage of plastic deformation with grain subdivision into two band families. It covered the situation with different average strains in the individual grains (the non-Taylor case) and the situation with identical average strains in the individual grains (the Taylor case). For the latter situation part I included solutions with 5 plus 3 and with 4 plus 4 active slip systems in the two band families, respectively. In part II we deal with the subsequent stage of plastic deformation (finite strains) for the Taylor case with four active slip systems in each band family. In the subsequent stage the cooperation between the two band families leads to an energetic advantage for grain subdivision, and it leads to a simulated texture with decreased sharpness in accordance with experimental observations. Finally, the physics behind grain subdivision are discussed on the basis of the results in Parts I and II and various general considerations. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： dislocations microstructures crystal plasticity metallic materials polycrystalline material numerical algorithms

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On the constitutive modeling of coupled thermomechanical phase-change problems

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INTERNATIONAL JOURNAL OF PLASTICITY 2001年第12期17卷 1565-1622页

作者： de Saracibar, CA Cervera, M Chiumenti, M UPC ETS Ingenieros Caminos Canales & Puertos Int Ctr Numer Methods Engn CIMNE Barcelona 08034 Spain

This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/ elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. numerical s

关键词： solidification and melting thermomechanical processes constitutive behaviour finite elements numerical algorithms

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