Classical constitutive models exhibit strong mesh dependency during softening and the numerical responses tend towards perfectly brittle behavior upon mesh refinements. Such sensitivity can be avoided by adopting the ...
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Classical constitutive models exhibit strong mesh dependency during softening and the numerical responses tend towards perfectly brittle behavior upon mesh refinements. Such sensitivity can be avoided by adopting the gradient-enhanced formulation. The implicit approach incorporates the gradient contributions indirectly via an additional Helmholtz equation and requires only C-0 continuity. The explicit approach computes the gradient terms directly from the local field variables. Assuming a weak satisfaction of the yield function, C-1 continuity or C-0 continuity with additional degrees of freedoms in the penalty approach is required. This makes the explicit method less attractive computationally. However, the explicit approach is able to fully regularize some material models where the standard implicit method fails to perform. Drawing analogy to the over-nonlocal integral formulation, the over-implicit-gradient framework is proposed. In addition, an alternative framework for the explicit gradient method requiring only C-0 continuity is proposed. The regularizing effects of the abovementioned two gradient frameworks show promising applications to strain-softening materials. (C) 2009 Elsevier Ltd. All rights reserved.
A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The...
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A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation of the null-spaces of related block Toeplitz matrices, polynomial matrix factor extraction and linear polynomial matrix equations solving. (c) 2006 Elsevier Ltd. All rights reserved.
An algorithm for shape offsetting is presented that is based on level-set propagation. This algorithm avoids the topological problems encountered in traditional offsetting algorithms, and it deals with curvature singu...
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An algorithm for shape offsetting is presented that is based on level-set propagation. This algorithm avoids the topological problems encountered in traditional offsetting algorithms, and it deals with curvature singularities by including an 'entropy condition' in its numerical implementation.
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the dth order cumulant can be presented in the form of a d-dimensional tensor, the algorithm is p...
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In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the dth order cumulant can be presented in the form of a d-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of supersymmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of d! compared to the naive algorithm.
Using appropriate similarity transform, we present the partial differential equation formulation of both floating strike and fixed strike American lookback option models. We examine the early exercise policies of the ...
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Using appropriate similarity transform, we present the partial differential equation formulation of both floating strike and fixed strike American lookback option models. We examine the early exercise policies of the floating strike and fixed strike American lookback options, while the realized extrmum of the asset price can be monitored continuously or discretely, The characterizations of the optimal exercise prices of American lookback options are also discussed. For the numerical valuation of the American lookback options, several approaches for deriving efficient and accurate numerical results are addressed.
It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallograph...
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It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallographic texture. Such constitutive models are fairly general, and the identification of their parameters can readily be done on the basis of data obtained from a texture measurement. As a result, they are suitable for engineering applications such as elasticplastic finite element models for forming processes. However, the yield loci generated in this way are not automatically convex. Therefore, a new variant of the method has now been developed, which preserves the advantages of the old method, but for which convexity can at least been tested by means of a mathematical criterion. In addition, it has turned out to be possible to slightly modify plastic potentials which do not satisfy the criterion, in order to achieve convexity. An example of a plastic potential modified in this way is discussed. After modification, it was still a good analytical approximation of the plastic potential directly derived from the Taylor-Bishop-Hill theory on the basis of the crystallographic texture of the material. (C) 2003 Elsevier Ltd. All rights reserved.
The present simulations of jets illustrate the effects of sub-grid modelingbased on eddy viscosity in LES. The effective flow Reynolds number is found to be dramaticallydecreased using the dynamic Smagorinsky model, w...
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The present simulations of jets illustrate the effects of sub-grid modelingbased on eddy viscosity in LES. The effective flow Reynolds number is found to be dramaticallydecreased using the dynamic Smagorinsky model, whereas it seems to be preserved and to correspond tothe initial jet conditions using the selective filtering alone, This basic deficiency of theeddy-viscosity subgrid modeling can question its use for the study of free shear flows where theReynolds number is a key parameter, as for instance for the investigation of jet noise.
A study considers the fundamental problem of circular orbit phasing by performing a multiple-impulse maneuver. It is shown below that the peculiar properties of the considered problem allow a simpler procedure of find...
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A study considers the fundamental problem of circular orbit phasing by performing a multiple-impulse maneuver. It is shown below that the peculiar properties of the considered problem allow a simpler procedure of finding the globally optimal solution. It appears to be composed of two- and four-impulse maneuvers and switches between them as the phasing maneuver duration grows. Two-impulse maneuvers do not require any optimization, as they are unambiguously calculated as least-delta-v solutions to the multiple-revolution Lambert problem.
A different approach to the solution of a nonlinear set of algebraic equations is presented. It is basically a revision of the Newton iterative algorithm from a digital control point of view, The Newton algorithm is c...
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A different approach to the solution of a nonlinear set of algebraic equations is presented. It is basically a revision of the Newton iterative algorithm from a digital control point of view, The Newton algorithm is considered like a digital control algorithm that acts on a set of nonlinear algebraic equations. Its target is to find a value x* that satisfies the algebraic equation set. This value can be considered as a particular ''input'' of the equation set which gives a zero ''output'' while the iteration index can be considered as the clock of the digital system. From this point of view some correlations between the stability of digital systems and the Newton algorithm can be shown, This approach allows us to understand the reasons behind the convergence failure of some modified Newton algorithms such as source stepping, damping, and limiting that literature often reports as heuristic.
A possible mechanism of the self-sustained shock-wave oscillation caused by unsteady transonic shock boundary-layer interaction on a supercritical airfoil with fully separated flow at the shock wave is illustrated. Th...
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A possible mechanism of the self-sustained shock-wave oscillation caused by unsteady transonic shock boundary-layer interaction on a supercritical airfoil with fully separated flow at the shock wave is illustrated. The case of a shock wave oscillating on the upper airfoil surface about a mean position is considered (corresponding to Tijdeman's type A shock motion). Because of the movement of the shock, pressure waves are formed which propagate downstream in the separated flow region at a velocity ap. On reaching the trailing edge, the disturbances generate upstream moving waves at velocity au. These waves will interact with the shock and impart energy to maintain its oscillation. The loop is then completed and the period of the shock wave oscillation should agree with the time it takes for a disturbance to propagate from the shock to the trailing edge plus the duration for an upstream moving wave to reach the shock from the trailing edge. In this Note, experimental results supporting this model for self-sustained shock oscillation are presented.
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