Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non-linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-alpha algorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-alpha method. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid-point of a cycle. Copyright (C) 2003 John Wiley Sons, Ltd.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

The generalized element method /

"UILU-ENG 78 1738."

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

The cross-entropy method and its application to minimize the ripple of magnetic levitation forces of a maglev system

This paper explores firstly the potential of a new evolutionary method - the Cross-Entropy (CE) method in solving continuous inverse electromagnetic problems. For this purpose, an adaptive updating formula for the smoothing parameter, some mutation operation, and a new termination criterion are proposed. The proposed CE based metaheuristics is applied to reduce the ripple of the magnetic levitation forces of a prototype Maglev system. The numerical results have shown that the ripple of the magnetic levitation forces of the prototype system is reduced significantly after the design optimization using the proposed algorithm.

A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.

Round robin test: wear of nine dental restorative materials in six different wear simulators - supplement to the round robin test of 2005.

OBJECTIVE: The purpose of the present study was to submit the same materials that were tested in the round robin wear test of 2002/2003 to the Alabama wear method. METHODS: Nine restorative materials, seven composites (belleGlass, Chromasit, Estenia, Heliomolar, SureFil, Targis, Tetric Ceram) an amalgam (Amalcap) and a ceramic (IPS Empress) have been submitted to the Alabama wear method for localized and generalized wear. The test centre did not know which brand they were testing. Both volumetric and vertical loss had been determined with an optical sensor. After completion of the wear test, the raw data were sent to IVOCLAR for further analysis. The statistical analysis of the data included logarithmic transformation of the data, the calculation of relative ranks of each material within each test centre, measures of agreement between methods, the discrimination power and coefficient of variation of each method as well as measures of the consistency and global performance for each material. RESULTS: Relative ranks of the materials varied tremendously between the test centres. When all materials were taken into account and the test methods compared with each other, only ACTA agreed reasonably well with two other methods, i.e. OHSU and ZURICH. On the other hand, MUNICH did not agree with the other methods at all. The ZURICH method showed the lowest discrimination power, ACTA, IVOCLAR and ALABAMA localized the highest. Material-wise, the best global performance was achieved by the leucite reinforced ceramic material Empress, which was clearly ahead of belleGlass, SureFil and Estenia. In contrast, Heliomolar, Tetric Ceram and especially Chromasit demonstrated a poor global performance. The best consistency was achieved by SureFil, Tetric Ceram and Chromasit, whereas the consistency of Amalcap and Heliomolar was poor. When comparing the laboratory data with clinical data, a significant agreement was found for the IVOCLAR and ALABAMA generalized wear method. SIGNIFICANCE: As the different wear simulator settings measure different wear mechanisms, it seems reasonable to combine at least two different wear settings to assess the wear resistance of a new material.

Genetic Algorithms (Binary and Real Codes) for the Optimisation of a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mapeamento de jazidas de bauxitas no Distrito Paragominas – Açailândia (PA-MA) pelo método da sísmica de refração

Nos últimos 30 anos no Brasil, o mapeamento de camada bauxítica tem sido sempre efetuado através de perfilagens de poços. Neste estudo, aplicou-se o método da sísmica de refração rasa pela primeira vez, em cerca de 3.000m de perfis, em caráter experimental em algumas localidades ao longo da rodovia BR-10, assim como no Platô Esperança (região de Jabuti-PA) e perto da cidade de Açailândia (MA); com objetivo de delimitar a camada de bauxita. Embora se tenha utilizado, em algumas ocasiões, durante a interpretação, o método de distância crítica no cálculo de profundidade, foi possível, mediante o emprego do Método Recíproco Generalizado (GRM), o processamento e interpretação dos dados, para se obter a delimitação contínua da camada investigada. O GRM apresenta vantagens sobre os métodos tradicionais, tais como poder delimitar camadas onduladas, detetar camadas escondidas, além da sensibilidade para camadas com mergulho até 20°. A partir dós gráficos da análise de velocidade, foi calculada para a camada de bauxita uma velocidade média de 840 m/s, e mediante o emprego dos tempos de profundidade chegou-se a sua delimitação: ela possui um comportamento irregular, tendo uma espessura média de 5m. A pesquisa geofísica realizada nas três áreas-piloto tem grande importância porque o método utilizado poderá ser aplicado a outras regiões, em condições geológicas semelhantes.

A meta-heurística de busca dispersa aplicada no planejamento da expansão de sistemas de transmissão

Pós-graduação em Engenharia Elétrica - FEIS

The flexibility matrix o timber composite beams with a discrete connection system

This work presents a method for the analysis of timber composite beams which considers the slip in the connection system, based on assembling the flexibility matrix of the whole structure. This method is based on one proposed by Tommola and Jutila (2001). This paper extends the method to the case of a gap between two pieces with an arbitrary location at the first connector, which notably broadens its practical application. The addition of the gap makes it possible to model a cracked zone in concrete topping, as well as the case in which forming produces the gap. The consideration of induced stresses due to changes in temperature and moisture content is also described, while the concept of equivalent eccentricity is generalized. This method has important advantages in connection with the current European Standard EN 1995-1-1: 2004, as it is able to deal with any type of load, variable section, discrete and non-regular connection systems, a gap between the two pieces, and variations in temperature and moisture content. Although it could be applied to any structural system, it is specially suited for the case of simple supported and continuous beams. Working examples are presented at the end, showing that the arrangement of the connection notably modifies shear force distribution. A first interpretation of the results is made on the basis of the strut and tie theory. The examples prove that the use of EC-5 is unsafe when, as a rule of thumb, the strut or compression field between the support and the first connector is at an angle with the axis of the beam of less than 60º.

A two-stage win–win multiattribute negotiation model:optimization and then concession

Many automated negotiation models have been developed to solve the conflict in many distributed computational systems. However, the problem of finding win-win outcome in multiattribute negotiation has not been tackled well. To address this issue, based on an evolutionary method of multiobjective optimization, this paper presents a negotiation model that can find win-win solutions of multiple attributes, but needs not to reveal negotiating agents' private utility functions to their opponents or a third-party mediator. Moreover, we also equip our agents with a general type of utility functions of interdependent multiattributes, which captures human intuitions well. In addition, we also develop a novel time-dependent concession strategy model, which can help both sides find a final agreement among a set of win-win ones. Finally, lots of experiments confirm that our negotiation model outperforms the existing models developed recently. And the experiments also show our model is stable and efficient in finding fair win-win outcomes, which is seldom solved in the existing models. © 2012 Wiley Periodicals, Inc.

Genetic algorithms for discovery of matrix multiplication methods

We present a parallel genetic algorithm for nding matrix multiplication algo-rithms. For 3 x 3 matrices our genetic algorithm successfully discovered algo-rithms requiring 23 multiplications, which are equivalent to the currently best known human-developed algorithms. We also studied the cases with less mul-tiplications and evaluated the suitability of the methods discovered. Although our evolutionary method did not reach the theoretical lower bound it led to an approximate solution for 22 multiplications.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.