Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris` law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena. (C) 2010 Elsevier Ltd. All rights reserved.

A geometrical approach of 3-D FEA for educational purposes applied to electrostatic fields

A geometrical approach of the finite-element analysis applied to electrostatic fields is presented. This approach is particularly well adapted to teaching Finite Elements in Electrical Engineering courses at undergraduate level. The procedure leads to the same system of algebraic equations as that derived by classical approaches, such as variational principle or weighted residuals for nodal elements with plane symmetry. It is shown that the extension of the original procedure to three dimensions is straightforward, provided the domain be meshed in first-order tetrahedral elements. The element matrices are derived by applying Maxwell`s equations in integral form to suitably chosen surfaces in the finite-element mesh.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Reachability of the synchronous state in a mutually connected PLL network

Second-order phase locked loops (PLLs) are devices that are able to provide synchronization between the nodes in a network even under severe quality restrictions in the signal propagation. Consequently, they are widely used in telecommunication and control. Conventional master-slave (M-S) clock-distribution systems are being, replaced by mutually connected (MC) ones due to their good potential to be used in new types of application such as wireless sensor networks, distributed computation and communication systems. Here, by using an analytical reasoning, a nonlinear algebraic system of equations is proposed to establish the existence conditions for the synchronous state in an MC PLL network. Numerical experiments confirm the analytical results and provide ideas about how the network parameters affect the reachability of the synchronous state. The phase-difference oscillation amplitudes are related to the node parameters helping to design PLL neural networks. Furthermore, estimation of the acquisition time depending on the node parameters allows the performance evaluation of time distribution systems and neural networks based on phase-locked techniques. (c) 2008 Elsevier GmbH. All rights reserved.

Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277-283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127-132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del` Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517-522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Levine J., Martin, P., Rouchon, P. (1999). A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922-937]. (C) 2008 Elsevier Ltd. All rights reserved.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger`s column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger`s column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

On super-RS algebra and Drinfeld realization of quantum affine superalgebras

We describe the realization of the super-Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U-q [osp(1/2)((1))] and its degeneration - central extended super-Yangian double DY(h over bar) [osp(1/2)((1))].

Computation of bifurcation boundaries for power systems: A new Delta-plane method

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the Delta plane. The method exploits some quadratic and linear properties of the load now equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem.

Heat flow for Yang-Mills-Higgs fields, part I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.

Transport-Regional Equity Issue Revisited

Almeida E. S. de, Haddad E. A. and Hewings G. J. D. Transport-regional equity issue revisited, Regional Studies. The objective of this paper is to analyse the relationship between transport and regional equity in Minas Gerais, Brazil. Furthermore, the existence of a trade-off between economic performance and regional equity is investigated as well. To do so, the paper develops a spatial computable general equilibrium model based on Brocker and Schneider`s approach of 2002 to implement comparative static analysis, explicitly incorporating iceberg transportation costs. Four activities are modelled, namely production, final demand, transportation and exports. Two production factors are assumed: labour and other factors. The model has 12 domestic regions and three external regions. Four counterfactual experiments are developed based on decreases in transportation costs due to a `distance shortening`. The main findings indicate that if the transport infrastructure improvement is focused only among poor regions, the promotion of regional equity is insignificant. If the transport infrastructure improvement links are concentrated among rich regions, there is an increase in regional income inequalities. However, if the improvements are targeted to the roads linking poor regions and rich ones, there is greater promotion of regional equity. The same result will occur when improvements are made to all road links of the state. [image omitted] Almeida E. S. de, Haddad E. A. et Hewings G. J. D. La question du rapport entre le transport et l`equilibre regional vue sous un jour nouveau, Regional Studies. Cet article cherche a analyser le rapport entre le transport et l`equilibre regional en Minas Gerais au Bresil. En outre, on examine la presence d`un echange entre la performance economoique et l`equilibre regional. Pour le faire, on construit un modele geographique de l`equilibre general a utiliser sur ordinateur fonde sur l`approche de Brockner et Schneider en 2002 afin de mettre en oeuvre une analyse statique comparative qui comprend explicitement les frais de transport iceberg. On modelise quatre activites, a savoir, la production, la demande finale, le transport et l`exportation. On fait deux suppositions quant aux facteurs de production: la main-d`oevre et d`autres facteurs. Le modele embrasse douze regions internes et trois regions externes. On fait quatre experiences paradoxales fondees sur la baisse des frais de transport due a une `reduction des distances`. Les principaux resultats indiquent que si l`amelioration de l`equipement de transport ne porte que sur les regions defavorisees, la promotion de l`equilibre regional s`avere negligeable. Si l`amelioration de l`equipement de transport focalise les regions riches, il s`avere un creusement des ecarts des revenus regionaux. Cependant, si les ameliorations ciblent les routes qui relient les regions defavorisees aux regions riches, il s`avere une plus grande promotion de l`equilibre regional. Il en va de meme pour la situation ou on a apporte des amenagements a toutes les liaisons routieres de l`etat. Modele geographique de l`equilibre general a utiliser sur ordinateur Equilibre regional Peformance economique Frais de transport Almeida E. S. de, Haddad E. A. und Hewings G. J. D. Die Wiederaufnahme der Frage von Verkehrswesen im Verhaltnis zu regionaler Fairness, Regional Studies. Dieser Aufsatz beabsichtigt, die Beziehung zwischen Verkehrswesen und regionaler Fairness in Minas Gerais (Brasilien) zu analysieren und zugleich auch das Vorkommen von Einbussen entweder bei wirtschaftlicher Leistung der regionaler Fairness zu untersuchen. Zu diesem Zwecke wird ein auf dem Ansatz von Brocker und Schneider (2002) aufbauendes raumliches komputables allgemeines Gleichgewichtsmodell entwickelt, um vergleichende statistische Analysen durchzufuhren, wobei verborgene `Eisberg`-Transportkosten ausdrucklich berucksichtigt werden. Es werden vier Unternehmenstatigk eiten aufgefuhrt: Herstellung, Nachfrage, Transportwesen und Exporte, und zwei Produktionsfaktoren vorausgesetzt: Arbeitskrafte und andere Faktoren. Das Modell umfasst zwolf Inlandsregionen und drei externe Regionen. Es werden vier gegensatzliche Experimente entwickelt, die auf einer Abnahme der Transportkosten infolge einer `Verkurzung der Entfernungen` beruhen. Die Hauptbefunde weisen darauf hin, dass die Forderung regionaler Fairness unbedeutend bleibt, wenn die Verbesserungen der Transportinfrastruktur sich nur auf minderbemittelte Regionen konzentrieren; werden die Verbesserungen der Verbindungen der Transportinfrastruktur in wohlhabenden Regionen durchgefuhrt, so nehmen regionale Einkommensunterschiede zu. Wenn die Verbesserungen jedoch auf Strassen abzielen, die wohlhabende Regionen mit weniger bemittelten verbinden, wird regionale Fairness starker gefordert. Das gleiche Ergebnis wird sich einstellen, wenn Verbesserungen an allen Strassenverbindungen des Staates vorgenommen werden. Raumliches, komputables, allgemeines Gleichgewichtsmodell Regionale Fairness Wirtschaftsleistung Transportkosten Almeida E. S. de, Haddad E. A. y Hewings G. J. D. Revisando el tema de la igualdad del transporte en las regiones, Regional Studies. El objetivo de este documento es analizar la relacion entre el transporte y la igualdad regional en Minas Gerais, Brasil. Asimismo investigamos la existencia de una compensacion entre el rendimiento economico y la igualdad regional. Para ello desarrollamos un modelo de equilibrio general computable y espacial basado en el enfoque de Brocker y Schneider en 2002 para hacer un analisis estatico y comparativo, explicitamente incorporando los costes ocultos de transporte. Se modelan cuatro actividades: la produccion, la demanda final, el transporte y las exportaciones. Suponemos que existen dos factores de produccion: mano de obra y otros factores. En este modelo, existen doce regiones internas y tres regiones externas. Desarrollamos cuatro experimentos contrafactuales basados en la disminucion de los costes de transporte debido a una `acortamiento de las distancias`. Los principales resultados indican que si la mejora de la infraestructura del transporte se centra solo entre las regiones mas pobres, el fomento de la igualdad regional es insignificante. Si los enlaces de la mejora de la infraestructura del transporte se concentran en las regiones ricas, aumentan las desigualdades de ingresos regionales. Sin embargo, si se mejoran los enlaces de carreteras entre las regiones pobres y ricas, se fomenta mejor la igualdad regional. El mismo resultado ocurre cuando se mejoran los enlaces de todas las carreteras del estado. Modelo de equilibrio general computable y espacial Igualdad regional Rendimiento economico Costes de transporte.

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd