Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of precast concrete multi-storey buildings

This study deals with the reduction of the stiffness in precast concrete structural elements of multi-storey buildings to analyze global stability. Having reviewed the technical literature, this paper present indications of stiffness reduction in different codes, standards, and recommendations and compare these to the values found in the present study. The structural model analyzed in this study was constructed with finite elements using ANSYS® software. Physical Non-Linearity (PNL) was considered in relation to the diagrams M x N x 1/r, and Geometric Non-Linearity (GNL) was calculated following the Newton-Raphson method. Using a typical precast concrete structure with multiple floors and a semi-rigid beam-to-column connection, expressions for a stiffness reduction coefficient are presented. The main conclusions of the study are as follows: the reduction coefficients obtained from the diagram M x N x 1/r differ from standards that use a simplified consideration of PNL; the stiffness reduction coefficient for columns in the arrangements analyzed were approximately 0.5 to 0.6; and the variation of values found for stiffness reduction coefficient in concrete beams, which were subjected to the effects of creep with linear coefficients from 0 to 3, ranged from 0.45 to 0.2 for positive bending moments and 0.3 to 0.2 for negative bending moments.

Global Stability Analysis of a Compressible Turbulent Flow around a High-Lift Configuration

The purpose of this work is to analyze a complex high lift configuration for which significant regions of separated flow are present. Current state of the art methods have some diffculty to predict the origin and the progression of this separated flow when increasing the angle of attack. The mechanisms responsible for the maximum lift limit on multi-element wing con?gurations are not clear; this stability analysis could help to understand the physics behind the phenomenon and to find a relation between the flow separation and the instability onset. The methodology presented herein consists in the computation of a steady base flow solution based on a finite volume discretization and a proposal of the solution for a generalized eigenvalue problem corresponding to the perturbed and linearized problem. The eigenvalue problem has been solved with the Arnoldi iterative method, one of the Krylov subspace projection methods. The described methodology was applied to the NACA0012 test case in subsonic and in transonic conditions and, finally, for the first time to the authors knowledge, on an industrial multi-component geometry, such as the A310 airfoil, in order to identify low frequency instabilities related to the separation. One important conclusion is that for all the analyzed geometries, one unstable mode related to flow separation appears for an angle of attack greater than the one correspondent to the maximum lift coe?cient condition. Finally, an adjoint study was carried out in order to evaluate the receptivity and the structural sensitivity of the geometries, giving an indication of the domain region that could be modified resulting in the biggest change of the flowfield.

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier?Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart?Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Global linear and nonlinear stability of viscous confined plane wakes with co-flow

The global stability of confined uniform density wakes is studied numerically, using two-dimensional linear global modes and nonlinear direct numerical simulations. The wake inflow velocity is varied between different amounts of co-flow (base bleed). In accordance with previous studies, we find that the frequencies of both the most unstable linear and the saturated nonlinear global mode increase with confinement. For wake Reynolds number Re = 100 we find the confinement to be stabilising, decreasing the growth rate of the linear and the saturation amplitude of the nonlinear modes. The dampening effect is connected to the streamwise development of the base flow, and decreases for more parallel flows at higher Re. The linear analysis reveals that the critical wake velocities are almost identical for unconfined and confined wakes at Re ≈ 400. Further, the results are compared with literature data for an inviscid parallel wake. The confined wake is found to be more stable than its inviscid counterpart, whereas the unconfined wake is more unstable than the inviscid wake. The main reason for both is the base flow development. A detailed comparison of the linear and nonlinear results reveals that the most unstable linear global mode gives in all cases an excellent prediction of the initial nonlinear behaviour and therefore the stability boundary. However, the nonlinear saturated state is different, mainly for higher Re. For Re = 100, the saturated frequency differs less than 5% from the linear frequency, and trends regarding confinement observed in the linear analysis are confirmed.

Global linear stability of the boundary-layer flow over a rotating sphere

We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk. © 2014 Elsevier Masson SAS. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

A new intelligent algorithm for online voltage stability assessment and monitoring

This paper presents a new approach for assessing power system voltage stability based on artificial feed forward neural network (FFNN). The approach uses real and reactive power, as well as voltage vectors for generators and load buses to train the neural net (NN). The input properties of the NN are generated from offline training data with various simulated loading conditions using a conventional voltage stability algorithm based on the L-index. The performance of the trained NN is investigated on two systems under various voltage stability assessment conditions. Main advantage is that the proposed approach is fast, robust, accurate and can be used online for predicting the L-indices of all the power system buses simultaneously. The method can also be effectively used to determining local and global stability margin for further improvement measures.

Deformation and stability regression models for soil nail walls

Lateral displacement and global stability are the two main stability criteria for soil nail walls. Conventional design methods do not adequately address the deformation behaviour of soil nail walls, owing to the complexity involved in handling a large number of influencing factors. Consequently, limited methods of deformation estimates based on empirical relationships and in situ performance monitoring are available in the literature. It is therefore desirable that numerical techniques and statistical methods are used in order to gain a better insight into the deformation behaviour of soil nail walls. In the present study numerical experiments are conducted using a 2 4 factorial design method. Based on analysis of the maximum lateral deformation and factor-of-safety observations from the numerical experiments, regression models for maximum lateral deformation and factor-of-safety prediction are developed and checked for adequacy. Selection of suitable design factors for the 2 4 factorial design of numerical experiments enabled the use of the proposed regression models over a practical range of soil nail wall heights and in situ soil variability. It is evident from the model adequacy analyses and illustrative example that the proposed regression models provided a reasonably good estimate of the lateral deformation and global factor of safety of the soil nail walls.

Seismic Stability Analysis of a Himalayan Rock Slope

The seismic slope stability analysis of the right abutment of a railway bridge proposed at about 350 m above the ground level, crossing a river and connecting two huge hillocks in the Himalayas, India, is presented in this paper. The rock slopes are composed of highly jointed rock mass and the joint spacing and orientation are varying at different locations. Seismic slope stability analysis of the slope under consideration is carried out using both pseudo-static approach and time response approach as the site is located in seismic zone V as per the earth quake zonation maps of India. Stability of the slope is studied numerically using program FLAC. The results obtained from the pseudo-static analysis are presented in the form of Factor of Safety (FOS) and the results obtained from the time response analysis of the slope are presented in terms of horizontal and vertical displacements along the slope. The results obtained from both the analyses confirmed the global stability of the slope as the FOS in case of pseudo-static analysis is above 1.0 and the displacements observed in case of time response analysis are within the permissible limits. This paper also presents the results obtained from the parametric analysis performed in the case of time response analysis in order to understand the effect of individual parameters on the overall stability of the slope.

Novel algorithm for online voltage stability assessment based on feed forward neural network

This paper presents an artificial feed forward neural network (FFNN) approach for the assessment of power system voltage stability. A novel approach based on the input-output relation between real and reactive power, as well as voltage vectors for generators and load buses is used to train the neural net (NN). The input properties of the feed forward network are generated from offline training data with various simulated loading conditions using a conventional voltage stability algorithm based on the L-index. The neural network is trained for the L-index output as the target vector for each of the system loads. Two separate trained NN, corresponding to normal loading and contingency, are investigated on the 367 node practical power system network. The performance of the trained artificial neural network (ANN) is also investigated on the system under various voltage stability assessment conditions. As compared to the computationally intensive benchmark conventional software, near accurate results in the value of L-index and thus the voltage profile were obtained. Proposed algorithm is fast, robust and accurate and can be used online for predicting the L-indices of all the power system buses. The proposed ANN approach is also shown to be effective and computationally feasible in voltage stability assessment as well as potential enhancements within an overall energy management system in order to determining local and global stability indices

Relevance of local parallel theory to the linear stability of laminar separation bubbles

Laminar separation bubbles are thought to be highly non-parallel, and hence global stability studies start from this premise. However, experimentalists have always realized that the flow is more parallel than is commonly believed, for pressure-gradient-induced bubbles, and this is why linear parallel stability theory has been successful in describing their early stages of transition. The present experimental/numerical study re-examines this important issue and finds that the base flow in such a separation bubble becomes nearly parallel due to a strong-interaction process between the separated boundary layer and the outer potential flow. The so-called dead-air region or the region of constant pressure is a simple consequence of this strong interaction. We use triple-deck theory to qualitatively explain these features. Next, the implications of global analysis for the linear stability of separation bubbles are considered. In particular we show that in the initial portion of the bubble, where the flow is nearly parallel, local stability analysis is sufficient to capture the essential physics. It appears that the real utility of the global analysis is perhaps in the rear portion of the bubble, where the flow is highly non-parallel, and where the secondary/nonlinear instability stages are likely to dominate the dynamics.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

On the Stability and Equilibrium Points of Multistaged SI (n) R Epidemic Models

This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to n. The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time.