Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

Análise estática não linear de um edifício em betão armado

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Civil

Assessing the behaviour of RC beams subject to significant gravity loads under cyclic loads

Gravity loads can affect a reinforced concrete structure's response to seismic actions, however, traditional procedures for testing the beam behaviour do not take this effect into consideration. An experimental campaign was carried out in order to assess the influence of the gravity load on RC beam connection to the column subjected to cyclic loading. The experiments included the imposition of a conventional quasi-static test protocol based on the imposition of a reverse cyclic displacement history and of an alternative cyclic test procedure starting from the gravity load effects. The test results are presented, compared and analysed in this paper. The imposition of a cyclic test procedure that included the gravity loads effects on the RC beam ends reproduces the demands on the beams' critical zones more realistically than the traditional procedure. The consideration of the vertical load effects in the test procedure led to an accumulation of negative (hogging) deformation. This phenomenon is sustained with the behaviour of a portal frame system under cyclic loads subject to a significant level of the vertical load, leading to the formation of unidirectional plastic hinges. In addition, the hysteretic behaviour of the RC beam ends tested was simulated numerically using the nonlinear structural analysis software - OpenSees. The beam-column model simulates the global element behaviour very well, as there is a reasonable approximation to the hysteretic loops obtained experimentally. (C) 2013 Elsevier Ltd. All rights reserved.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Modelação numérica do punçoamento de lajes fungiformes reforçadas com parafusos

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Civil, Ramo de Estruturas

Modelação e reforço de vigas de betão armado com laminados de fibra de carbono

Com o atual estado da construção em Portugal, a reabilitação urbana é uma realidade. Com muitos dos edifícios a necessitarem de reforço, procurou-se abordar o comportamento real das estruturas, indo além da típica análise linear elástica. Desta forma, pretendeu-se aumentar o conhecimento acerca da modelação numérica não-linear de estruturas de betão armado, expondo modelos de cálculo relativamente simples e de fácil compreensão, com o objetivo de servir de base a uma avaliação da capacidade de carga de um elemento estrutural. O modelo de cálculo foi validado com recurso ao trabalho experimental de Bresler e Scordelis (1963). Analisou-se o comportamento até à rotura de três vigas ensaiadas à flexão. Posteriormente, foi realizado um estudo paramétrico de algumas propriedades do betão com vista à discussão do melhor de ajuste. Em seguida, já no campo do reforço estrutural, simulou-se numericamente vigas reforçadas com CFRP, com recurso à técnica EBR e NSM. Comparam-se os resultados numéricos com os ensaios experimentais de Cruz et al. (2011a). Avaliou-se ainda o desempenho de soluções alternativas com variações na área e comprimento dos laminados. Para finalizar, foi desenvolvida uma campanha experimental com diferentes áreas de reforço. Conceberam-se e executaram-se três vigas de betão armado sobre as quais se instalaram laminados de CFRP. Os resultados experimentais são apresentados e discutidos à luz dos resultados do respetivo modelo numérico. No cômputo geral, o presente trabalho permitiu aferir a validade de modelos não-lineares na previsão do comportamento efetivo das estruturas até à rotura. Assinala-se a concordância em vários resultados experimentais analisados. Ficaram também patentes os principais fenómenos ligados ao reforço de vigas com CFRP, focados nos respetivos modelos de cálculo e nos resultados experimentais apresentados.

A framework for robustness assessment in the context of corroded RC structures

Structural robustness is an emergent concept related to the structural response to damage. At the present time, robustness is not well defined and much controversy still remains around this subject. Even if robustness has seen growing interest as a consequence of catastrophic consequences due to extreme events, the fact is that the concept can also be very useful when considered on more probable exposure scenarios such as deterioration, among others. This paper intends to be a contribution to the definition of structural robustness, especially in the analysis of reinforced concrete structures subjected to corrosion. To achieve this, first of all, several proposed robustness definitions and indicators and misunderstood concepts will be analyzed and compared. From this point and regarding a concept that could be applied to most type of structures and dam-age scenarios, a robustness definition is proposed. To illustrate the proposed concept, an example of corroded reinforced concrete structures will be analyzed using nonlinear analysis numerical methods based on a contin-uum strong discontinuities approach and isotropic damage models for concrete. Finally the robustness of the presented example will be assessed.

Estudo paramétrico do punçoamento em lajes fungiformes através de análise numérica

Dissertação para obtenção do Grau de Mestre em Engenharia Civil, Ramo de Estruturas

Robustness of corroded reinforced concrete structures

Short Term Scienti c Mission, COST ACTION TU-0601

Modelo de base físico para a consideração da influência da cabeça da ancoragem na capacidade de carga de lajes fungiformes reforçadas por introdução de novas armaduras

Dissertação para obtenção do Grau de Mestre em Engenharia Civil - Ramo de Estruturas e Geotecnia

Assessment of the performance of steel fibre reinforced self-compacting concrete in elevated slabs

The reinforcement mechanisms at the cross section level assured by fibres bridging the cracks in steel fibre reinforced self-compacting concrete (SFRSCC) can be significantly amplified at structural level when the SFRSCC is applied in structures with high support redundancy, such is the case of elevated slab systems. To evaluate the potentialities of SFRSCC as the fundamental material of elevated slab systems, a ¼ scale SFRSCC prototype of a residential building was designed, built and tested. The extensive experimental program includes material tests for characterizing the relevant properties of SFRSCC, as well as structural tests for assessing the performance of the prototype at serviceability and ultimate limit conditions. Three distinct approaches where adopted to derive the constitutive laws of the SFRSCC in tension that were used in finite element material nonlinear analysis to evaluate the reliability of these approaches in the prediction of the load carrying capacity of the prototype.

A performance-based method for seismic evaluation of masonry walls strengthened with RC layers

A conventional method for seismic strengthening of masonry walls is externally application of reinforced concrete layer (shotcrete). However, due to the lack of analytical and experimental information on the behavior of strengthened walls, the design procedures are usually followed based on the empirical relations. Using these design procedures have resulted in massive strengthening details in retrofitting projects. This paper presents a computational framework for nonlinear analysis of strengthened masonry walls and its versatility has been verified by comparing the numerical and experimental results. Based on the developed numerical model and available experimental information, design relations and failure modes are proposed for strengthened walls in accordance with the ASCE 41 standard. Finally, a sample masonry structure has been strengthened using the proposed and available conventional methods. It has been shown that using the proposed method results in lower strengthening details and appropriate (ductile) failure modes

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.