This study intends to develop a useful tool for the investigation of the behavior of three-dimensional elastic frame structures undergoing large deformations and large rotations, using a mini-computer with an attached array processor. An updated Lagrangian finite element formulation is established by employing conventional two node-twelve degree of freedom beam elements. In order to trace the pre- and post-buckling equilibrium path, an improved nonlinear solution procedure is proposed. The software is designed to make it possible to solve large-scale problems on a mini-computer by adopting a hypermatrix scheme and the segmentation into a number of processors which are independent programs. The software is simulated to estimate the performance of the software on a combined mini-computer/array processor system. By using the simulator time measurements are performed for three different cases of large-scale three-dimensional frame structure models, which verify the usefulness of the array processor in the solution of non-linear finite element structural problems. With the use of the hypermatrix scheme, an alternative solution algorithm for system of linear equations is proposed. The accuracy of the finite element formulation and the effectiveness of the solution algorithms implemented are demonstrated by carefully selected two- and three-dimensional frame examples. Finally, directions for further research are discussed.

Estudamos uma classe de campos de vetores seccionalmente lineares no plano denotada por X. Tais campos aparecem frequentemente em modelos matemáticos aplicados à engenharia. Baseados no trabalho de J. Sotomayor e R. Garcia [SG03], impondo condições sobre as singularidades, órbitas periódicas e separatrizes, definimos um conjunto de campos de vetores que são estruturalmente estáveis em X. Provamos que esse conjunto é aberto, denso e tem medida de Lebesgue total em X, o qual é um espaço vetorial de dimensão finita. / We study a class of piecewise-linear vector fields in the plane denoted by X. These vector fields appear often in mathematical models applied to Engineering. Based on Jorge Sotomayor and Ronaldo Garcia paper [SG03], we impose conditions on singularities, periodic orbits and separatrices, to define a set of vector fields structurally stable in X. We give a proof that this set is open, dense and has full Lebesgue measure in X, that is a finite dimensional vector space.

O objetivo principal deste trabalho é o estudo da estabilidade estrutural dos atratores de semigrupos. Começamos este trabalho apresentando o conceito e propriedades básicas de semigrupos que possuem atratores globais. Estudamos, então, semigrupos gradientes e dinamicamente gradientes, mostrando que eles são equivalentes e que uma pequena perturbação autônoma de um semigrupo gradiente continua sendo gradiente. Estudamos as variedades estável e instável de um ponto de equilíbrio hiperbólico e o comportamento de soluções periódicas sob perturbação. Concluímos este trabalho com o estudo dos semigrupos Morse-Smale. / The main goal of this work is the study of structural stability of global attractors. We start this work by presenting the concept and basic properties of semigroups and global attractors. We then studied gradient and dinamically gradient semigroups, showing that these concepts are equivalent and that a small autonomous pertubation of a gradient semigroup remains a gradient semigroup. We studied the stable and unstable manifolds in the neighbourhood of a hyperbolic equilibrium point and the behavior of periodic solutions under perturbation. Finally, we studied the Morse-Smale semigroups.

O objetivo deste trabalho é provar um Closing Lema Parcial para variedades bidimensionais compactas, orientáveis ou não--orientáveis. Para enunciá--lo, considere um campo vetorial \\linebreak $X\\in\\mathfrak^r(M)$, $r\\ge 2$, de classe $C^r$ em uma variedade bidimensional compacta $M$, e seja $\\Sigma$ um segmento transversal a $X$ passando por um ponto recorrente não--trivial $p$ de $X$. Seja $P:\\Sigma\\to\\Sigma$ a correspondente transformação de primeiro retorno. O primeiro resultado deste trabalho consiste em mostrar que se $P$ tem a propriedade de que para todo $n\\ge N$ e $x\\in{m dom}\\,(P^n)$, $\\vert DP^n(x)\\vert<\\lambda$, onde $N\\in\\N$ e $0<\\lambda<1$, então existe um campo vetorial $Y$ arbitrariamente próximo de $X$ na topologia $C^r$ tendo uma trajetória periódica passando por $p$. O segundo resultado consiste em apresentar condições, sobre os expoentes de Lyapunov de $P$, para que $\\vert DP^n\\vert<\\lambda$ para todo $n\\ge N$. Nesta tese, também incluímos um resultado sobre a estabilidade assintótica no infinito de campos planares diferenciáveis, mas não necessariamente de classe $C^1$. / The aim of this work is to provide a Partial $C^r$ Closing Lemma for compact surfaces, orientable or non--orientable. To state it, let $X\\in\\mathfrak^r(M)$, $r\\ge 2$, be a $C^r$ vector field on a compact surface $M$ and let $\\Sigma$ be a transverse segment to $X$ passing through a non--trivial recurrent point $p$ of $X$. Let $P:\\Sigma\\to\\Sigma$ be the corresponding first return map. The first result of this work consists in showing that if $P^n$ has the property that for all $n\\ge N$ and $x\\in{m dom}\\,(P^n)$, $\\vert DP^n(x)\\vert<\\lambda$, where $N\\in\\N$ e $0<\\lambda<1$, then there exists a vector field $Y$ arbitrarily close to $X$ in the $C^r$ topology such that $p$ is a periodic point of $Y$. The second result consists in presenting sufficient conditions, upon the Lyapunov exponents of $P$, so that $\\vert DP^n\\vert<\\lambda$ for all $n\\ge N$. In this thesis, we also include a result concerning the asymptotic stability at infinity of planar differentiable vector fields, not necessarily of class $C^1$.

We generalize the notions of structural stability and hyperbolicity for the family of (multivalued) complex maps Hc(z) = zr + c; where r > 1 is rational and zr = exp r log z: We discovered that Hc is structurally stable at every hyperbolic parameter satisfying the escaping condition. Surprisingly, there may be infinitely many attracting periodic points for Hc. The set of such points gives rise to the dual Julia set, which is a Cantor set coming from a Conformal Iterated Funcion System. Both the Julia set and its dual are projections of holomorphic motions of dynamical systems (single valued maps) defined on compact subsets of Banach spaces, denoted by Xc and Wc, respectively. For c close to zero: (1) we show that Jc is a union of quasiconformal arcs around the unit circle; (2) the set Xc is an holomorphic motion of the solenoid X0; (3) using the formalism of Gibbs states we exhibit an upper bound for the Hausdorff dimension of Jc; which implies that Jc has zero Lebesgue measure. / Generalizamos as noções de estabilidade estrutural e hiperbolicidade para a família de correspondências holomorfas Hc(z) = zr + c; onde r > 1 é racional e zr = exp r log z: Descobrimos que Hc é estruturalmente estável em todos os parâmetros hiperbólicos satisfazendo a condição de fuga. Tipicamente Hc possui infinitos pontos periódicos atratores, fato totalmente inesperado, uma vez que este número é sempre finito para aplicações racionais. O conjunto de tais pontos dá origem ao chamado conjunto de Julia dual, que é um conjunto de Cantor proveniente de um Conformal Iterated Function System. Tanto o conjunto de Julia e quanto seu dual são projeções de movimentos holomorfos de sistemas definidos em subconjuntos compactos denotados por Xc e Wc; respectivamente de um espaço de Banach. Para todo c próximo de zero: (1) mostramos que Jc é reunião de arcos quase-conformes próximos do círculo unitário; (2) o conjunto Xc é um movimento holomorfo do solenóide X0; (3) utilizando o formalismo dos estados de Gibbs, exibimos um limitante superior para a dimensão de Hausdorff de Jc. Consequentemente, Jc possui medida de Lebesgue nula.

No description available.

Unreinforced masonry (URM) construction, which has been widely used in the United States, presents a large threat to life safety and regional economic development because of its poor seismic resistance. In this research, the nonlinear seismic properties of URM structures were investigated via a quasi-static test of a full-scale two-story URM building and associated analytical and numerical studies. The tests of the 24ft. by 24ft. in plan 22ft. high URM building revealed that the damage was characterized by (1) the formation of large discrete cracks in the masonry walls and (2) the rocking and sliding of URM piers. Both of these results were consistent with the predictions based on individual component properties obtained in previous research. However, the tests also revealed significant global behavior phenomena, including flange effects, overturning moment effects, and the formation of different effective piers in a perforated wall. This global behavior greatly affected the response of the URM building tested. In order to understand the nonlinear behavior of the test structure, a series of analytical studies were conducted. First, at the material level, a mechanical key model was proposed to describe the failure of URM assemblages under a biaxial state of stress. Second, at the component level, an effective pier model was developed to illustrate the mixed failure modes of a URM pier and its nonlinear force-deformation relationship. Third, at the structure level, a nonlinear pushover model was built using the mechanical models at the material and component levels to describe the nonlinear properties of a URM building. This nonlinear pushover model and a three-dimensional finite element model were employed to analyze the test structure. Both gave results in good agreement with the test data. Improvements to current provisions for the evaluation of existing masonry structures were proposed.

Metal building frames are typically designed using welded prismatic and web-tapered members with doubly-symmetric and/or singly-symmetric cross sections. Until recently, the base U.S. provisions for design of frames with web-tapered members were provided in the AISC ASD (1989) and LRFD (1999) Specifications. Unfortunately, these previous AISC provisions address only a small range of practical designs. As a result, metal building manufacturers have tended to develop their own methods for design of the wide range of nonprismatic member geometries and configurations encountered in practice. This research develops new design procedures for design of frames using general prismatic members and web-tapered members. An equivalent prismatic member concept utilized in prior research and the prior AISC provisions is generalized to accommodate the broad range of member types and configurations commonly used in metal building industry. Furthermore, the new design procedures incorporate many of the improvements achieved in the AISC (2005&2010) Specifications to metal building frame design. These improvements include a new stability design method, the direct analysis method, more complete considerations of different column buckling limit states (flexural, torsional and flexural-torsional buckling), and improved axial load and flexural resistance provisions. This research develops practical design-based procedures for simplified calculation of the elastic buckling resistances of prismatic and web-tapered members to facilitate the application of the proposed design methods. In addition, this research performs a relatively comprehensive assessment of beam lateral torsional buckling (LTB) behavior and strength of prismatic and web-tapered members using refined virtual test simulation. It is demonstrated that web-tapered members behave in a comparable fashion to prismatic members. Based on the virtual simulation study, recommendations for potential improvement of the AISC LTB resistance equations are provided. Lastly, the strength behavior of several representative metal building frames is studied in detail using the same virtual test simulation capabilities developed and applied for the assessment of the beam LTB resistances.

The spans of precast prestressed concrete bridge girders have become longer to provide more economical and safer transportation structures. As the spans have increased, so has the depth of the girders which in turn have increased the slenderness of the girders. Slenderness in a beam or girder would increase the likelihood that a stability failure would occur. Stability failures could pose a danger to construction personnel due to the sudden nature in which a stability failure would occur. Furthermore, stability failures of prestressed concrete girders during construction would cause a detrimental economic impact due to the costs associated with the failure of the girder, the ensuing construction delays, damage to construction equipment and potential closures to highways over which the bridge was being constructed. An experimental and analytical study was performed to determine the stability behavior of prestressed concrete beams. Two stability phenomenons were investigated: (1) lateral-torsional buckling and (2) global stability. An emphasis was placed on the effects of initial imperfections on the stability behavior; the effect elastomeric bearing pads and support rotational stiffness was investigated. The experimental study involved testing six rectangular prestressed concrete beams for lateral-torsional buckling, a PCI BT-54 for thermal deformations and the same PCI BT-54 for global stability. The 32-ft. long rectangular beams were 4-in. wide and 40-in. deep. The PCI BT-54 had a 100-ft. long span. A material and geometric nonlinear, incremental load analysis was performed on the six rectangular beams. The nonlinear analyses matched the experimental load versus lateral displacement and load versus rotation behavior, and the analysis predicted the experimental maximum load within an error of 2%. The nonlinear analysis was extrapolated to several different initial imperfection conditions to parametrically study the effect of initial lateral displacement and initial rotation on the inelastic lateral-torsional buckling load. A simplified expression for lateral-torsional stability of beams with initial imperfections was developed. The data from the parametric study were used to develop reduction parameters for both initial sweep and initial rotation. The rollover stability behavior of the PCI BT-54 was investigated experimentally, and it was found that support end rotations and the elastomeric bearing pads had an adverse effect on the global stability. The nonlinear analysis was employed with the addition of a bearing pad model. It was found that the behavior was sensitive to the bearing pad stiffness properties and the assumption of uniform bearing. From the research, it was apparent that rollover stability was the controlling stability phenomenon for precast prestressed concrete bridge girders, not lateral-torsional buckling.

No description available.