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## Análise de problemas elásticos não lineares geométricos empregando o método dos elementos finitos posicional; Elastic nonlinear geometric analysis with positional finite element method

Maciel, Daniel Nelson
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
75.87%

## Análise não linear geométrica de pórticos planos considerando ligações semirrígidas elastoplásticas; Geometric nonlinear analysis of plane frames considering elastoplastic semi-rigid connections

Reis, Marcelo Campos Junqueira
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
46.02%

## Análise estática não linear plana de pontes estaiadas e determinação das frequências naturais e modos de vibração; Nonlinear static analysis of plane cable-stayed bridges and determination of natural frequencies and vibration modes

Moreira Filho, Carlos Augusto
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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As pontes estaiadas são exemplos de estruturas esbeltas e flexíveis onde a capacidade de utilização dos materiais tem grande importância. Neste sentido, para garantir a melhor utilização dos materiais envolvidos (aço e concreto, por exemplo), é preciso determinar as forças de protensão aplicadas aos cabos. A melhor distribuição dos momentos fletores no tabuleiro de ponte é aquela obtida com uma viga contínua. Pontes estaiadas fornecem apoios elásticos ao tabuleiro. O presente trabalho emprega o método da anulação dos deslocamentos, MAD, para obter as forças axiais a que os cabos estarão submetidos de modo a aproximar o comportamento do tabuleiro ao de uma viga contínua. O método MAD. proporciona uma estrutura economicamente mais viável. O código computacional desenvolvido realiza análises estática e modal por meio do método dos elementos finitos, MEF. A análise estática utilizada é a não linear geométrica, considerando as não linearidades do efeito de catenária do cabo, e dos elementos submetidos à compressão. O material é assumido no campo do regime elástico linear. A ponte é modelada por elementos de treliça plana com módulo de elasticidade de Dischinger, para simular os cabos, e elementos de pórtico plano para os elementos do tabuleiro e da torre. O carregamento da estrutura considera a atuação apenas do peso-próprio dos elementos estruturais. O código computacional desenvolvido permite...

## Sobre análise não linear geométrica de edifícios considerando o empenamento dos núcleos estruturais e a interação solo-estrutura; On geometric nonlinear analysis of tall buildings structures considering the warping of the structural cores and the soil-structure interaction

Silva, Wagner Queiroz
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
45.97%

## Geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral finite elements with reduced integration

Azevedo, Ricardo Lessa; Awruch, Armando Miguel
Tipo: Artigo de Revista Científica Formato: application/pdf
ENG
Relevância na Pesquisa
55.87%
This work presents a geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral isoparametric elements. The main features of the present formulation are: (a) the element matrices are obtained using reduced integrations with hourglass control; (b) an explicit Taylor-Galerkin scheme is used to carry out the dynamic analysis, solving the corresponding equations of motion in terms of velocity components; (c) the Truesdell stress rate tensor is used; (d) the vector processor facilities existing in modern supercomputers were used. The results obtained are comparable with previous solutions in terms of accuracy and computational performance.

## Geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral finite elements with reduced integration

Azevedo,Ricardo Lessa; Awruch,Armando Miguel
Fonte: The Brazilian Society of Mechanical Sciences Publicador: The Brazilian Society of Mechanical Sciences
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
55.87%
This work presents a geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral isoparametric elements. The main features of the present formulation are: (a) the element matrices are obtained using reduced integrations with hourglass control; (b) an explicit Taylor-Galerkin scheme is used to carry out the dynamic analysis, solving the corresponding equations of motion in terms of velocity components; (c) the Truesdell stress rate tensor is used; (d) the vector processor facilities existing in modern supercomputers were used. The results obtained are comparable with previous solutions in terms of accuracy and computational performance.

## CS-ASA: a new computational tool for advanced analysis of steel frames

Fonte: Escola de Minas Publicador: Escola de Minas
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
45.97%
A new computational tool for advanced static and dynamic analyses of steel framed structures based on the Finite Element Method has been developed and is presented herein. Two sources of nonlinearity can be considered in these analyses, i.e.: the geometric, which considers the nonlinear effects of structure displacements; and the physical, which considers the nonlinear effects of the mechanical characteristics of the material used in civil construction. Loading, geometric and residual stress imperfections can also be considered. To illustrate some of the features and capabilities that differentiate this tool from existing commercial programs, static and dynamic stability analyses of some structural systems with rigid and semi-rigid connections are evaluated. The results obtained by other researchers are used to validate the nonlinear formulations and numerical solution methodologies implemented in CS-ASA, and to attest the efficiency of the structural analysis program presented herein.

## Análise não-linear de treliças pelo método dos elementos finitos posicional; Nonlinear analysis of trusses using the positional finite element method

Lacerda, Estéfane George Macedo de
Fonte: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Engenharia Civil; MECÂNICA DAS ESTRUTURAS, ESTRUTURAS DE CONCRETO E ALVENARIA E MATERIAIS E PROCESSOS CONSTRUTIVOS Publicador: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Engenharia Civil; MECÂNICA DAS ESTRUTURAS, ESTRUTURAS DE CONCRETO E ALVENARIA E MATERIAIS E PROCESSOS CONSTRUTIVOS
Tipo: Dissertação Formato: application/pdf
POR
Relevância na Pesquisa
45.82%
This work presents the positional nonlinear geometric formulation for trusses using different strain measures. The positional formulation presents an alternative approach for nonlinear problems. This formulation considers nodal positions as variables of the nonlinear system instead of displacements (widely found in literature). The work also describes the arc-length method used for tracing equilibrium paths with snap-through and snap-back. Numerical applications for trusses already established in the literature and comparisons with other studies are provided to prove the accuracy of the proposed formulation; Este trabalho apresenta a formulação posicional não linear geométrica para treliças usando diferentes medidas de deformação. A formulação posicional é uma abordagem alternativa para problemas não lineares. Essa formulação considera as posições nodais como variáveis do sistema não linear em vez dos deslocamentos (que é largamente utilizado na literatura). O trabalho também descreve o método do comprimento de arco, usado para traçar caminhos de equilíbrio com snap-through e snap-back. Aplicações numéricas com treliças já consagradas na literatura e comparações com outros trabalhos são fornecidos para provar a acurácia da formulação proposta

## Geometric analysis of trapezoidal hills subject to vertically incident SH waves

V??lez Zuluaga, Susana
Fonte: Universidad EAFIT; Maestr??a en Ingenier??a; Escuela de Ingenier??a Publicador: Universidad EAFIT; Maestr??a en Ingenier??a; Escuela de Ingenier??a
Tipo: masterThesis; Tesis de Maestr??a; acceptedVersion
SPA
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Topographic effects have been shown to play a significant role on the local ground response during earthquakes -- However, due to the large number of involved parameters the problem is rarely considered in seismic design regulations -- Recently, there has been a tremendous development by the engineering community, regarding methods and computational infrastructure to address the problem via numerical simulations -- Although numerically based models may give accurate results when fed with appropriate field data, the obtained solutions are still very limited and strongly dependent on unknown factors like the input excitation -- Therefore, there is a clear need to develop strong conceptual understanding allowing practising engineers to arrive at first order approximations, useful to validate complex numerical solutions -- In this work we explore the use of purely geometrical methods in the determination of the dynamic response of trapezoidal geometries to vertically incident horizontally polarized shear waves -- The geometries may be considered representative of hills or earth embankments, depending on its characteristic dimensions -- The hill response is first found with a frequency domain based boundary element code and the results are later analysed using a geometric approach...

## Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws

Chen, Gui-Qiang; Xiang, Wei; Zhang, Yongqian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and corresponding characteristic fields to be linearly degenerate. The approach is based on our careful construction of more accurate auxiliary approximation to weakly nonlinear geometric optics, the properties of wave front-tracking approximate solutions, the behavior of solutions to the approximate asymptotic equations, and the standard semigroup estimates. To illustrate this approach more clearly, we focus first on the Cauchy problem for the hyperbolic systems with compact support initial data of small bounded variation and establish that the $L^1-$estimate between the entropy solution and the geometric optics expansion function is bounded by $O(\varepsilon^2)$, {\it independent of} the time variable. This implies that the simpler geometric optics expansion functions can be employed to study the behavior of general entropy solutions to hyperbolic systems of conservation laws. Finally, we extend the results to the case with non-compact support initial data of bounded variation.; Comment: 30 pages, 2 figures

## Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross-Pitaevskii equation

Jackson, Russell K.; Weinstein, Michael I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.86%
Gross-Pitaevskii and nonlinear Hartree equations are equations of nonlinear Schroedinger type, which play an important role in the theory of Bose-Einstein condensation. Recent results of Aschenbacher et. al. [AFGST] demonstrate, for a class of 3- dimensional models, that for large boson number (squared L^2 norm), N, the ground state does not have the symmetry properties as the ground state at small N. We present a detailed global study of the symmetry breaking bifurcation for a 1-dimensional model Gross-Pitaevskii equation, in which the external potential (boson trap) is an attractive double-well, consisting of two attractive Dirac delta functions concentrated at distinct points. Using dynamical systems methods, we present a geometric analysis of the symmetry breaking bifurcation of an asymmetric ground state and the exchange of dynamical stability from the symmetric branch to the asymmetric branch at the bifurcation point.; Comment: 22 pages, 7 figures

## A Nonlinear Adiabatic Theorem for Coherent States

Carles, Rémi; Kammerer, Clotilde Fermanian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.8%
We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the nonlinear evolution preserves the separation of modes, in a scaling such that nonlinear effects are critical (the envelope equation is nonlinear). The proof relies on a fine geometric analysis of the role of spectral projectors, which is compatible with the treatment of nonlinearities. We also prove a nonlinear superposition principle for these adiabatic wave packets.; Comment: 21 pages, no figure

## Barrier methods for critical exponent problems in geometric analysis and mathematical physics

Erway, Jennifer; Holst, Michael
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.74%
We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem and the Einstein constraint equations, which simultaneously contain several challenging features: high spatial dimension n >= 3, varying (potentially non-smooth) coefficients, critical (even super-critical) nonlinearity, non-monotone nonlinearity (arising from a non-convex energy), and spatial domains that are typically Riemannian manifolds rather than simply open sets in Rn. These problems may exhibit multiple solutions, although only positive solutions typically have meaning. This creates additional complexities in both the theory and numerical treatment of such problems, as this feature introduces both non-uniqueness as well as the need to incorporate an inequality constraint into the formulation. In this work, we consider numerical methods based on Galerkin-type discretization, covering any standard bases construction (finite element, spectral, or wavelet), and the combination of a barrier method for nonconvex optimization and global inexact Newton-type methods for dealing with nonconvexity and the presence of inequality constraints. We first give an overview of barrier methods in non-convex optimization...

## Nonlinear geometric optics for reflecting uniformly stable pulses

Coulombel, Jean-Francois; Williams, Mark
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.81%
We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small wavelengths. Pulses reflecting off fixed noncharacteristic boundaries are considered under the assumption that the underlying boundary problem is uniformly spectrally stable in the sense of Kreiss. There are two respects in which these results make rigorous earlier formal treatments of pulses. First, we give a rigorous construction of leading pulse profiles in problems where pulses traveling with many distinct group velocities are, unavoidably, present; and second, we provide a rigorous error analysis which yields a rate of convergence of approximate to exact solutions as the wavelength approaches zero. Unlike wavetrains, interacting pulses do not produce resonances that affect leading order profiles. However, our error analysis shows the importance of estimating pulse interactions in the construction and estimation of correctors. Our results apply to a general class of systems that includes quasilinear problems like the compressible Euler equations; moreover, the same methods yield a stability result for uniformly stable Euler shocks perturbed by highly oscillatory pulses.

## Multiphase weakly nonlinear geometric optics for Schrodinger equations

Carles, Rémi; Dumas, Eric; Sparber, Christof
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.89%
We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation on the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrodinger equation on the torus in negative order Sobolev spaces.; Comment: 29 pages

## Resonant leading term geometric optics expansions with boundary layers for quasilinear hyperbolic boundary problems

Hernandez, Matthew
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.79%
We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to show approximate solutions tend to the exact solutions in the small wavelength limit. Recent work [2] by Coulombel, Gues, and Williams studied the case of reflecting wave trains whose expansions involve only real phases. We treat generic boundary frequencies by incorporating into our expansions both real and nonreal phases. Nonreal phases introduce difficulties such as approximately solving complex transport equations and result in the addition of boundary layers with exponential decay. This also prevents us from doing an error analysis based on almost-periodic profiles as in [2].; Comment: 38 pages

## Intrinsic Geometric Analysis of the Network Reliability and Voltage Stability

Gupta, N.; Tiwari, B. N.; Bellucci, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.89%
This paper presents the intrinsic geometric model for the solution of power system planning and its operation. This problem is large-scale and nonlinear, in general. Thus, we have developed the intrinsic geometric model for the network reliability and voltage stability, and examined it for the IEEE 5 bus system. The robustness of the proposed model is illustrated by introducing variations of the network parameters. Exact analytical results show the accuracy as well as the efficiency of the proposed solution technique.; Comment: 8 pages, 4 figures, 2 tables, Index Terms -- Circuit modeling, geometric modeling, parameter space method, power system reliability, power system stability, transmission planning, nonlinear methods, geometric controls, components optimization

Dumas, Eric
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.75%
We give an idea of the evolution of mathematical nonlinear geometric optics from its foundation by Lax in 1957, and present applications in various fields of mathematics and physics.

## Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents

Chueshov, Igor; Lasiecka, Irena
Tipo: Artigo de Revista Científica
## On the geometric flows solving K\"ahlerian inverse $\sigma_k$ equations
In this note, we extend our previous work on the inverse $\sigma_k$ problem. Inverse $\sigma_{k}$ problem is a fully nonlinear geometric PDE on compact K\"ahler manifolds. Given a proper geometric condition, we prove that a large family of nonlinear geometric flows converges to the desired solution of the given PDE.; Comment: to appear in Pacific Journal of Mathematics