Earthquake ground motion can induce out-of-phase vibrations between adjacent structures due to differences in dynamic characteristics, which can result in impact or pounding of the structures if the at-rest separation is insufficient to accommodate the relative displacements. In bridges, seismic pounding between adjacent decks or between deck and abutment can result in localized deck damage, bearing failure, damage to shear keys and abutments, and even contribute to the collapse of bridge spans. This study investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed in MATLAB incorporating the effects of inelastic frame action, nonlinear hinge behavior and abutments. The equations of motion of the bridge response to longitudinal ground excitation are assembled and solved using the fourth-order Runge-Kutta method. Pounding is simulated using contact force-based models such as the linear spring, Kelvin and Hertz models, as well as the momentum-based stereomechanical method. In addition, a Hertz contact model with nonlinear damping (Hertzdamp model) is also introduced to model impact. The primary factors controlling the pounding response are identified as the frame period ratio, ground motion effective period ratio, restrainer stiffness ratio and frame ductility ratio. Pounding is most critical for highly out-of-phase frames. Impact models without energy dissipation overestimate the stiff system displacements by 15%-25% for highly out-of-phase, elastic systems experiencing moderate to strong ground excitation. The Hertzdamp model is found to be the most effective in representing impact. Traditional column hysteresis models such as the elasto-plastic and bilinear models underestimate the stiff system amplification and overestimate the flexible system amplification due to impact, when compared with stiffness and strength degrading models. Strength degradation and pounding are critical on the stiff system response to near field ground motions, for highly out-of-phase systems. Current design procedures are adequate in capturing the nonlinear hinge response when the bridge columns are elastic, but require revisions such as the introduction of time dependent reduction factors, and a frame design period to work for inelastic situations. Finally, a bilinear truss element with a gap is proposed for implementing energy dissipating impact models in commercial structural software.

No description available.

Neste trabalho, desenvolve-se um método de fronteira imersa para o estudo de escoamento compressível modelado pelas equações de Euler bidimensionais. O método de discretização de diferenças finitas é empregado, usando o método de Steger-Warming de ordem dois para discretizar as variáveis espaciais e o esquema de Runge-Kutta de ordem quatro para discretizar as variáveis temporais. O método da fronteira imersa foi empregado para o estudo de aeroelasticidade computacional em uma seção típica de aerofólio bidimensional com dois movimentos prescritos: torsional e vertical, com o objetivo de se verifcar a eficiência do método e sua aplicabilidade para problemas em aeroelasticidade computacional. Neste estudo desenvolveu-se também um programa de computador para simular escoamentos compressíveis de fluido invíscido utilizando a metodologia proposta. A verificação do código gerado foi feita utilizando o método das soluções manufaturadas e o problema de reflexão de choque oblíquo. A validação foi realizada comparando-se os resultados obtidos para o escoamento ao redor de uma seção circular e de uma seção de aerofólio NACA 0012 com os resultados experimentais, para cada caso. / In this work, an immersed boundary method is developed to study compressible flow modeled by the two-dimensional Euler equations. The finite difference method is employed, using the second order Steger-Warming method to discretizate the space variables and the fourth order Runge-Kutta method to discretizate the time variables. The immersed boundary method was employed to study computational aeroelasticity on a typical two-dimensional airfoil section with two prescribed motion: pitching and plunging, in order to verify the efficiency of the numerical method and its applicability in computational aeroelasticity problems. In this work, a computer program was developed to simulate compressible flows for inviscid fluids using the methodology proposed. The verification of the computational code was performed using the method of manufactured solutions and the oblique shock wave reflection problem. The validation was performed comparing the obtained results for flows around a circular section and a NACA 0012 airfoil section with the experimental results, for each case.

Schwerpunkt dieser Arbeit ist die Untersuchung einer Klasse von Diskretisierungsmethoden für nichtlineare optimale Steuerungsprobleme mit gewöhnlichen Differentialgleichungen und Steuerungsbeschränkung sowie die Durchführung von numerischen Experimente. Die theoretischen Untersuchungen basieren aus einem gekoppeltes Parametrisierungs-Diskretisierungsschema aus stückweise polinomialen Ansatz für die Steuerung und einen Runge-Kutta-Verfahren zur Integration der Zustands-Differentialgleichung. Die Konvergenzordnung der Lösung wird unter Regularitätsbedingung und Optimalitätsbedingung 2.Ordnung ermittelt. Außerdem wird eine Möglichkeit zur numerischen Berechnung der Gradienten über internen numerischen Differentiation erläutert. Schließlich werden einige numerischen Resultate gegeben und die Abhängigkeiten zur den theoretischen Konvergenzresultate diskutiert. / The focal point of this work is the investigation of a class of discretization methods for nonlinear optimal control problems governed by ordinary differential equations with control restrictions, as well as the implementation of some numerical experiments. The theoretical investigations are based on a coupledparameterization-discretization pattern, a piecewise linear parameterization representation of the control, and the application of a Runge Kutta method for the integration of the differential state equation. The rate of convergence of the solution is obtained with the help of regularity conditions and the second order optimality conditions. Furthermore, we also present in this paper a possibility of the numerical computation of the gradients via numerical differentiation. Finally some numerical results are given and their relationship to the theoretical convergence results are discussed.

Dans cette thèse, nous étudions et développons différentes familles de schémas d’intégration en temps pour les EDO linéaires. Dans la première partie, après avoir introduit les définitions et propriétés utilisées pour construire les schémas en temps, nous présentons deux méthodes de discrétisation en espace et une revue des schémas de Runge-Kutta (RK) qui sont couramment utilisés dans la littérature. Dans la seconde partie on présente une méthodologie pour construire deux familles de schémas A-stable pour un ordre quelcomque. Puis on fournit des schémas explicites, construits en maximisant leur nombre CFL pour un profil de spectre donné. Ces schémas explicites sont ensuite combinés aux schémas implicites A-stable, pour construire des schémas localement implicites que nous décrivons. En plus des tests de validations des schémas pour des problèmes en dimension un et deux de l’espace, nous présentons des résultats numériques obtenus en résolvant des problèmes de propagation d’ondes acoustiques et électromagnétiques en dimensions trois dans la troisième partie. / In this thesis, we study and develop different families of time integration schemes for linear ODEs. After presenting the space discretisation methods and a review of classical Runge-Kutta schemes in the first part, we construct high-order A-stable time integration schemes for an arbitrary order with low-dissipation and low-dispersion effects in the second part. Then we develop explicit schemes with an optimal CFL number for a typical profile of spectrum. The obtained CFL number and the efficiency on the typical profile for each explicit scheme are given. Pursuing our aim, we propose a methodology to construct locally implicit methods of arbitrary order. We present the locally implicit methods obtained from the combination of the A-stable implicit schemes we have developed and explicit schemes with optimal CFL number. We use them to solve the acoustic wave equation and provide convergence curves demonstrating the performance of the obtained schemes. In addition of the different 1D and 2D validation tests performed while solving the acoustic wave equation, we present numerical simulation results for 3D acoustic wave and the Maxwell’s equations in the last part.

Neste trabalho, desenvolve-se um método de fronteira imersa para o estudo de escoamento compressível modelado pelas equações de Euler bidimensionais. O método de discretização de diferenças finitas é empregado, usando o método de Steger-Warming de ordem dois para discretizar as variáveis espaciais e o esquema de Runge-Kutta de ordem quatro para discretizar as variáveis temporais. O método da fronteira imersa foi empregado para o estudo de aeroelasticidade computacional em uma seção típica de aerofólio bidimensional com dois movimentos prescritos: torsional e vertical, com o objetivo de se verifcar a eficiência do método e sua aplicabilidade para problemas em aeroelasticidade computacional. Neste estudo desenvolveu-se também um programa de computador para simular escoamentos compressíveis de fluido invíscido utilizando a metodologia proposta. A verificação do código gerado foi feita utilizando o método das soluções manufaturadas e o problema de reflexão de choque oblíquo. A validação foi realizada comparando-se os resultados obtidos para o escoamento ao redor de uma seção circular e de uma seção de aerofólio NACA 0012 com os resultados experimentais, para cada caso. / In this work, an immersed boundary method is developed to study compressible flow modeled by the two-dimensional Euler equations. The finite difference method is employed, using the second order Steger-Warming method to discretizate the space variables and the fourth order Runge-Kutta method to discretizate the time variables. The immersed boundary method was employed to study computational aeroelasticity on a typical two-dimensional airfoil section with two prescribed motion: pitching and plunging, in order to verify the efficiency of the numerical method and its applicability in computational aeroelasticity problems. In this work, a computer program was developed to simulate compressible flows for inviscid fluids using the methodology proposed. The verification of the computational code was performed using the method of manufactured solutions and the oblique shock wave reflection problem. The validation was performed comparing the obtained results for flows around a circular section and a NACA 0012 airfoil section with the experimental results, for each case.

No description available.

The main aim of this work is to study the thermal conductivity of base fluid with mild inclusion of nanoparticles. We perform numerical study for transportation of Maxwell nanofluids with activation energy and Cattaneo–Christov flux over an extending sheet along with mass transpiration. Further, bioconvection of microorganisms may support avoiding the possible settling of nanoentities. We formulate the theoretical study as a nonlinear coupled boundary value problem involving partial derivatives. Then ordinary differential equations are obtained from the leading partial differential equations with the help of appropriate similarity transformations. We obtain numerical results by using the Runge–Kutta fourth-order method with shooting technique. The effects of various physical parameters such as mixed convection, buoyancy ratio, Raleigh number, Lewis number, Prandtl number, magnetic parameter, mass transpiration on bulk flow, temperature, concentration, and distributions of microorganisms are presented in graphical form. Also, the skin friction coefficient, Nusselt number, Sherwood number, and motile density number are calculated and presented in the form of tables. The validation of numerical procedure is confirmed through its comparison with the existing results. The computation is carried out for suitable inputs of the controlling parameters.

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The main objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) in which the governing differential equation is simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. This scheme is applied to forward differentiation method (Euler's method) and to second order Runge-kutta method of this work.