Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2007. / Bauchau, Olivier, Committee Member ; Hodges, Dewey, Committee Chair ; Singhose, William, Committee Member ; Costello, Mark, Committee Member ; Flannery, Raymond, Committee Member.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 195-198). Also available on the Internet.

abstract: This thesis focuses on the continued extension, validation, and application of combined thermal-structural reduced order models for nonlinear geometric problems. The first part of the thesis focuses on the determination of the temperature distribution and structural response induced by an oscillating flux on the top surface of a flat panel. This flux is introduced here as a simplified representation of the thermal effects of an oscillating shock on a panel of a supersonic/hypersonic vehicle. Accordingly, a random acoustic excitation is also considered to act on the panel and the level of the thermo-acoustic excitation is assumed to be large enough to induce a nonlinear geometric response of the panel. Both temperature distribution and structural response are determined using recently proposed reduced order models and a complete one way, thermal-structural, coupling is enforced. A steady-state analysis of the thermal problem is first carried out that is then utilized in the structural reduced order model governing equations with and without the acoustic excitation. A detailed validation of the reduced order models is carried out by comparison with a few full finite element (Nastran) computations. The computational expedience of the reduced order models allows a detailed parametric study of the response as a function of the frequency of the oscillating flux. The nature of the corresponding structural ROM equations is seen to be of a Mathieu-type with Duffing nonlinearity (originating from the nonlinear geometric effects) with external harmonic excitation (associated with the thermal moments terms on the panel). A dominant resonance is observed and explained. The second part of the thesis is focused on extending the formulation of the combined thermal-structural reduced order modeling method to include temperature dependent structural properties, more specifically of the elasticity tensor and the coefficient of thermal expansion. These properties were assumed to vary linearly with local temperature and it was found that the linear stiffness coefficients and the "thermal moment" terms then are cubic functions of the temperature generalized coordinates while the quadratic and cubic stiffness coefficients were only linear functions of these coordinates. A first validation of this reduced order modeling strategy was successfully carried out. / Dissertation/Thesis / M.S. Aerospace Engineering 2011

As estruturas, particularmente na engenharia civil, podem apresentar ruína quando atingem sua capacidade resistente ou quando perdem sua estabilidade, sendo, portanto atribuição básica do engenheiro de estruturas o estudo de ambas as situações. A instabilidade de uma estrutura pode surgir de dois modos, a saber: por ocorrência de uma bifurcação de equilíbrio ou por ocorrência de um ponto limite, também conhecido por snap-through, onde o aumento do carregamento provoca uma diminuição da rigidez da estrutura, até que esta se anula no ponto limite (REIS; CAMOTIM, 2012). Estruturas como arcos, treliças e calotas esféricas abatidas, presentes em grandes coberturas, são tipos de estruturas que podem apresentar esta instabilidade, em que há a passagem dinâmica da estrutura para uma configuração de equilíbrio afastada e estável, saltando para essa configuração pós-crítica envolvendo grandes deslocamentos e inversão da curvatura. Se, no entanto, o carregamento é dinâmico, como, por exemplo, harmônico, a resposta do sistema adquire uma grande riqueza de possíveis comportamentos, em função da amplitude e frequência desse carregamento. As respostas podem resultar vibrações periódicas de vários períodos diferentes, quase periódicas, caóticas etc. Este trabalho tem como objetivo fazer um estudo da estabilidade estática e dinâmica do problema da treliça simples de duas barras (treliça de Von Mises) e do arco abatido senoidal, de comportamento elástico linear, com o estabelecimento das equações de equilíbrio na configuração deformada, i.e., levando em conta a não linearidade geométrica. A avaliação da resposta, bem como a caracterização de sua estabilidade, se dará pela apresentação das cargas críticas de instabilidade do sistema perfeito, exibição do comportamento de pós-instabilidade e, com a integração numérica do modelo matemático, o estudo geométrico dado pelos planos de fase, mapas de Poincaré, diagramas de bifurcação e fronteira de estabilidade. / Structures, particularly in civil engineering, can ruin when they reach their strength capacity or when they lose their stability. So, it is the basic assignment of the structural engineer to study both situations. The instability of a structure can arise in two ways, namely: by the occurrence of bifurcation of equilibrium or by the occurrence of a snap-through, where an increase of the loading causes a decrease in structure stiffness, until the stiffness is annulled in the limit point (REIS, CAMOTIM, 2012). Structures such as arches, trusses and domes, present in large roofs, are types of structures that may present this kind of instability, in which there is the dynamic passage of the structure to a far away stable equilibrium configuration, jumping to this post-critical configuration involving large displacements and reversal of the curvature. If, however, the load is dynamic, such as harmonic, the response of the system acquires a great wealth of possible behaviors, depending on the amplitude and frequency of this loading. The responses may result in periodic vibrations of several different periods, almost periodic, chaotic, etc. This work intends to study the static and the dynamic stability of the Von Mises truss and the shallow arc of linear elastic behavior, with the establishment of the equilibrium equations in the deformed configuration, i.e., taking into account the geometric non-linearity. The evaluation of the response, as well as the characterization of its stability, will be done by numerical integration of the mathematical model and geometric study of the phase planes, Poincaré maps, bifurcation diagrams and stability border.

Este trabalho trata da análise dinâmica bidimensional de treliças de aço e pórticos de concreto armado, onde estudam-se os efeitos da não-linearidade física desses materiais e os efeitos da não-linearidade geométrica de tais estruturas. Neste contexto, define-se a equação geral que descreve o comportamento de estruturas discretizadas por elementos finitos, utilizando-se o Princípio dos Trabalhos Virtuais para estruturas em movimento. Para a integração temporal dessa equação, utiliza-se um método implícito de integração numérica, onde adota-se um processo previsor-corretor com auxílio das equações generalizadas de Newmark. Na análise da não-linearidade geométrica, define-se o campo de deformações através de uma função quadrática dos deslocamentos, que ocorrem ao longo de cada elemento finito, sendo que para treliças planas consideram-se todas as parcelas provenientes de tal relação e para pórticos planos desprezam-se os termos que contém produtos de parcelas de ordem superior. Para descrever a posição de equilíbrio do sistema estrutural ao longo do processo de integração numérica, utiliza-se a formulação Lagrangeana atualizada que resulta na dedução das matrizes de rigidez incrementais secante e tangente. Com relação à não-linearidade física do aço, elabora-se uma modelagem numérica através da utilização de um diagrama tensão x deformação bilinear, destacando-se os modelos cinemático, isotrópico e independente. Já para a não-linearidade física do concreto armado, elabora-se uma modelagem numérica através da utilização dos modelos propostos pelo CEB e pelo ACI, onde corrige-se o valor do momento de inércia em função do grau de fissuração do elemento. Estas modelagens contemplam, também, o comportamento para carregamento cíclico e sua inversão. Para finalizar, apresentam-se com posterior análises qualitativa e quantitativa dos resultados. / This work deals with the two-dimensional dynamic analysis of steel trusses and reinforced concrete frames. The physical non-linear effects of these materials as well as the geometrical non-linearity of such structures are studied. In this context, a general equation that describes the behaviour of structures approximated by finite elements is defined, using the Virtual Works Principle for structures in movement. In order to integrate this differential equation along the time an implicit procedure is adopted based on the predictor-corrector process taking into account the Newmark\'s generalised equations. For the geometrical non-linear analysis, the deformation field is defined by assuming displacements approximated along each finite element by quadratic shape functions. All terms resulting from that assumption are taken into account for the plane trusses, while for plane frame, terms representing higher order products are neglected. In order to describe the equilibrium position of the structural system, during the numeric integration process, the updated Lagrangean formulation is used to give the secant and tangent incremental stiffness matrices. Regarding the steel non-linear physical behaviour, a numerical procedure is achieved based on a bilinear stress-strain curve that is able to describe kinematic, isotropic and independent responses. For the reinforced concrete physical non-linear behaviour the well known CEB and ACI models were taken to derive and implement the numeric process. In this case, the moment of inertia is corrected according to the element level of cracking. These models also consider the material behaviour when cyclic loads are applied causing stress sign inversion. Finally, numeric examples are presented to illustrate the quality and accuracy of obtained results.

In recent years, experiments have been carried out to evaluate the performance of water-filled cushion cells used to attenuate energy of automobile collisions. The water-filled cushion cell is a vinyl plastic cylinder of 6 inches nominal outside diameter, 1/4 inch wall thickness, 40 inches length, closed at the bottom by a cast-in-place vinyl plug and partially closed by a bolted-in vinyl diaphragm at the upper end. These cells are designed to be installed in the path of a crashing automobile to absorb and dissipate the kinetic energy of impact. Properly designed cushions could be used as one means of saving life and property.

This thesis investigated the application of seismic analysis methods and the response of idealized shear frames subjected to seismic loading. To complete this research, a Design Basis Earthquake (DBE) for a project site in San Luis Obispo, CA, and five past earthquake records were considered. The DBE was produced per the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE 7-10) and used for application of the Equivalent Lateral Force Procedure (ELFP) and Response Spectrum Analysis (RSA). When applying RSA, the modal peak responses were combined using the Absolute Sum (ABS), Square-Root-of-the-Sum-of-Squares (SRSS), and Complete Quadratic Combination (CQC) method. MATLAB scripts were developed to produce several displacement, velocity, and acceleration spectrums for each earthquake. Moreover, MATLAB scripts were written to yield both analytical and numerical solutions for each system through application of Linear Time History Analysis (THA). To obtain analytical solutions, two implicit forms of the Newmark-beta Method were employed: the Average Acceleration Method and the Linear Acceleration Method. To generate a comparison, the ELFP, RSA, and THA methods were applied to shear frames up to ten stories in height. The system parameters that impacted the accuracy of each method and the response of the systems were analyzed, including the effects of classical damping and nonclassical damping models. In addition to varying levels of Rayleigh damping, non-linear hysteric friction spring dampers (FSDs) were implemented into the systems. The design of the FSDs was based on target stiffness values, which were defined as portions of the system’s lateral stiffness. To perform the required Nonlinear Time History Analysis (NTHA), a SAP2000 model was developed. The efficiencies of the FSDs at each target stiffness, with and without the addition of low levels of viscous modal damping are analyzed. It was concluded that the ELFP should be supplemented by RSA when performing seismic response analysis. Regardless of system parameters, the ELFP yielded system responses 30% to 50% higher than RSA when combing responses with the SRSS or CQC method. When applying RSA, the ABS method produced inconsistent and inaccurate results, whereas the SRSS and CQC results were similar for regular, symmetric systems. Generally, the SRSS and CQC results were within 5% of the analytical solution yielded through THA. On the contrary, for irregular structures, the SRSS method significantly underestimated the response, and the CQC method was four to five times more accurate. Additionally, both the Average Acceleration Method and Linear Acceleration Method yielded numerical solutions with errors typically below 1% when compared with the analytical solution. When implemented into the systems, the FSDs proved to be most efficient when designed to have stiffnesses that were 50% of the lateral stiffness of each story. The addition of 1% modal damping to the FSDs resulted in quicker energy dissipation without significantly reducing the peak response of the system. At a stiffness of 50%, the FSDs reduced the displacement response by 40% to 60% when compared with 5% modal damping. Additionally, the FSDs at low stiffnesses exhibited the effects of negative lateral stiffness due to P-delta effects when the earthquake ground motions were too weak to induce sliding in the ring assemblies.

No description available.

No description available.

Experimental spatial dynamics modeling is a new approach to dynamics modeling using high-spatial-density experimental data from a scanning laser Doppler vibrometer (LDV). This instrument measures the surface velocity of vibrated structures. Time-signal data from the LDV is statistically modeled with multiple linear regression for harmonically excited structures. A weighted least-squares discrete finite element formulation is developed to solve for the complex-valued continuous 3-D velocity response field from sampled velocity data. The formulation is derived from the steady-state solution of the differential equation with spatial and temporal components of harmonic structural dynamic response. Linear, quadratic, cubic, and cubic B-spline basis functions are used to form isoparametric finite elements in the dynamic response model. Velocity measurements acquired from multiple positions are transformed into a single model that minimizes the least-squares error between the experimental data and the field equations in the 3-D shell element model. A multiple point nonlinear registration algorithm is developed to determine position and orientation of the LDV relative to the test structure. Polygonal shape models are successfully integrated with the experimental spatial dynamic response models via polygon ray intersection. Finite element shape models are generated from simple flat surfaces or extracted from existing finite element models of 3-D structures. By postprocessing the model solution, many dynamic properties including rotations, full-field strains and stresses, and acoustic prediction are derived from the dynamic response representation. Visualization software was developed for animation of the 3-D spatial dynamic response models with superimposed color to represent the postprocessed results. The interactive graphics allow presentation and investigation of the experimental spatial dynamics. To examine the method, an analytical test model is defined to simulate the surface velocity response of a structure with both in-plane and out-of-plane harmonic vibration. Random and uniformly spaced measurements of the simulated dynamic system are acquired from multiple locations. Applications of experimental spatial dynamics modeling, postprocessing, and visualization are also demonstrated with five different test structures. Through mesh refinement, increase in order of the basis functions, and additional sampling, the finite element models are converged to statistically qualified solutions. / Ph. D.