Highly nonlinear structures exhibit complex responses to external loads, and often become unstable. In this thesis, I consider structures with either a nonlinear geometric response or material response. Geometrically nonlinear bistable shells have two stable configurations and can reversibly change between them via snap-through instabilities. This snap-through behavior can cause large geometric deformations in response to small changes in loading, and thus is ideal for designing various devices. For materially nonlinear structures, one recent focus is the potential to utilize granular jamming to construct structures. However, it is not yet fully understood how the stability of such nonlinear structures is governed by geometric and materials properties. This thesis aims to answer this question and propose design guidelines for engineering applications. This research will focus on the statics and dynamics of spherical shells, prestressed bistable shells and elastogranular columns. For spherical shells, we aim to find out under what geometric criteria can a shell be turned inside out, and as the shell goes through the snap-through instability, what dictates the shape and speed of it. Geometric criteria to predict whether a spherical shell is bistable or monostable is proposed based on precisely fabricated soft spherical shells. Point load indentation tests were performed to determine how stable a spherical shell is in its everted configuration. The results show a distinct difference between shallow shells and deep shells, which led to further studies on the snapping dynamics of spherical shells. High speed videos are recorded to track the motion of the apex of an everted spherical shell during its snap-through process, and we find that as the spherical shell goes from shallow to deep, the axisymmetric snapping will transform into asymmetric snapping. This change in snapping modes greatly affects the snapping dynamics of the everted spherical shells, and the shapes they adopt through the instability. Besides spherical shells, we also analyzed prestressed, bistable, cylindrical shells. Prestressed bistable shells fabricated by stretching and bonding multiple layers of elastomers can have various geometric shapes and can snap under external stimuli, but the governing parameters for the fabrication and snapping are not known yet. An analytical model was proposed based on non-Euclidean Plate Theory to predict the mean curvature of the prestressed shell, and the amount of stimulus that is needed to trigger the snapping. Numerical simulations are performed to compare with the analytical results. Based on the proposed theory, for given fabrication parameters and material properties, the final mean curvature of the bistable prestressed shell can be predicted accurately, as well as the amount of stretch that is needed to trigger snapping. This study can be used to design smart actuators or other soft, smart devices. To study material nonlinear structures, we use a mixture of grains and rods to enable the formation of stable structures via granular jamming. Understanding how these constituents govern the mechanical properties of the jammed structures is crucial for devising relevant engineering designs. We examine freestanding columns composed of rocks and string, and propose a simple physical model to explain the resulting structure’s mechanical behavior. The results indicate that exterior fiber mainly contributes to stiffness, while interior fiber increases the stored elastic energy and absorbed total energy of the structures under certain external load. By assembling the grains and strings in an engineer way, structures with robust mechanical properties can be formed. The results provide guidelines that allow the design of jammed elastogranular structures with desired mechanical properties. The research results of this thesis will open and guide a variety of possibilities in designing functional responsive devices or jamming structures.

During the design and development stages of mechanical structures, after each modification made in order to satisfy design criteria, dynamic characteristics of the structure change and should be determined through reanalyzing the structure dynamically. Due to the significance of computational time and cost in design processes, it is inevitable for structural modification methods, especially for large systems, to become involved in predicting the dynamic behavior of modified structures from those of the original and modifying structures. Since most engineering structures are inherently nonlinear, linear approach may not be valid no more. Therefore, conventional structural modification methods can not be directly used, instead a nonlinear structural modification method needs to be employed. In this thesis, it is aimed to adapt an effective linear structural modification method to structures with nonlinear modification or coupling. The amplitude dependencies of nonlinearities are modeled by using describing function method. Mathematical formulations are embedded in a computer program developed in MATLAB&reg / with a graphical user interface. The software uses modal analysis results of ANSYS&reg / for the original structure and dynamic stiffness matrix and nonlinearity information that belong to the modifying structure in order to calculate dynamic response of the modified structure. The approach is verified by applying it to both discrete and real test structures previously studied in literature and generated discrete structures, then comparing the results with prior ones and ones obtained via time domain integration, respectively. Several other case studies are also included in order to demonstrate the applicability and to investigate the performance of the method. It is concluded in this study that the structural modification method proposed can be successfully and efficiently used for structures with nonlinear modification or coupling.

Submitted by SIDNEY BRUCE SHIKI null (sbshiki@gmail.com) on 2016-04-02T14:43:01Z No. of bitstreams: 1 Thesis_PhD_SBShiki.pdf: 10090180 bytes, checksum: c44d2ebecbed6d011cf61ceabdfd3494 (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-04-05T14:42:00Z (GMT) No. of bitstreams: 1 shiki_sd_dr_ilha.pdf: 10090180 bytes, checksum: c44d2ebecbed6d011cf61ceabdfd3494 (MD5) / Made available in DSpace on 2016-04-05T14:42:00Z (GMT). No. of bitstreams: 1 shiki_sd_dr_ilha.pdf: 10090180 bytes, checksum: c44d2ebecbed6d011cf61ceabdfd3494 (MD5) Previous issue date: 2016-03-04 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Estruturas com comportamento não-linear são frequentes em dinâmica estrutural, principalmente considerando componentes parafusados, com juntas, folgas ou estruturas flexíveis sujeitas à grandes deslocamentos. Desse modo, o monitoramento de estruturas com métodos lineares clássicos, como os baseados em parâmetros modais, podem falhar drasticamente em caracterizar efeitos não-lineares. Neste trabalho foi proposta a utilização de séries de Volterra para identificação de sistemas mecânicos não-lineares em aplicações de detecção de danos e quantificação de parâmetros. A propriedade deste modelo de representar separadamente os componentes de resposta linear e não-linear do sistema foi aplicada para se construir índices de dano que evidenciam a necessidade de modelagem não-linear. Além disso métricas de resíduo linear e não-linear dos termos do modelo de Volterra são empregadas para identificar modelos paramétricos da estrutura. As metodologias propostas são ilustradas em bancadas experimentais de modo a evidenciar a importância de fenômenos não-lineares para o monitoramento de estruturas. / Nonlinear structures are frequent in structural dynamics, specially considering screwed components, with joints, clearance or flexible components presenting large displacements. In this sense the monitoring of systems based on classical linear methods, as the ones based on modal parameters, can drastically fail to characterize nonlinear effects. This thesis proposed the use of Volterra series for nonlinear system identification aiming applications in damage detection and parameter quantification. The property of this model of representing the linear and nonlinear components of the response of a system was used to formulate damage features to make clear the need of nonlinear modeling. Also metrics based on the linear and nonlinear residues of the terms of the Volterra model were employed to identify parametric models of the structure. The proposed methodologies are illustrated in experimental setups to show the relevance of nonlinear phenomena in the structural health monitoring. / FAPESP: 2012/04757-6 / FAPESP: 2013/25148-0 / FAPESP: 2012/21195-1 / FAPESP: 2015/03560-2

Orientador: Samuel da Silva / Abstract: Nonlinear structures are frequent in structural dynamics, specially considering screwed components, with joints, clearance or flexible components presenting large displacements. In this sense the monitoring of systems based on classical linear methods, as the ones based on modal parameters, can drastically fail to characterize nonlinear effects. This thesis proposed the use of Volterra series for nonlinear system identification aiming applications in damage detection and parameter quantification. The property of this model of representing the linear and nonlinear components of the response of a system was used to formulate damage features to make clear the need of nonlinear modeling. Also metrics based on the linear and nonlinear residues of the terms of the Volterra model were employed to identify parametric models of the structure. The proposed methodologies are illustrated in experimental setups to show the relevance of nonlinear phenomena in the structural health monitoring. / Resumo: Estruturas com comportamento não-linear são frequentes em dinâmica estrutural, principalmente considerando componentes parafusados, com juntas, folgas ou estruturas flexíveis sujeitas à grandes deslocamentos. Desse modo, o monitoramento de estruturas com métodos lineares clássicos, como os baseados em parâmetros modais, podem falhar drasticamente em caracterizar efeitos não-lineares. Neste trabalho foi proposta a utilização de séries de Volterra para identificação de sistemas mecânicos não-lineares em aplicações de detecção de danos e quantificação de parâmetros. A propriedade deste modelo de representar separadamente os componentes de resposta linear e não-linear do sistema foi aplicada para se construir índices de dano que evidenciam a necessidade de modelagem não-linear. Além disso métricas de resíduo linear e não-linear dos termos do modelo de Volterra são empregadas para identificar modelos paramétricos da estrutura. As metodologias propostas são ilustradas em bancadas experimentais de modo a evidenciar a importância de fenômenos não-lineares para o monitoramento de estruturas. / Doutor

Bridge networks are expensive and complex infrastructures and are essential components of today's transportation systems. Despite the advancement in computer aided modeling and increasing the computational power which is increasing the accessibility for developing the fragility curves of bridges, the complexity of the problem and uncertainties involved in fragility analysis of the bridge structures in addition to difficulties in validating the results obtained from the analysis requires precaution in utilization of the results as a decision making tool. The main focus of this research is to address, study and treatment of uncertainties incorporated in various steps of performance based assessments (PBA) of the bridge structures. In this research the uncertainties is divided into three main categories. First, the uncertainties that come from ground motions time and frequency content alteration because of scarcity of the recorded ground motions in the database. Second, uncertainties associated in the modeling and simulation procedure of PBA, and third uncertainties originated from simplistic approach and methods utilized in the conventional procedure of PBA of the structures. Legitimacy of the scaling of ground motions is studied using the response of several simple nonlinear systems to amplitude scaled ground motions suites. Bias in the response obtained compared to unscaled records for both as recorded and synthetic ground motions. Results from this section of the research show the amount of the bias is considerable and can significantly affect the outcome of PBA. The origin of the bias is investigated and consequently a new metric is proposed to predict the bias induced by ground motion scaling without nonlinear analysis. Results demonstrate that utilizing the predictor as a scaling parameter can significantly reduce the bias for various nonlinear structures. Therefore utilizing the new metric as the intensity measuring parameter of the ground motions is recommended in PBA. To address the uncertainties associated in the modeling and simulation, MSSS concrete girder bridge class were selected due to the frequency of the construction in USCS region and lack of seismic detailing. A large scale parameters screening study is performed using Placket-Burman experimental design that considers a more complete group of parameters to decrease the computational expense of probabilistic study of the structure's seismic response. Fragility analysis for MSSS bridge is performed and the effect of removing the lesser important parameters the probabilistic demand model was investigated. This study reveals parameters reduction based on screening study techniques can be utilized to increase efficiency in fragility analysis procedure without compromising the accuracy of the outcome. The results from this study also provides more direct information on parameter reduction for PBA as well as provide insight into where future investments into higher fidelity finite element and constitutive models should be targeted. Conventional simplistic PBA approach does not account for the fundamental correlation between demand and capacity models. A more comprehensive PBA approach is presented and fragility analysis is performed with implementation of a new formulation in the component fragility analysis for MSSS bridge class and the outcome is compared with the one from conventional procedure. The results shows the correlation between demand and capacity affects the outcome of PBA and the fragility functions variation is not negligible. Therefore using the presented approach is necessary when accuracy is needed.