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These derivatives can therefore be incorporated with the traditional integration schemes to evolve the numerical representation of the macroscale observable.
These equation-free techniques have been effectively applied in Coarse Projective Integration, Coarse Bifurcation Analysis and Coarse Dynamic Renormalization of multiscale systems. In my research, I extended the Coarse Projective Integration and Coarse Dynamic Renormalization to macroscopically multidimensional particle systems. Marginal and conditional inverse cumulative distribution functions ICDF were utilized to serve as the macroscale observables and it was shown that it was easy to find orthogonal basis for these observables.
As a matter of fact, with these observables, multidimensional problems were converted to effectively one-dimensional problems, and Coarse Projective Integration and Coarse Renormalization can be implemented on a reduced macroscale slow manifold. It was also found that the Coarse Renormalization for self-similar multidimensional multiscale systems requires only a single template condition, instead of multiple template conditions as originally expected.
The proposed technique was applied to a Brownian particle system in a Couette flow and produced results that had a good match to true evolutions and theoretical predictions. Sequential data assimilations have been utilized in diverse scientific and engineering fields to retrieve model predictions via experimental measurements. However, their applications were limited to single-scale problems, where model predictions at one scale were retrieved or calibrated only by measurements in that scale.
For multiscale systems for which microscopic observations are usually not available, it is expected to utilize measurements in macroscale to update microscopic model states. This therefore introduces problems of multiscale data assimilation. In my research, two techniques for the multiscale data assimilation were proposed. One technique coupled the model states across different scales to form an extended state.
A newly devised data assimilation method, the ensemble Kalman filter EnKF , was applied to update this extended model state, from which the updated states in different scales can then be extracted. The other technique employed the Coarse Time-Stepper.
The microscopic states were first restricted to the macroscale slow manifold, where corresponding macroscale states were updated or retrieved via the EnKF. The updated macroscale states were subsequently lifted back to the microscale space and updated state statistics in the microscale can thus be obtained. Estimations on boundary particle fluxes and on particle positions in a one-dimensional domain were used respectively to exemplify the two proposed techniques and they were shown to be able to give updated statistics that agreed well with true statistics.
Performance based design PBD is emerging as the guiding principle for the next generation of structural design specifications. PBD provides the engineer with greater flexibility to select appropriate performance criteria and prediction techniques, but also demands more sophisticated analyses. The presence of uncertainty in structural analysis, behavior and design — especially in the prediction of new performance measures — requires a probabilistic approach to PBD.
The first component of this research considers reliability-based specifications for PBD, using the example of advanced analysis of steel frames. Design by advanced analysis uses non-linear structural analyses to predict system performance measures.
Current advanced analysis proposals use the resistance factors of the load and resistance factor design LRFD specifications with no probabilistic justification.
The probabilities of failure of sixteen, two-story, two-bay steel frames, design by both LRFD and advanced analysis are estimated using Monte Carlo simulation and importance sampling schemes. The simulated strength and load distributions are used to develop resistance factors for the limit states of first plastic hinge and plastic collapse. The results indicate that design by advanced analysis can maintain the desired reliability for system failure, but may result in unsatisfactory serviceability performance.
Two particular difficulties of reliability-based specifications for design by advanced analysis are discussed — practical calibration for system-based limit states, and the determination of resistance factors applicable to a wide class of structures.
The second component of this research applies Bayesian surrogate models to engineering design, which is viewed as an iterative process of information gathering and decision making. A Bayesian surrogate model relates individual design variables to system performance, including both aleatory and epistemic uncertainties. Bayesian surrogate models can incorporate prior knowledge, update knowledge based on evidence, and propose design revisions.
A Bayesian network is used to update the parameters of the surrogate model based on information collected from trial designs. Techniques of Bayesian experimental design are applied to propose design revisions which maximize the expected information gain or relative entropy. The Bayesian surrogate framework is applied to several structural design examples. The results suggest the need to develop new information criteria specific to engineering design and PBD.
Fundamental period and damping ratio are two of the most important parameters involved in dynamic analyses of buildings. These parameters are usually assigned constant values typically through the use of simplified models or by using engineering judgment.
The variability associated with these values is frequently ignored. Measurements of these parameters in the completed structure may or may not match those assumed at the design stage and the effects and implications of such differences are usually not fully explored or understood.
To develop models that reliably estimate the values of period and damping expected in actual structures, a comprehensive database of full-scale measurements was compiled and rigorously analyzed. An analysis of variance ANOVA identifies the number of stories for the period data and the number of stories and level of vibration for the damping data a key factors that potentially affect each parameter.
Estimation models are developed for different combinations of factors and model performance, which is measured through the standard error, is observed to improve with additional factors. Models are greatly simplified through constrained variations in model coefficients and ar considered to appreciably improve the state-of-the-art in period and damping estimation.
The large quantity of data allows for a proper and careful analysis of the variability in each estimation model. Model variability is quantified through two functions: A rigorous form representing the model variability is provided along with a much simpler form developed for possible inclusion into standards. The effect of parameter variability on seismic response estimates was investigated. A proposed, performance-driven design procedure identifies period and damping values that achieve a specified level of performance.
For a general seismic design spectrum, the engineer can apply a level of conservatism to the performance level or to period and damping selection from regions of practical values, which are defined through the parameter distributions.
The effects of variability reduction are observed and possible direction for future development is discussed. Models of uncertainty have wide application beyond reliability estimation. In this talk, a model related to computer science approaches is used to solve problems in global optimization and structural mechanics. In contrast to usual statistical methods, a classifier that uses Bayesian classification trees is adopted. In this method, human expertise is quantitatively modeled and used to construct the feature space.
Knowledge functions are defined in the feature space, approximating the distribution of promising designs. Within feature space, promising designs, which can be widely scattered in the original high-dimensional design space, become concentrated in a relatively small number of discrete subregions.
Knowledge function provides an efficient way to generate the starting points for multi-start global optimization strategy. Furthermore, the classifier provides an efficient knowledge transfer mechanism through reuse of the knowledge functions for solving related, more complex problems. The method is demonstrated in the design of thin-walled steel columns, where the design space is too large to be effectively handled by common evolutionary techniques such as genetic algorithms.
The method is also demonstrated with an entirely different problem of an analysis of a composite material with random properties. Microfluidic Systems are increasingly stimulating considerable interest in both industry and academia. In the construction of high fidelity models capable of adequately predicting the behavior of these devices, uncertainty quantification UQ emerges as a main ingredient for resource allocation, engineering design, and model validation.
This thesis demonstrates the application of a UQ methodology based on a spectral polynomial chaos approach to the modeling of electrokinetically and pressure-driven microchannel flow. A numerical study of band crossing chemical reactions is first conducted and general solution trends are interpreted in terms of a reduced set of dimensionless parameters.
The capability of UQ techniques is then illustrated in the context of reduced design models for straight and serpentine channels. Using stochastic UQ tools, deterministic design rules are converted into design envelopes, highlighting the impact of uncertainties in design and operating parameters. Finally, the UQ methodology is extended to fully coupled 2D model for electrokinetically pumped microchannel flow of a reacting mixture.
Case studies are presented which investigate sample dispersive mechanisms due to buffer disturbances and random variability in zeta potential. An important consideration in the design of long-span bridges is the effect of wind loading on the bridge response.
While these techniques have predominantly been compared with each other, there has been few opportunities to evaluate them using actual bridge responses. Motivated by this idea, a long-term full-scale measurement program was conducted on a cable-stayed bridge for measuring its response under a range of meteorological conditions.
The measured responses were compared with predictions obtained from a multi-mode frequency-domain approach, which was able to capture the coupling between closely spaced modes of the structure. Where possible, input parameters used in the analysis were calibrated using measured quantities at the bridge, to ensure that they were representative.
Also, vortex-induced vibrations of the bridge were investigated, and such events were carefully identified.
The response comparisons showed that the predictions were in good agreement with measured values, successfully capturing the buffeting response. A parameter study identified the vertical wind spectrum to be one of the primary factors influencing bridge response, and indicated that proper calibration of spectral models used in the analysis provided improved predictions for some of the records.
One of the new challenges in Civil Engineering involves the analysis of uncertainty in complex engineering systems.
As the accuracy of measurements increases and new composite materials are introduced, we start looking into the behavior of systems that span a wide range of scales from the atomic scale to the scale of continuum mechanics.
The study on the role of uncertainty and its propagation should serve as a principal guideline that one must follow in investigation. Of particular interest to us are systems comprised of materials with microstructure that cannot be neglected in comparison to the size of the systems. In modeling such materials, the classical continuum mechanics, or the local theory, may lead to predictions deviating due to neglecting nonlocal interactions between microstructures and the accompanying effects.
Basic modifications must be made to the local theory as we start to investigate the nonlocal effects. The objective of the present research is to construct a material model that is consistent with the variability of heterogeneity and nonlocal interactions of material at the microstructure.
The modeling of microstructural variability, the propagation of uncertainties across scales and the prediction of response uncertainties are the emphases in this modeling procedure. This dissertation focuses on the theoretical treatment for the stochastic modeling of materials with random microstructures in the framework of nonlocal theories. In this work, the random microstructural interactions are represented by the integration of subscale variables and become a part of the constitutive equation for global state variables as in the classical nonlocal field theory.
The integration reflects the contribution from the subscale to the global states. The global behavior, being the overall contributions accumulated from all the scales, must satisfy the admissible condition and boundary conditions. In this manner the behavior of a multiscale system can be stated as a boundary value problem. Recent natural disasters, such as the earthquakes at Northridge, California and Kobe, Japan and hurricanes Hugo and Andrew, have inflicted enormous economic losses on the public and the insurance industry.
These losses and resulting impacts have led to renewed interest in development and implementation of performance-based design PBD. The performance levels in typical PBD recommendations are mapped to measurable structural responses and limit states. To facilitate this development, an efficient procedure to assess system reliabilities of realistic structures accurately is needed.
This dissertation is dedicated to developing such a procedure. Analysis of the reliability of complex structural systems requires an efficient simulation procedure coupled with finite element analysis. Directional simulation DS is among the most efficient methods for system reliability analysis in the sense that every direction can yield information about system failure.
However, the randomly generated directions may not represent the underlying probability distributions very well when the number of directions is limited. Various point sets, which are collectively named deterministic point sets DPS herein and have been developed in different domains of science and engineering, have high fidelity in representing the distribution and can reduce simulation error.
DPS from the uniform distribution are emphasized herein, since the uniform distribution is commonly used in DS. Extensive tests on the efficiency and accuracy of these point sets in system reliability analysis are conducted.
Fekete point sets are shown to have some particularly attractive features in terms of accuracy. Two types of neural networks, namely the feed-forward back-propagation network and the radial basis network, are utilized to further improve the efficiency in a two-phase point refinement scheme based on the Fekete method.
The neural network works as a parallel concept to importance sampling in identifying the regions in hyperspace that contribute significantly to the failure probability. Load space formulation has been shown to be particularly useful in limiting the number of calls to the finite element programs in system reliability analysis.
These techniques are demonstrated using several realistic plane steel structures. With the help of the load space formulation, the FeketeNN method can achieve accurate estimates of the system failure probabilities efficiently. In the rational prediction of the behavior of physical systems, models are often relied upon.
These predictive tools are calibrated in terms of parameters, on the basis of data. A recurrent phenomenon in this context s the random scatter in model parameters.
Stochastic models have thus been developed, in which the parameters are treated as a random entity. The probabilistic characterization of the parameters is often hampered by practical limitations and induces inaccuracies in the stochastic predictions of the response. This thesis reports a novel methodology to estimate the error in stochastic model-based predictions.
It relies on the response representation in a Polynomial-Chaos basis. The error is approximated via Taylor expansion and thus hinges on the explicit computation of the stochastic response gradient. The computed error estimate sheds light on the sensitivity of particular response statistics with respect to statistics of the stochastic parameters. This helps to raise the confidence in the model predictions. The method is demonstrated on two model problems, involving a Bernoulli beam with random bending rigidity and the potential flow in a porous medium with random conductivity.
In both cases the parameters are modelled as a random field and are discretized with the Karhunen-Loeve expansion. The finite element method is used for the spatial discretization.
This dissertation presents results of an experimental and theoretical investigation of the cross-anisotropic behavior of gravitationally deposited sands under general three-dimensional loading conditions. The laboratory study included a series of cubical triaxial tests using a true triaxial apparatus with improved accuracy of measurements and control. Stress-strain behavior and strength, failure patterns and shear banding, volumetric response and dilative properties were analyzed in view of the inherent material anisotropy.
A series of high-pressure isotropic compression tests were performed on Santa Monica beach and Nevada sands using four different densities and two specimen deposition methods. The evolution of the inclination of the plastic strain increment vector to the hydrostatic axis with pressure was evaluated and analyzed using different elastic models.
A principle of rotation of the principal stress coordinate system to account for the experimentally observed transverse isotropic effects was introduced.
A cross-anisotropic constitutive model was derived based on the existing model for isotropic materials. A thorough analysis of response of each component of the modified model was performed.
The new model was implemented to predict the results of the cubical triaxial tests producing good fits with the experimental data. The objective of the present work is to quantify and manage the confidence in model-based predictions associated with complex systems as exemplified by pollution transport in a watershed system.
A probabilistic framework is adopted for representing uncertainty and a constrained optimization problem is posed, the solution of which provides the strategy for resource allocation that will maximize the target confidence. The hydrologic cycle, which involves multi-physics phenomena, is the driving force behind the transport of pollutants in the watershed.
Mechanisms for pollutant transport which are addressed in this work include surface runoff and advection in streams and rivers. These different modes of transport when coupled together form an integrated transport model for a given watershed. The thesis addresses the flow of data and information between the components making up this model. Given the nature of this problem which features natural variability and complex boundary conditions, the properties of the parameters of the sub-models are modeled as spatially, and sometimes temporally, varying random processes.
The Karhunen-Loeve expansion is used to represent these processes in terms of a denumerable set of random variables. Then, as a result, the predicted state variables are identified with their coordinates with respect to a basis formed by the Polynomial Chaos random variables. Once the coefficients in the Polynomial Chaos representation have been computed, a complete probabilistic characterization of the state variables processes can be obtained.
It is worth noting that a treatment to the interaction across the interfaces of the sub-models is essential for the proper analysis of the propagation. An optimization algorithm scheme is then developed that incorporates budget constraint component, while minimizing the uncertainty of the final prediction by selectively reducing the uncertainty of the input parameters. The thesis makes original contributions to the computational modeling of integrated uncertain systems and to the management of uncertainty in the associated predictions.
An improved understanding of the behavior of ships after running aground could lessen the environmental and economic damage caused by ship groundings. Wave forces often push grounded ships towards the beach, sometimes so far ashore that they become unreachable by salvage vessels. An estimate of the distance a grounded ship may migrate in a given time would help ship owners, insurers, and government officials make critical decisions in the initial hours after a ship grounding.
The present study analyzes linear and nonlinear grounded ship motions, both experimentally and theoretically. Experiments were conducted to measure the motion response of an embedded ship hull at model-scale to both small-amplitude and solitary waves.
The predicted oscillatory motion responses, based upon prior theoretical work on the linear motion of grounded ships, are compared to results from the small-amplitude wave experiments.
A new method is presented to predict the distance a grounded ship will migrate ashore in a given time. This method shows good correlation with the migration distances observed in the solitary wave experiments.
Many cable-stayed bridges around the world have exhibited excessive wind-induced vibrations of the main stays, inducing undue stresses and fatigue in the cables. To suppress these vibrations, fluid dampers are often attached to stays near the anchorages.
To enable effective and economical design of such dampers, it is important to develop a thorough understanding of the dynamics of a stay cable with attached damper.
To investigate the dynamics of the cable-damper system, a fairly simple model is first considered: An analytical formulation of the free vibration problem is used to explore the solution characteristics, revealing that damper-induced frequency shifts play an important role in characterizing the response of the system due to the concentrated nature of the damping force.
A critical value of the damper coefficient is identified, and for a supercritical damper, certain modes of vibration are completely suppressed, while others emerge, including a non-oscillatory decaying mode. The influence of bending stiffness is considered using a dynamic stiffness formulation of the free-vibration problem for a tensioned beam with attached damper.
Many of the solution characteristics observed in this case are reminiscent of those for the taut string, and damper-induced frequency shifts are again important. The nature of the boundary conditions has a significant effect when bending stiffness is appreciable, and for a damper located near the end of a tensioned beam, significantly higher damping ratios can be achieved if the supports are not fixed against rotation. Dampers can also have nonlinear characteristics, either unintentionally or by design, and equivalent linear solutions are developed for the vibrations of a taut string with two different types of nonlinear dampers: Relevant nondimensional parameter groupings are identified, and asymptotic approximations are obtained relating these nondimensional parameters to the modal damping ratios for cases when the damper-induced frequency shifts are small.
The nature of the dependence of nonlinear damper performance on the amplitude and mode of vibration is investigated, revealing some potential advantages that may be offered by a nonlinear damper over a linear damper. Many dams have been in service for over 50 years, during which time important advances in the methodologies for evaluation of natural phenomena hazards have caused the design-basis events to be revised upwards, in some cases significantly. Many existing dams fail to meet these revised safety criteria and structural rehabilitation to meet newly revised criteria may be costly and difficult.
A probabilistic safety analysis PSA provides a rational safety assessment and decision-making tool managing the various sources of uncertainty that may impact dam performance. Fragility analysis, which depicts the uncertainty in the safety margin above specified hazard levels, is a fundamental tool in a PSA. This study presents a methodology for developing fragilities of concrete gravity dams to assess their performance against hydrologic and seismic hazards.
Models of varying degree of complexity and sophistication were considered and compared. The hydrologic fragilities showed that the Bluestone Dam is unlikely to become unstable at the revised probable maximum flood PMF , but it is likely that there will be significant cracking at the heel of the dam. On the other hand, the seismic fragility analysis indicated that sliding is likely, if the dam were to be subjected to a maximum credible earthquake MCE.
Moreover, there will likely be tensile cracking at the neck of the dam at this level of seismic excitation. Probabilities of relatively severe limit states appear to be only marginally affected by extremely rare events e.
Moreover, the risks posed by the extreme floods and earthquakes were not balanced for the Bluestone Dam, with seismic hazard posing a relatively higher risk. The macroscopic engineering properties of soil depend on microstructure features of the soil: Due to the small size of clay particles, physico-chemical interactions, mainly double-layer repulsive interaction and van der Waals attractive interaction, between clay particles are as important as mechanical interactions.
This thesis attempts to study the three-dimensional behavior of cohesive soil from the microstructure point of view with the help of the discrete element method. Rational and practical procedures to calculate the double-layer repulsive force and van der Waals attractive force between two cuboid clay particles in three-dimensional space are developed.
Using cuboids to represent clay particles, a three-dimensional discrete element method program for cohesive soil is developed. One-dimensional compression of kaolinite assembly is simulated using a randomly generated particle numerical assembly. The discrete element program is capable of capturing the representative trend of the compression behavior in terms of compressibility and anisotropy. Quantitatively the numerical results are in the same range of laboratory experimental results.
A preliminary study of the influence of pore fluid chemistry on the behavior of cohesive soil is conducted using the discrete element method. Results from a change of wall pressure as well as the number of mechanical contacts are presented. Many engineering systems have parameters that demonstrate significant random variation in space or in time.
The stochastic finite element method SFEM , which incorporates the uncertainty of system parameters into the finite element formulation, has become a powerful tool in analyzing complex engineering problems.
The commonly used lower-order perturbation-based SFE analysis is often limited to linear or mildly nonlinear problems with small variability.
Simulation-based SFE analysis is more flexible, and is applicable to virtually all types of problems. However, the efficiency of simulation-based SFE analysis is a research issue due to the computational cost of the repetitive FE analyses involved in the simulation.
The need to properly model system uncertainties gives rise to many of the numerical difficulties in a simulation-based SFE analysis and such models must be developed to achieve computational efficiency. This study addresses the effect of uncertainties on the modeling and solution of stochastic problems from a different perspective by identifying characteristics introduced by the uncertainties that can be utilized to improve the efficiency of the SFE structural analysis.
The process of selecting proper initializations for random samples and using the solution of the closest neighboring sample as the initialization. A computationally efficient method based on a sample tree data structure was developed to implement this optimal initialization strategy. These methods were applied in stability and modal analyses of random beam and frame structures. While uncertainty often introduces numerical complexity, it also has features that, when considered appropriately, can alleviate the numberical difficulty and improve the overall efficiency of a stochastic analysis.
In recent years there has been an increased interest in applying fiber-reinforced polymer FRP reinforcing bars for concrete, as an alternative to steel reinforcing bars. While many experimental bond studies have been conducted for a variety of different bars, modeling efforts to both quantify the underlying bond mechanisms and the resulting behavior have been very limited. Smaller scale rib-scale models explicitly represent the surface structure of the bar and can thus be used to characterize the underlying mechanisms associated with the mechanical interlocking and to help optimize the surface structure of a bar.
Existing rib-scale models have not addressed the progressive failure of the constituent materials, an issue addressed in this study. There is also a need to model the bond behavior of these bars at a scale amenable to the analysis of structural components. The model provides a macroscopic characterization of the bond behavior within the mathematical framework of elastoplasticity theory.
The model incorporates a non-associated flow rule and elastoplastic coupling. Rib-scale models for several specimens are developed to represent the mechanisms that produce the bond behavior.
An elastoplastic-damage model within the framework of continuum damage mechanics is developed to characterize the plastic and damage behavior of the matrix and fibers. A simple adhesion model is developed to represent the fiber-matrix interaction. The rib-scale models are able to reproduce the bond strengths of three independent experimental studies with acceptable accuracy.
The predicted failure modes and surface structure damage are consistent with experimental observations. Fill out, securely sign, print or email your CHP Art.
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