Browsing by Author "Stanciulescu, Ilinca"
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Item A general condition for the existence of unconnected equilibria for symmetric arches(Elsevier, 2018) Zhou, Yang; Stanciulescu, IlincaThis paper presents a semi-analytical study of unconnected equilibrium states for symmetric curved beams. Using the Fourier series approximation, a general condition for the existence of unconnected equilibria for symmetric shallow arches is derived for the first time. With this derived condition, we can directly determine whether or not a shallow arch with specific initial configuration and external load has remote unconnected equilibria. These unconnected equilibria cannot be obtained in experiments or nonlinear finite element simulations without performing a proper perturbation first. The derived general condition is then applied to curved beams with different initial shapes and external loads. It is found that initially symmetric parabolic arches under a uniformly distributed vertical force can have multiple groups of unconnected equilibria, depending on the initial rise of the structure. However, small symmetric geometric deviations are required for parabolic arches under a central point load, and half-sine arches under a central point load or a uniformly distributed load to have unconnected equilibria. The validity of the analytical derivations of the nonlinear equilibrium solutions and the general condition for the existence of unconnected equilibria are verified by nonlinear finite element methods.Item A lower bound on snap-through instability of curved beams under thermomechanical loads(Elsevier, 2012) Stanciulescu, Ilinca; Mitchell, Toby; Chandra, Yenny; Eason, Thomas; Spottswood, MichaelA non-linear finite element formulation (three dimensional continuum elements) is implemented and used for modeling dynamic snap-through in beams with initial curvature. We identify a non-trivial (non-flat) configuration of the beam at a critical temperature value below which the beam will no longer experience snap-through under any magnitude of applied quasi-static load for beams with various curvatures. The critical temperature is shown to successfully eliminate snap-through in dynamic simulations at quasistatic loading rates. Thermomechanical coupling is included in order to model a physically minimal amount of damping in the system, and the resulting post-snap vibrations are shown to be thermoelastically damped. We propose a test to determine the critical snap-free temperature for members of general geometry and loading pattern; the analogy between mechanical prestress and thermal strain that holds between the static and dynamic simulations is used to suggest a simple method for reducing the vulnerability of thin-walled structural members to dynamic snap-through in members of large initial curvature via the introduction of initial pretension.Item A numerical investigation of snap-through in a shallow arch-like model(Elsevier, 2013) Chandra, Yenny; Stanciulescu, Ilinca; Virgin, Lawrence N.; Eason, Thomas G.; Spottswood, Stephen M.Slender curved structures may experience a loss of stability called snap-through, causing the curvature on part or all of the structure to invert inducing fatigue damage. This paper presents a framework for analyzing the transient responses of slender curved structures. A numerical study of snap-through in a shallow arch-like model under periodic excitations is performed on a simplified model and on a detailed finite element model. The boundaries that separate the snap-through and no snap-through regions in the forcing parameters space are identified. Various post-snap responses are analyzed. The effects of initial conditions on the snap-through boundaries and post-snap responses are examined. Forcing parameters that lead to chaotic response are identified.Item Adaptive Techniques Applied to the Sequentially Optimized Meshfree Approximation(2014-04-22) Mittelman, Rachel; Akin, John Edward.; Stanciulescu, Ilinca; Meade, Andrew J., Jr.This thesis advances the meshless Sequentially Optimized Meshfree Approximation (SOMA) from a fixed grid to an adaptive one by applying residual-based adaptive techniques. In its fixed grid form, SOMA constructs an approximation of an equation solution using optimized radial basis functions (RBFs), but deletes the RBF parameters once each basis function is appropriately added. The first proposed method saves this information, constructs an approximation of the solution, and intelligently adds points to the problem domain. The second proposed method is a flexible interpolation scheme which does not require this basis saving technique, although the two techniques can be combined. When applied to various equations, these adaptive algorithms demonstrate the convergence required to achieve a satisfactory level of precision, saving time and computational effort for the same mathematical result as a denser grid. Applications of this algorithm include function approximation as well as differential equations which demonstrate its capability and robustness.Item Application of Compact, Geometrically Complex Shape Memory Alloy Devices for Seismic Enhancement of Highway Bridge Expansion Joints(2014-04-25) McCarthy, Emily Ruth; Padgett, Jamie E.; Stanciulescu, Ilinca; Lou, Jun; DesRoches, ReginaldHighway bridges are an important part of transportation networks. They provide connectivity across waterways, ravines and other roadways, reducing commuting times and facilitating social community. The disruption of their effective operation caused by earthquake damage has lasting effects based on repair costs, road closure times, traffic rerouting causing extended commute times and additional CO2 emissions, and the potential prevention of emergency responders being able to reach affected regions. Bridge expansion joints have historically been recognized as the most vulnerable component in the bridge system during these seismic events, causing dramatic disruption to bridge functionality because of their location in bridges (points of discontinuity in deck systems). Expansion joint systems are placed in these locations of discontinuity and accommodate bridge movements from thermal effects while facilitating safe driving surfaces across large gaps in the roadway. Commonly installed systems are not designed to survive seismic events, instead failure is assumed and replacement necessary to return the bridge to its functional state. When damaged, the large gaps they span can be un-crossable without external intervention, resulting in non-functioning bridges even when the structural system remains sound. Expensive and complex expansion systems exist, which prevent seismic damage, however they are used mostly in highly seismic regions and limitedly elsewhere. This dissertation provides an expansion joint design that is economical and superior in seismic performance to the commonly installed service level expansion joints so that more bridges in moderate seismic regions can be equipped with expansion systems able to accommodate large longitudinal displacement demands from earthquakes. The use of innovative shape memory alloy (SMA) springs enables a single support bar modular bridge expansion joint (one type of large capacity expansion joint) to accommodate seismic level longitudinal displacements while maintaining existing performance behavior for service level thermal expansion demands. Through limited alteration of the existing configuration, costs are minimized. The resulting design is experimentally and analytically shown to be superior in performance and able to prevent expansion joint system failure during dynamic loading. The use of fragility curves, which are probabilistic statements of demand exceeding capacity, offers a means of measuring performance over a range of earthquake intensities. Convolution with seismic hazard curves for some moderate seismic zones in the US over a range of time intervals provide information on lifetime seismic risk, valuable information for a cost benefit analysis that concludes investment in SMA springs for enhancement of modular bridge expansion joints is worthwhile for the cost reduction they offer over the life of the bridge.Item Can complex systems really be simulated?(Association for Computing Machinery, 2014) Kalmar-Nagy, Tamas; Stanciulescu, IlincaThe simulation of complex systems is important in many fields of science and in real-world applications. Such systems are composed of many interacting subsystems. There might exist different software packages for simulating the individual subsystems and co-simulation refers to the simultaneous execution of multiple interacting subsystem simulators. Simulation or co-simulation, if not designed properly, can return misleading numerical solutions (unstable numerical solutions for what is in fact a stable system or vice versa). To understand the cause of these numerical artifacts, we first propose a simple mathematical model for co-simulation, and then construct stability charts. These charts shed light on transitions between stable and unstable behaviour in co-simulation. Our goal is to understand the stability properties of the simulated and co-simulated representation of the continuous system. We will achieve this goal by expressing the trace and determinant of the discretized system in terms of the trace and determinant of the continuous system to establish stability criteria.Item Characterizing Dynamic Transitions Associated with Snap-Through of Clamped Shallow Arches(Elsevier, 2013) Chandra, Yenny; Wiebe, Richard; Stanciulescu, Ilinca; Virgin, Lawrence N.; Spottswood, Stephen M.; Eason, Thomas G.Slender curved structures can often be found as components of complex structures in civil, mechanical, and aerospace systems. Under extreme loadings, a curved structure might undergo snap-through buckling, i.e., the structure is forced to its inverted configuration, inducing fatigue. Therefore, it is important to identify the stability boundaries of structures and to obtain an accurate description of their performance if the response moves beyond those boundaries. In this paper, a combined experimentalヨcomputational framework is used to analyze the transient behavior of clamped-clamped shallow arches. We examine, both experimentally and using Finite Element Analysis (FEA), the response of shallow arches under harmonic distributed loading. Various types of responses are identified and regions in the forcing parameter space that lead to snap-through and chaotic responses are determined.Item Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System(The American Society of Mechanical Engineers, 2012) Wiebe, R.; Virgin, L. N.; Stanciulescu, Ilinca; Spottswood, S.M.; Eason, T.G.Geometrically nonlinear structures often possess multiple equilibrium configurations. Under extreme conditions of excitation, it is possible for these structures to exhibit oscillations about and between these co-existing configurations. This behavior may have serious implications for fatigue in the context of aircraft surface panels. Snap-through is a name often given to sudden changes in dynamic behavior associated with mechanical instability (buckling). This is an often encountered problem in hypersonic vehicles in which severe thermal loading and acoustic excitation conspire to create an especially hostile environment for structural elements. In this paper, a simple link model is used, experimentally and numerically, to investigate the mechanisms of snap-through buckling from a phenomenological standpoint.Item Computational Analysis of Curved Structures Exhibiting Instabilities(2017-02-14) Zhou, Yang; Stanciulescu, IlincaThe United States Air Force and the National Aeronautics and Space Administration have made great efforts and spent untold resources to develop reusable hypersonic vehicles since the early 1950s. In spite of great progress, many scientific and technical challenges still exist. This thesis focuses on developing a robust and efficient computational framework for analyzing snap-through, which is a particular concern for the commonly used slender curved structural components of reusable hypersonic vehicles since it can significantly exacerbate fatigue failure. Snap-through is a type of instability where a curved structure suddenly jumps to a remote configuration. This behavior is highly nonlinear involving sudden and large deformations. Snap-through is a dynamic instability triggered by the loss of stability of an equilibrium state. Examining equilibria and their stability is useful and necessary before costlier transient simulations of snap-through. Curved structures undergoing snap-through can have equilibrium states that cannot be captured by path following algorithms. Two types of ``hidden" equilibria are identified: secondary equilibrium branches bifurcated from the primary path and coexisting equilibria unconnected with the primary path. A numerical procedure that combines branch-switching and arclength methods is proposed to retrieve bifurcated secondary branches, and an analytical approach is introduced to obtain unconnected equilibria. With knowledge of the entire equilibrium manifold, transient simulations of snap-through are then investigated. Time integration of snap-through is very challenging because it is a highly nonlinear behavior involving sudden jumps. Even state-of-the-art schemes fail to provide accurate and efficient long-time predictions. This dissertation extends the preliminary work on an efficient composite scheme with significantly enhanced numerical accuracy and computational efficiency in simulating snap-through. In the design of slender curved components of reusable hypersonic vehicles, it is beneficial to efficiently identify the stability boundaries that separate non-snap from post-snap responses for different designs and loading conditions. Obtaining stability boundaries directly from parametric studies is computationally costly even with the most efficient algorithms. To alleviate the cost, an alternative approach to quickly approximate dynamic stability boundaries is proposed. This approach significantly decreases the number of transient simulations needed and therefore greatly accelerates the exploration of dynamic stability boundaries.Item Computational framework for the analysis of hybrid masonry systems using an improved non-local technique(2014-12-05) Gao, Zhenjia; Stanciulescu, Ilinca; Padgett, Jamie; Lou, Jun; Willam, KasparHybrid masonry structures combine the ductility of steel components with the shear strength of reinforced masonry panels. The goal of this research is to provide a sound basis for the design of an optimal type of hybrid structure that can be implemented as a new lateral-force-resisting system in high seismic regions. The most challenging part in the hybrid structure simulation is to capture the behaviour of concrete under different loading scenarios. This thesis sets up a computational framework for the analysis of hybrid masonry systems using an improved non-local technique, including the contributions such as: adopting the consistent linearisation technique to improve the computational efficiency of the non-local one-scalar damage model; presenting a new way to calibrate parameters in the tension damage law in the two-scalar damage model by correlating them to the ones in the one-scalar damage model; designing a data structure to save the domain information for each material point in order to apply the non-local technique; proposing an automatic parameter calibration procedure based on the Nelder-Mead simplex method for the two-scalar damage model utilizing the global system testing data; proposing and identifying the internal variable to be non-localized to enhance a new damage model to obtain the mesh regularization solution. Finally, this thesis performs a system-level numerical study of the energy dissipation mechanisms of hybrid masonry structures under cyclic loading. The numerical studies extrapolate test data to a wider range of structural configurations in terms of various connector strengths and different masonry panels to maximize seismic energy dissipation. This work also investigates the influence of the load transfer mechanism on the lateral strength, stiffness, energy dissipation capacity and deformation pattern of the hybrid system. Findings from the numerical studies performed in this work confirm the feasibility of using hybrid structures in high seismic areas.Item Computational modeling of fibrous biological tissues and bio-inspired materials(2016-09-23) Jin, Tao; Stanciulescu, IlincaMany bio and bio-inspired materials are composed of fiber network structures embedded in ground matrices and can be categorized as fibrous biomaterials. Understanding the structure-function relationship of these materials provides insight into the pathophysiology of various diseases, such as arteriosclerosis, and advances many biomedical applications, such as artificial heart valves. Combining numerical methods with experimental technologies is effective for investigating these relationships. A new computational framework is proposed to simulate the mechanical behavior of fibrous biomaterials. First, the microscopic fiber structure is synthetically generated via a random walk algorithm and incorporated into finite element (FE) simulations based on the embedded fiber approach. The material parameters involved in the generation of these fiber structures have physical or geometric interpretations and can potentially be obtained from experiments. The element residual and stiffness matrix are then derived via a variational approach. Moreover, FE simulations can be easily combined with the Monte Carlo method to consider the material structure randomness and describe the material average behavior. Since the number of degrees of freedom of the discretized system remains unchanged, the proposed framework maintains the computational efficiency of FE simulations while taking into consideration the material microscopic structure. Poly(ethylene glycol) diacrylate (PEGDA) hydrogel is one bio-inspired material used for tissue engineered heart valves. As an example of applying the proposed framework, various factors including pattern ratio, orientation, and waviness can be numerically investigated for their influence on the mechanical behavior of patterned PEGDA hydrogels. Moreover, a (toe-heel-linear) three-region stress-strain relationship typically exhibited by biological tissues is depicted by properly tuning the hydrogel properties. Studying these properties provides input for better hydrogel design. Arterial walls are another example of biological tissues that can effectively use the proposed framework. Structure-function relationships of different arterial wall layers are examined by using layer-specific experimental data. Material structures like fiber dispersion caused by fiber angular distribution and waviness are both considered. Additionally, the material parameters used in the proposed framework can be linked to phenomenological parameters in the homogenized modeling approach. By linking these parameters, it is possible to calculate the phenomenological parameters directly from the quantities measured in experiments.Item Computational modeling of the arterial wall based on layer-specific histological data(Springer, 2016) Jin, Tao; Stanciulescu, IlincaArterial walls typically have a heterogeneous structure with three different layers (intima, media, and adventitia). Each layer can be modeled as a fiber-reinforced material with two families of relatively stiff collagenous fibers symmetrically arranged within an isotropic soft ground matrix. In this paper, we present two different modeling approaches, the embedded fiber (EF) approach and the angular integration (AI) approach, to simulate the anisotropic behavior of individual arterial wall layers involving layer-specific data. The EF approach directly incorporates the microscopic arrangement of fibers that are synthetically generated from a random walk algorithm and captures material anisotropy at the element level of the finite element formulation. The AI approach smears fibers in the ground matrix and treats the material as homogeneous, with material anisotropy introduced at the constitutive level by enhancing the isotropic strain energy with two anisotropic terms. Both approaches include the influence of fiber dispersion introduced by fiber angular distribution (departure of individual fibers from the mean orientation) and take into consideration the dispersion caused by fiber waviness, which has not been previously considered. By comparing the numerical results with the published experimental data of different layers of a human aorta, we show that by using histological data both approaches can successfully capture the anisotropic behavior of individual arterial wall layers. Furthermore, through a comprehensive parametric study, we establish the connections between the AI phenomenological material parameters and the EF parameters having straightforward physical or geometrical interpretations. This study provides valuable insight for the calibration of phenomenological parameters used in the homogenized modeling based on the fiber microscopic arrangement. Moreover, it facilitates a better understanding of individual arterial wall layers, which will eventually advance the study of the structure–function relationship of arterial walls as a whole.Item Design of vibration inspired bi-orthogonal wavelets for signal analysis(2013-07-24) Phan, Quan; Dick, Andrew J.; Spanos, Pol D.; Stanciulescu, IlincaIn this thesis, a method to calculate scaling function coefficients for a new bi-orthogonal wavelet family derived directly from an impulse response waveform is presented. In literature, the Daubechies wavelets (DB wavelet) and the Morlet wavelet are the most commonly used wavelets for the dyadic wavelet transform (DWT) and the continuous wavelet transform (CWT), respectively. For a specific vibration signal processing application, a wavelet basis that is similar or is derived directly from the signal being studied proves to be superior to the commonly used wavelet basis. To assure a wavelet basis has a direct relationship to the signal being studied, a new formula is proposed to calculate coefficients which capture the characteristics of an impulse response waveform. The calculated coefficients are then used to develop a new bi-orthogonal wavelet family.Item Direct calculation of critical points in parameter sensitive systems(Elsevier, 2013) Moghaddasie, Behrang; Stanciulescu, IlincaAt critical points along the equilibrium path, sudden and sometimes catastrophic changes in the structural behaviour are observed. The equilibrium path, load-bearing capacity and locations of critical points can be sensitive to variations in parameters, such as geometrical imperfections, multi-parameter loadings, temperature and material properties. This paper introduces an incremental-iterative procedure to directly calculate the critical load for parameterized elastic structures. A modified Newton's method is proposed to simultaneously set the residual force and the minimum eigenvalue of the tangent stiffness matrix to zero by using an iterative algorithm. To demonstrate the performance of this method, numerical examples are presented.Item Effect of Surface Friction on Tire-Pavement Contact Stresses during Vehicle Maneuvering(American Society of Civil Engineers, 2013) Wang, Hao; Al-Qadi, Imad L.; Stanciulescu, IlincaAccurate modeling of tire-pavement contact behavior plays an important role in the analysis of pavement performance and vehicle stability control. A threedimensional (3-D) tire-pavement interaction model was developed using the finite element method (FEM) to analyze the forces and contact stresses generated during vehicle maneuvering (free rolling, braking/acceleration, and cornering). A pneumatic radial-ply tire structure with rubber and reinforcement was simulated. The steady-state tire rolling process was simulated using an Arbitrary Lagrangian Eulerian (ALE) formulation. An improved friction model that considers the effect of sliding speed on friction coefficients was implemented to analyze the effects of pavement surface friction on contact stresses, friction forces, and cornering forces. The results show that the magnitudes and non-uniformity of contact stresses are affected by vehicle maneuvering conditions. As the pavement surface friction increases, the tangential tire-pavement contact stresses at various rolling conditions (free rolling, braking/acceleration, and cornering) and the vertical contact stresses at the cornering condition increase. It is reasonable to use the constant friction coefficient when predicting tire-pavement contact stresses at the free rolling condition or at the cornering condition with small slip angles. However, it is important to use the sliding-velocity-dependent friction model when predicting the friction force at tire braking.Item Equilibria and stability boundaries of shallow arches under static loading in a thermal environment(Elsevier, 2013) Moghaddasie, Behrang; Stanciulescu, IlincaThe structural behaviour of shallow arches is complex and can be influenced by many parameters. In this paper, the response of a half-sine shallow arch under static loading in a thermal environment is investigated. The arch has pinned supports and the material behaviour is assumed elastic. The exact displacement field, load-bearing capacity and the locus of critical points are obtained. Boundaries of domains with different stability behaviours (e.g., different number of limit and bifurcation points) are also determined. Three types of loading (concentrated, uniform and asymmetrical uniform) are examined. The primary equilibrium paths are verified against results obtained from finite element simulations. The proposed method is robust and accurate.Item Fast approximations of dynamic stability boundaries of slender curved structures(Elsevier, 2017) Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, MichaelCurved beams and panels can often be found as structural components in aerospace, mechanical and civil engineering systems. When curved structures are subjected to dynamic loads, they are susceptible to dynamic instabilities especially dynamic snap-through buckling. The identification of the dynamic stability boundary that separate the non-snap and post-snap responses is hence necessary for the safe design of such structures, but typically requires extensive transient simulations that may lead to high computation cost. This paper proposes a scaling approach that reveals the similarities between dynamic snap-through boundaries of different structures. Such identified features can be directly used for fast approximations of dynamic stability boundaries of slender curved structures when their geometric parameters or boundary conditions are varied. The scaled dynamic stability boundaries of half-sine arches, parabolic arches and cylindrical panels are studied.Item Frequency domain analysis of linear and nonlinear structures with applications to impact force identification and micro-resonator design(2013-12-06) Ghaderi, Pooya; Akin, John Edward.; Stanciulescu, Ilinca; Dick, Andrew J.The modeling and analysis of structures using frequency-domain methods simplify the procedure of the modeling and analysis and provides better understanding of the response of the structures. There are different applications in frequency-domain structural modeling and analysis such as modeling and analysis in impact engineering, wave propagation in structures, and micro-resonators. The identification of the impact force and the impact location in structures are important for monitoring the condition of the structures and also for the design of the future structures. The complexity and nonlinearity of the impact incident makes it impractical to measure the impact force directly. In this study, a new method that uses the spectral finite element method (SFEM) is introduced in order to identify and locate the applied impact force. Using SFEM facilitates for the successfully identification of the high frequency content in the impact forces. Also, using SFEM allows for the identification of the impact force independent of the location of the impact force. The impact force identification and localization method is verified by experimental results. For designing and analyzing micro-resonators, it is required to do the frequency-analysis of these structures which provide the frequency characteristics and the frequency-response of the structures. In this study, a novel class of parametrically excited micro-resonators is introduced. The micro-resonator takes advantage of piezo-electric excitation which improves the performance of the micro-resonator over that of the micro-resonators with electrostatic excitation for certain applications.Item A GPU-based preconditioned Newton-Krylov solver for flexible multibody dynamics(Wiley, 2015) Serban, Radu; Melanz, Daniel; Li, Ang; Stanciulescu, Ilinca; Jayakumar, Paramsothy; Negrut, DanThis paper describes an approach to numerically approximate the time evolution of multibody systems with flexible (compliant) components. Its salient attribute is that at each time step, both the formulation of the system equations of motion and their numerical solution are carried out using parallel computing on graphics processing unit cards. The equations of motion are obtained using the absolute nodal coordinate formulation, yet any other multibody dynamics formalism would fit equally well the overall solution strategy outlined herein. The implicit numerical integration method adopted relies on a Newton-Krylov methodology and a parallel direct sparse solver to precondition the underlying linear system. The proposed approach, implemented in a software infrastructure available under an open-source BSD-3 license, leads to improvements in overall simulation times of up to one order of magnitude when compared with matrix-free parallel solution approaches that do not use preconditioning.Item High fidelity numerical study of nonlinear impact wave propagation: methods, analysis, and applications(2014-11-06) Liu, Yu; Dick, Andrew J; Akin, John E; Stanciulescu, IlincaVarious systems and structures are subjected to impact loading in industrial and military applications. Many of these impact loads have very high magnitudes and very short durations, resulting in high frequency content. Under some conditions, the response to these loading conditions can be significantly influenced by nonlinearities. The goal of this thesis is to develop new tools for studying the nonlinear wave propagation which can result from this extreme impact loading and provide an in-depth understanding of the underlying physical process. It consists of analytical, numerical, and experimental studies. Two new numerical methods are developed for high fidelity simulation of nonlinear wave propagations: the alternating frequency-time finite element method (AFT-FEM) and the alternating wavelet-time finite element method (AWT-FEM). A perturbation based approach is developed to derive analytical formula of the wavenumber for one-dimensional rod model. By employing these numerical and analytical methods, numerical simulations of wave propagations in both infinite and finite domains for one-dimensional and two-dimensional structures are conducted to explore nonlinear behaviors in the responses. Experimental efforts are also made to verify numerical results of impact wave propagation. Through comparison with other existing numerical approaches, the advantages of AWT-FEM in computational efficiency and high fidelity are demonstrated and the method is employed for applications of nonlinear force identification and drill-string stability monitoring.
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