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Identification of modal parameters of a space frame structure is a complex assignment due to a large number of degrees of freedom, close natural frequencies, and different vibrating mechanisms. Research has been carried out on the modal identification of rather simple truss structures. So far, less attention has been given to complex three-dimensional truss structures. This work develops a vibration-based methodology for determining modal information of three-dimensional space truss structures. The method uses a relatively complex space truss structure for its verification. Numerical modelling of the system gives modal information about the expected vibration behaviour. The identification process involves closely spaced modes that are characterised by local and global vibration mechanisms. To distinguish between local and global vibrations of the system, modal strain energies are used as an indicator. The experimental validation, which incorporated a modal analysis employing the stochastic subspace identification method, has confirmed that considering relatively high model orders is required to identify specific mode shapes. Especially in the case of the determination of local deformation modes of space truss members, higher model orders have to be taken into account than in the modal identification of most other types of structures.
As an optimization that starts from a randomly selected structure generally does not guarantee reasonable optimality, the use of a systemic approach, named the ground structure, is widely accepted in steel-made truss and frame structural design. However, in the case of reinforced concrete (RC) structural optimization, because of the orthogonal orientation of structural members, randomly chosen or architect-sketched framing is used. Such a one-time fixed layout trend, in addition to its lack of a systemic approach, does not necessarily guarantee optimality. In this study, an approach for generating a candidate ground structure to be used for cost or weight minimization of 3D RC building structures with included slabs is developed. A multiobjective function at the floor optimization stage and a single objective function at the frame optimization stage are considered. A particle swarm optimization (PSO) method is employed for selecting the optimal ground structure. This method enables generating a simple, yet potential, real-world representation of topologically preoptimized ground structure while both structural and main architectural requirements are considered. This is supported by a case study for different floor domain sizes.
This study proposes an efficient Bayesian, frequency-based damage identification approach to identify damages in cantilever structures with an acceptable error rate, even at high noise levels. The catenary poles of electric high-speed train systems were selected as a realistic case study to cover the objectives of this study. Compared to other frequency-based damage detection approaches described in the literature, the proposed approach is efficiently able to detect damages in cantilever structures to higher levels of damage detection, namely identifying both the damage location and severity using a low-cost structural health monitoring (SHM) system with a limited number of sensors; for example, accelerometers. The integration of Bayesian inference, as a stochastic framework, in the proposed approach, makes it possible to utilize the benefit of data fusion in merging the informative data from multiple damage features, which increases the quality and accuracy of the results. The findings provide the decision-maker with the information required to manage the maintenance, repair, or replacement procedures.
The polymeric clay nanocomposites are a new class of materials of which recently have become the centre of attention due to their superior mechanical and physical properties. Several studies have been performed on the mechanical characterisation of these nanocomposites; however most of those studies have neglected the effect of the interfacial region between the clays and the matrix despite of its significant influence on the mechanical performance of the nanocomposites.
There are different analytical methods to calculate the overall elastic material properties of the composites. In this study we use the Mori-Tanaka method to determine the overall stiffness of the composites for simple inclusion geometries of cylinder and sphere. Furthermore, the effect of interphase layer on the overall properties of composites is calculated. Here, we intend to get ounds for the effective mechanical properties to compare with the analytical results. Hence, we use linear displacement boundary conditions (LD) and uniform traction boundary conditions (UT) accordingly. Finally, the analytical results are compared with numerical results and they are in a good agreement.
The next focus of this dissertation is a computational approach with a hierarchical multiscale method on the mesoscopic level. In other words, in this study we use the stochastic analysis and computational homogenization method to analyse the effect of thickness and stiffness of the interfacial region on the overall elastic properties of the clay/epoxy nanocomposites. The results show that the increase in interphase thickness, reduces the stiffness of the clay/epoxy naocomposites and this decrease becomes significant in higher clay contents. The results of the sensitivity analysis prove that the stiffness of the interphase layer has more significant effect on the final stiffness of nanocomposites. We also validate the results with the available experimental results from the literature which show good agreement.
The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.
This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.
In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion.
One major research focus in the Material Science and Engineering Community in the past decade has been to obtain a more fundamental understanding on the phenomenon 'material failure'. Such an understanding is critical for engineers and scientists developing new materials with higher strength and toughness, developing robust designs against failure, or for those concerned with an accurate estimate of a component's design life. Defects like cracks and dislocations evolve at
nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. In engineering applications, the global response of the system is often governed by the behaviour at the smaller length scales. Hence, the sub-scale behaviour must be computed accurately for good predictions of the full scale behaviour.
Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. Since the atomistic dimensions are of the order of Angstroms ( A), approximately 85 billion atoms are required to model a 1 micro- m^3 volume of Copper. Therefore, pure atomistic models are prohibitively expensive with everyday engineering computations involving macroscopic cracks and shear bands, which are much larger than the atomistic length and time scales. To reduce the computational effort, multiscale methods are required, which are able to couple a continuum description of the structure with an atomistic description. In such paradigms, cracks and dislocations are explicitly modeled at the atomistic scale, whilst a self-consistent continuum model elsewhere.
Many multiscale methods for fracture are developed for "fictitious" materials based on "simple" potentials such as the Lennard-Jones potential. Moreover, multiscale methods for evolving cracks are rare. Efficient methods to coarse grain the fine scale defects are missing. However, the existing multiscale methods for fracture do not adaptively adjust the fine scale domain as the crack propagates. Most methods, therefore only "enlarge" the fine scale domain and therefore drastically increase computational cost. Adaptive adjustment requires the fine scale domain to be refined and coarsened. One of the major difficulties in multiscale methods for fracture is to up-scale fracture related material information from the fine scale to the coarse scale, in particular for complex crack problems. Most of the existing approaches therefore were applied to examples with comparatively few macroscopic cracks.
Key contributions
The bridging scale method is enhanced using the phantom node method so that cracks can be modeled at the coarse scale. To ensure self-consistency in the bulk, a virtual atom cluster is devised providing the response of the intact material at the coarse scale. A molecular statics model is employed in the fine scale where crack propagation is modeled by naturally breaking the bonds. The fine scale and coarse scale models are coupled by enforcing the displacement boundary conditions on the ghost atoms. An energy criterion is used to detect the crack tip location. Adaptive refinement and coarsening schemes are developed and implemented during the crack propagation. The results were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale method is one of the first adaptive multiscale method for fracture.
A robust and simple three dimensional coarse graining technique to convert a given atomistic region into an equivalent coarse region, in the context of multiscale fracture has been developed. The developed method is the first of its kind. The developed coarse graining technique can be applied to identify and upscale the defects like: cracks, dislocations and shear bands. The current method has been applied to estimate the equivalent coarse scale models of several complex fracture patterns arrived from the pure atomistic simulations. The upscaled fracture pattern agree well with the actual fracture pattern. The error in the potential energy of the pure atomistic and the coarse grained model was observed to be acceptable.
A first novel meshless adaptive multiscale method for fracture has been developed. The phantom node method is replaced by a meshless differential reproducing kernel particle method. The differential reproducing kernel particle method is comparatively more expensive but allows for a more "natural" coupling between the two scales due to the meshless interpolation functions. The higher order continuity is also beneficial. The centro symmetry parameter is used to detect the crack tip location. The developed multiscale method is employed to study the complex crack propagation. Results based on the meshless adaptive multiscale method were observed to be in excellent agreement with the pure atomistic simulations.
The developed multiscale methods are applied to study the fracture in practical materials like Graphene and Graphene on Silicon surface. The bond stretching and the bond reorientation were observed to be the net mechanisms of the crack growth in Graphene. The influence of time step on the crack propagation was studied using two different time steps. Pure atomistic simulations of fracture in Graphene on Silicon surface are presented. Details of the three dimensional multiscale method to study the fracture in Graphene on Silicon surface are discussed.
This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom–atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.
A phantom-node method is developed for three-node shell elements to describe cracks. This method can treat arbitrary cracks independently of the mesh. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Several numerical examples are presented to illustrate the proposed method.
This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting “edge-based” smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, “super-convergence” and “ultra-accurate” solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.
The current study attempts to recognise an adequate classification for a semi-rigid beam-to-column connection by investigating strength, stiffness and ductility. For this purpose, an experimental test was carried out to investigate the moment-rotation (M-theta) features of flush end-plate (FEP) connections including variable parameters like size and number of bolts, thickness of end-plate, and finally, size of beams and columns. The initial elastic stiffness and ultimate moment capacity of connections were determined by an extensive analytical procedure from the proposed method prescribed by ANSI/AISC 360-10, and Eurocode 3 Part 1-8 specifications. The behaviour of beams with partially restrained or semi-rigid connections were also studied by incorporating classical analysis methods. The results confirmed that thickness of the column flange and end-plate substantially govern over the initial rotational stiffness of of flush end-plate connections. The results also clearly showed that EC3 provided a more reliable classification index for flush end-plate (FEP) connections. The findings from this study make significant contributions to the current literature as the actual response characteristics of such connections are non-linear. Therefore, such semirigid behaviour should be used to for an analysis and design method.
Polymeric nanocomposites (PNCs) are considered for numerous nanotechnology such as: nano-biotechnology, nano-systems, nanoelectronics, and nano-structured materials. Commonly , they are formed by polymer (epoxy) matrix reinforced with a nanosized filler. The addition of rigid nanofillers to the epoxy matrix has offered great improvements in the fracture toughness without sacrificing other important thermo-mechanical properties. The physics of the fracture in PNCs is rather complicated and is influenced by different parameters. The presence of uncertainty in the predicted output is expected as a result of stochastic variance in the factors affecting the fracture mechanism. Consequently, evaluating the improved fracture toughness in PNCs is a challenging problem.
Artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) have been employed to predict the fracture energy of polymer/particle nanocomposites. The ANN and ANFIS models were constructed, trained, and tested based on a collection of 115 experimental datasets gathered from the literature. The performance evaluation indices of the developed ANN and ANFIS showed relatively small error, with high coefficients of determination (R2), and low root mean square error and mean absolute percentage error.
In the framework for uncertainty quantification of PNCs, a sensitivity analysis (SA) has been conducted to examine the influence of uncertain input parameters on the fracture toughness of polymer/clay nanocomposites (PNCs). The phase-field approach is employed to predict the macroscopic properties of the composite considering six uncertain input parameters. The efficiency, robustness, and repeatability are compared and evaluated comprehensively for five different SA methods.
The Bayesian method is applied to develop a methodology in order to evaluate the performance of different analytical models used in predicting the fracture toughness of polymeric particles nanocomposites. The developed method have considered the model and parameters uncertainties based on different reference data (experimental measurements) gained from the literature. Three analytical models differing in theory and assumptions were examined. The coefficients of variation of the model predictions to the measurements are calculated using the approximated optimal parameter sets. Then, the model selection probability is obtained with respect to the different reference data.
Stochastic finite element modeling is implemented to predict the fracture toughness of polymer/particle nanocomposites. For this purpose, 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone is generated. The crack propagation is simulated by the cohesive segments method and phantom nodes. Considering the uncertainties in the input parameters, a polynomial chaos expansion (PCE) surrogate model is construed followed by a sensitivity analysis.
Encapsulation-based self-healing concrete (SHC) is the most promising technique for providing a self-healing mechanism to concrete. This is due to its capacity to heal fractures effectively without human interventions, extending the operational life and lowering maintenance costs. The healing mechanism is created by embedding capsules containing the healing agent inside the concrete. The healing agent will be released once the capsules are fractured and the healing occurs in the vicinity of the damaged part. The healing efficiency of the SHC is still not clear and depends on several factors; in the case of microcapsules SHC the fracture of microcapsules is the most important aspect to release the healing agents and hence heal the cracks. This study contributes to verifying the healing efficiency of SHC and the fracture mechanism of the microcapsules. Extended finite element method (XFEM) is a flexible, and powerful discrete crack method that allows crack propagation without the requirement for re-meshing and has been shown high accuracy for modeling fracture in concrete. In this thesis, a computational fracture modeling approach of Encapsulation-based SHC is proposed based on the XFEM and cohesive surface technique (CS) to study the healing efficiency and the potential of fracture and debonding of the microcapsules or the solidified healing agents from the concrete matrix as well. The concrete matrix and a microcapsule shell both are modeled by the XFEM and combined together by CS. The effects of the healed-crack length, the interfacial fracture properties, and microcapsule size on the load carrying capability and fracture pattern of the SHC have been studied. The obtained results are compared to those obtained from the zero thickness cohesive element approach to demonstrate the significant accuracy and the validity of the proposed simulation. The present fracture simulation is developed to study the influence of the capsular clustering on the fracture mechanism by varying the contact surface area of the CS between the microcapsule shell and the concrete matrix. The proposed fracture simulation is expanded to 3D simulations to validate the 2D computational simulations and to estimate the accuracy difference ratio between 2D and 3D simulations. In addition, a proposed design method is developed to design the size of the microcapsules consideration of a sufficient volume of healing agent to heal the expected crack width. This method is based on the configuration of the unit cell (UC), Representative Volume Element (RVE), Periodic Boundary Conditions (PBC), and associated them to the volume fraction (Vf) and the crack width as variables. The proposed microcapsule design is verified through computational fracture simulations.
The fracture of microcapsules is an important issue to release the healing agent for healing the cracks in encapsulation-based self-healing concrete. The capsular clustering generated from the concrete mixing process is considered one of the critical factors in the fracture mechanism. Since there is a lack of studies in the literature regarding this issue, the design of self-healing concrete cannot be made without an appropriate modelling strategy. In this paper, the effects of microcapsule size and clustering on the fractured microcapsules are studied computationally. A simple 2D computational modelling approach is developed based on the eXtended Finite Element Method (XFEM) and cohesive surface technique. The proposed model shows that the microcapsule size and clustering have significant roles in governing the load-carrying capacity and the crack propagation pattern and determines whether the microcapsule will be fractured or debonded from the concrete matrix. The higher the microcapsule circumferential contact length, the higher the load-carrying capacity. When it is lower than 25% of the microcapsule circumference, it will result in a greater possibility for the debonding of the microcapsule from the concrete. The greater the core/shell ratio (smaller shell thickness), the greater the likelihood of microcapsules being fractured.
Determining the earthquake hazard of any settlement is one of the primary studies for reducing earthquake damage. Therefore, earthquake hazard maps used for this purpose must be renewed over time. Turkey Earthquake Hazard Map has been used instead of Turkey Earthquake Zones Map since 2019. A probabilistic seismic hazard was performed by using these last two maps and different attenuation relationships for Bitlis Province (Eastern Turkey) were located in the Lake Van Basin, which has a high seismic risk. The earthquake parameters were determined by considering all districts and neighborhoods in the province. Probabilistic seismic hazard analyses were carried out for these settlements using seismic sources and four different attenuation relationships. The obtained values are compared with the design spectrum stated in the last two earthquake maps. Significant differences exist between the design spectrum obtained according to the different exceedance probabilities. In this study, adaptive pushover analyses of sample-reinforced concrete buildings were performed using the design ground motion level. Structural analyses were carried out using three different design spectra, as given in the last two seismic design codes and the mean spectrum obtained from attenuation relationships. Different design spectra significantly change the target displacements predicted for the performance levels of the buildings.
Recently, the demand for residence and usage of urban infrastructure has been increased, thereby resulting in the elevation of risk levels of human lives over natural calamities. The occupancy demand has rapidly increased the construction rate, whereas the inadequate design of structures prone to more vulnerability. Buildings constructed before the development of seismic codes have an additional susceptibility to earthquake vibrations. The structural collapse causes an economic loss as well as setbacks for human lives. An application of different theoretical methods to analyze the structural behavior is expensive and time-consuming. Therefore, introducing a rapid vulnerability assessment method to check structural performances is necessary for future developments. The process, as mentioned earlier, is known as Rapid Visual Screening (RVS). This technique has been generated to identify, inventory, and screen structures that are potentially hazardous. Sometimes, poor construction quality does not provide some of the required parameters; in this case, the RVS process turns into a tedious scenario. Hence, to tackle such a situation, multiple-criteria decision-making (MCDM) methods for the seismic vulnerability assessment opens a new gateway. The different parameters required by RVS can be taken in MCDM. MCDM evaluates multiple conflicting criteria in decision making in several fields. This paper has aimed to bridge the gap between RVS and MCDM. Furthermore, to define the correlation between these techniques, implementation of the methodologies from Indian, Turkish, and Federal Emergency Management Agency (FEMA) codes has been done. The effects of seismic vulnerability of structures have been observed and compared.
A Machine Learning Framework for Assessing Seismic Hazard Safety of Reinforced Concrete Buildings
(2020)
Although averting a seismic disturbance and its physical, social, and economic disruption is practically impossible, using the advancements in computational science and numerical modeling shall equip humanity to predict its severity, understand the outcomes, and equip for post-disaster management. Many buildings exist amidst the developed metropolitan areas, which are senile and still in service. These buildings were also designed before establishing national seismic codes or without the introduction of construction regulations. In that case, risk reduction is significant for developing alternatives and designing suitable models to enhance the existing structure’s performance. Such models will be able to classify risks and casualties related to possible earthquakes through emergency preparation. Thus, it is crucial to recognize structures that are susceptible to earthquake vibrations and need to be prioritized for retrofitting. However, each building’s behavior under seismic actions cannot be studied through performing structural analysis, as it might be unrealistic because of the rigorous computations, long period, and substantial expenditure. Therefore, it calls for a simple, reliable, and accurate process known as Rapid Visual Screening (RVS), which serves as a primary screening platform, including an optimum number of seismic parameters and predetermined performance damage conditions for structures. In this study, the damage classification technique was studied, and the efficacy of the Machine Learning (ML) method in damage prediction via a Support Vector Machine (SVM) model was explored. The ML model is trained and tested separately on damage data from four different earthquakes, namely Ecuador, Haiti, Nepal, and South Korea. Each dataset consists of varying numbers of input data and eight performance modifiers. Based on the study and the results, the ML model using SVM classifies the given input data into the belonging classes and accomplishes the performance on hazard safety evaluation of buildings.
A vast number of existing buildings were constructed before the development and enforcement of seismic design codes, which run into the risk of being severely damaged under the action of seismic excitations. This poses not only a threat to the life of people but also affects the socio-economic stability in the affected area. Therefore, it is necessary to assess such buildings’ present vulnerability to make an educated decision regarding risk mitigation by seismic strengthening techniques such as retrofitting. However, it is economically and timely manner not feasible to inspect, repair, and augment every old building on an urban scale. As a result, a reliable rapid screening methods, namely Rapid Visual Screening (RVS), have garnered increasing interest among researchers and decision-makers alike. In this study, the effectiveness of five different Machine Learning (ML) techniques in vulnerability prediction applications have been investigated. The damage data of four different earthquakes from Ecuador, Haiti, Nepal, and South Korea, have been utilized to train and test the developed models. Eight performance modifiers have been implemented as variables with a supervised ML. The investigations on this paper illustrate that the assessed vulnerability classes by ML techniques were very close to the actual damage levels observed in the buildings.
In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases.
The Marmara Region (NW Turkey) has experienced significant earthquakes (M > 7.0) to date. A destructive earthquake is also expected in the region. To determine the effect of the specific design spectrum, eleven provinces located in the region were chosen according to the Turkey Earthquake Building Code updated in 2019. Additionally, the differences between the previous and updated regulations of the country were investigated. Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV) were obtained for each province by using earthquake ground motion levels with 2%, 10%, 50%, and 68% probability of exceedance in 50-year periods. The PGA values in the region range from 0.16 to 0.7 g for earthquakes with a return period of 475 years. For each province, a sample of a reinforced-concrete building having two different numbers of stories with the same ground and structural characteristics was chosen. Static adaptive pushover analyses were performed for the sample reinforced-concrete building using each province’s design spectrum. The variations in the earthquake and structural parameters were investigated according to different geographical locations. It was determined that the site-specific design spectrum significantly influences target displacements for performance-based assessments of buildings due to seismicity characteristics of the studied geographic location.
Methods based on B-splines for model representation, numerical analysis and image registration
(2015)
The thesis consists of inter-connected parts for modeling and analysis using newly developed isogeometric methods. The main parts are reproducing kernel triangular B-splines, extended isogeometric analysis for solving weakly discontinuous problems, collocation methods using superconvergent points, and B-spline basis in image registration applications.
Each topic is oriented towards application of isogeometric analysis basis functions to ease the process of integrating the modeling and analysis phases of simulation.
First, we develop reproducing a kernel triangular B-spline-based FEM for solving PDEs. We review the triangular B-splines and their properties. By definition, the triangular basis function is very flexible in modeling complicated domains. However, instability results when it is applied for analysis. We modify the triangular B-spline by a reproducing kernel technique, calculating a correction term for the triangular kernel function from the chosen surrounding basis. The improved triangular basis is capable to obtain the results with higher accuracy and almost optimal convergence rates.
Second, we propose an extended isogeometric analysis for dealing with weakly discontinuous problems such as material interfaces. The original IGA is combined with XFEM-like enrichments which are continuous functions themselves but with discontinuous derivatives. Consequently, the resulting solution space can approximate solutions with weak discontinuities. The method is also applied to curved material interfaces, where the inverse mapping and the curved triangular elements are considered.
Third, we develop an IGA collocation method using superconvergent points. The collocation methods are efficient because no numerical integration is needed. In particular when higher polynomial basis applied, the method has a lower computational cost than Galerkin methods. However, the positions of the collocation points are crucial for the accuracy of the method, as they affect the convergent rate significantly. The proposed IGA collocation method uses superconvergent points instead of the traditional Greville abscissae points. The numerical results show the proposed method can have better accuracy and optimal convergence rates, while the traditional IGA collocation has optimal convergence only for even polynomial degrees.
Lastly, we propose a novel dynamic multilevel technique for handling image registration. It is application of the B-spline functions in image processing. The procedure considered aims to align a target image from a reference image by a spatial transformation. The method starts with an energy function which is the same as a FEM-based image registration. However, we simplify the solving procedure, working on the energy function directly. We dynamically solve for control points which are coefficients of B-spline basis functions. The new approach is more simple and fast. Moreover, it is also enhanced by a multilevel technique in order to prevent instabilities. The numerical testing consists of two artificial images, four real bio-medical MRI brain and CT heart images, and they show our registration method is accurate, fast and efficient, especially for large deformation problems.
The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger–Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.
The lattice dynamics properties are investigated for twisting bilayer graphene. There are big jumps for the inter-layer potential at twisting angle θ=0° and 60°, implying the stability of Bernal-stacking and the instability of AA-stacking structures, while a long platform in [8,55]° indicates the ease of twisting bilayer graphene in this wide angle range. Significant frequency shifts are observed for the z breathing mode around θ=0° and 60°, while the frequency is a constant in a wide range [8,55]°. Using the z breathing mode, a mechanical nanoresonator is proposed to operate on a robust resonant frequency in terahertz range.
We perform both classical molecular dynamics simulations and beam model calculations to investigate the Young's modulus of kinked silicon nanowires (KSiNWs). The Young's modulus is found to be highly sensitive to the arm length of the kink and is essentially inversely proportional to the arm length. The mechanism underlying the size dependence is found to be the interplay between the kink angle potential and the arm length potential, where we obtain an analytic relationship between the Young's modulus and the arm length of the KSiNW. Our results provide insight into the application of this novel building block in nanomechanical devices.
The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the ab initio calculation and applying the quantum mechanical non-equilibrium Green’s function approach. Specially, there are two main findings from our calculation: (1) the thermal conductivity can reach a high value of 310 Wm−1 K−1 in a 100 nm polyethylene chain at room temperature and the thermal conductivity increases with the length of the chain; (2) the Young’s modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain 32.85%±0.05% (ultimate) strain before undergoing structural phase transition into gaseous ethylene.
This paper presents several aspects of characterization of welding heat source parameters in Goldak’s double ellipsoidal model using Sysweld simulation of welding of two overlapping beads on a substrate steel plate. The overlap percentages ranged from 40% to 80% in increments of 10%. The new material properties of the fused metal were characterized using Weldware and their continuous cooling transformation curves. The convective and radiative heat transfer coefficients as well as the cooling time t8/5 were estimated using numerical formulations from relevant standards. The effects of the simulation geometry and mesh discretization were evaluated in terms of the factor F provided in Sysweld. Eventually, the parameters of Goldak’s double ellipsoidal heat source model were determined for the welding simulation of overlapping beads on the plate and the simulated bead geometry, extent of the molten pool and the HAZ were compared with the macrographs of cross-sections of the experimental weldments. The results showed excellent matching, thus verifying this methodology for determination of welding heat source parameters.
Matrix-free voxel-based finite element method for materials with heterogeneous microstructures
(2019)
Modern image detection techniques such as micro computer tomography
(μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis.
However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm.
This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained.