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Material properties play a critical role in durable products manufacturing. Estimation of the precise characteristics in different scales requires complex and expensive experimental measurements. Potentially, computational methods can provide a platform to determine the fundamental properties before the final experiment. Multi-scale computational modeling leads to the modeling of the various time, and length scales include nano, micro, meso, and macro scales. These scales can be modeled separately or in correlation with coarser scales. Depend on the interested scales modeling, the right selection of multi-scale methods leads to reliable results and affordable computational cost. The present dissertation deals with the problems in various length and time scales using computational methods include density functional theory (DFT), molecular mechanics (MM), molecular dynamics (MD), and finite element (FE) methods.
Physical and chemical interactions in lower scales determine the coarser scale properties. Particles interaction modeling and exploring fundamental properties are significant challenges of computational science. Downscale modelings need more computational effort due to a large number of interacted atoms/particles. To deal with this problem and bring up a fine-scale (nano) as a coarse-scale (macro) problem, we extended an atomic-continuum framework. The discrete atomic models solve as a continuum problem using the computationally efficient FE method. MM or force field method based on a set of assumptions approximates a solution on the atomic scale. In this method, atoms and bonds model as a harmonic oscillator with a system of mass and springs. The negative gradient of the potential energy equal to the forces on each atom. In this way, each bond's total potential energy includes bonded, and non-bonded energies are simulated as equivalent structural strain energies. Finally, the chemical nature of the atomic bond is modeled as a piezoelectric beam element that solves by the FE method.
Exploring novel materials with unique properties is a demand for various industrial applications. During the last decade, many two-dimensional (2D) materials have been synthesized and shown outstanding properties. Investigation of the probable defects during the formation/fabrication process and studying their strength under severe service life are the critical tasks to explore performance prospects. We studied various defects include nano crack, notch, and point vacancy (Stone-Wales defect) defects employing MD analysis. Classical MD has been used to simulate a considerable amount of molecules at micro-, and meso- scales. Pristine and defective nanosheet structures considered under the uniaxial tensile loading at various temperatures using open-source LAMMPS codes. The results were visualized with the open-source software of OVITO and VMD.
Quantum based first principle calculations have been conducting at electronic scales and known as the most accurate Ab initio methods. However, they are computationally expensive to apply for large systems. We used density functional theory (DFT) to estimate the mechanical and electrochemical response of the 2D materials. Many-body Schrödinger's equation describes the motion and interactions of the solid-state particles. Solid describes as a system of positive nuclei and negative electrons, all electromagnetically interacting with each other, where the wave function theory describes the quantum state of the set of particles. However, dealing with the 3N coordinates of the electrons, nuclei, and N coordinates of the electrons spin components makes the governing equation unsolvable for just a few interacted atoms. Some assumptions and theories like Born Oppenheimer and Hartree-Fock mean-field and Hohenberg-Kohn theories are needed to treat with this equation. First, Born Oppenheimer approximation reduces it to the only electronic coordinates. Then Kohn and Sham, based on Hartree-Fock and Hohenberg-Kohn theories, assumed an equivalent fictitious non-interacting electrons system as an electron density functional such that their ground state energies are equal to a set of interacting electrons. Exchange-correlation energy functionals are responsible for satisfying the equivalency between both systems. The exact form of the exchange-correlation functional is not known. However, there are widely used methods to derive functionals like local density approximation (LDA), Generalized gradient approximation (GGA), and hybrid functionals (e.g., B3LYP). In our study, DFT performed using VASP codes within the GGA/PBE approximation, and visualization/post-processing of the results realized via open-source software of VESTA.
The extensive DFT calculations are conducted 2D nanomaterials prospects as anode/cathode electrode materials for batteries. Metal-ion batteries' performance strongly depends on the design of novel electrode material. Two-dimensional (2D) materials have developed a remarkable interest in using as an electrode in battery cells due to their excellent properties. Desirable battery energy storage systems (BESS) must satisfy the high energy density, safe operation, and efficient production costs. Batteries have been using in electronic devices and provide a solution to the environmental issues and store the discontinuous energies generated from renewable wind or solar power plants. Therefore, exploring optimal electrode materials can improve storage capacity and charging/discharging rates, leading to the design of advanced batteries.
Our results in multiple scales highlight not only the proposed and employed methods' efficiencies but also promising prospect of recently synthesized nanomaterials and their applications as an anode material. In this way, first, a novel approach developed for the modeling of the 1D nanotube as a continuum piezoelectric beam element. The results converged and matched closely with those from experiments and other more complex models. Then mechanical properties of nanosheets estimated and the failure mechanisms results provide a useful guide for further use in prospect applications. Our results indicated a comprehensive and useful vision concerning the mechanical properties of nanosheets with/without defects. Finally, mechanical and electrochemical properties of the several 2D nanomaterials are explored for the first time—their application performance as an anode material illustrates high potentials in manufacturing super-stretchable and ultrahigh-capacity battery energy storage systems (BESS). Our results exhibited better performance in comparison to the available commercial anode materials.
Rechargeable lithium ion batteries (LIBs) play a very significant role in power supply and storage. In recent decades, LIBs have caught tremendous attention in mobile communication, portable electronics, and electric vehicles. Furthermore, global warming has become a worldwide issue due to the ongoing production of greenhouse gases. It motivates solutions such as renewable sources of energy. Solar and wind energies are the most important ones in renewable energy sources. By technology progress, they will definitely require batteries to store the produced power to make a balance between power generation and consumption. Nowadays,rechargeable batteries such as LIBs are considered as one of the best solutions. They provide high specific energy and high rate performance while their rate of self-discharge is low.
Performance of LIBs can be improved through the modification of battery characteristics. The size of solid particles in electrodes can impact the specific energy and the cyclability of batteries. It can improve the amount of lithium content in the electrode which is a vital parameter in capacity and capability of a battery. There exist diferent sources of heat generation in LIBs such as heat produced during electrochemical reactions, internal resistance in battery. The size of electrode's electroactive particles can directly affect the produced heat in battery. It will be shown that the smaller size of solid particle enhance the thermal characteristics of LIBs.
Thermal issues such as overheating, temperature maldistribution in the battery, and thermal runaway have confined applications of LIBs. Such thermal challenges reduce the Life cycle of LIBs. As well, they may lead to dangerous conditions such as fire or even explosion in batteries. However, recent advances in fabrication of advanced materials such as graphene and carbon nanotubes with extraordinary thermal conductivity and electrical properties propose new opportunities to enhance their performance. Since experimental works are expensive, our objective is to use computational methods to investigate the thermal issues in LIBS. Dissipation of the heat produced in the battery can improve the cyclability and specific capacity of LIBs. In real applications, packs of LIB consist several battery cells that are used as the power source. Therefore, it is worth to investigate thermal characteristic of battery packs under their cycles of charging/discharging operations at different applied current rates. To remove the produced heat in batteries, they can be surrounded by materials with high thermal conductivity. Parafin wax absorbs high energy since it has a high latent heat. Absorption high amounts of energy occurs at constant temperature without phase change. As well, thermal conductivity of parafin can be magnified with nano-materials such as graphene, CNT, and fullerene to form a nano-composite medium. Improving the thermal conductivity of LIBs increase the heat dissipation from batteries which is a vital issue in systems of battery thermal management. The application of two-dimensional (2D) materials has been on the rise since exfoliation the graphene from bulk graphite. 2D materials are single-layered in an order of nanosizes which show superior thermal, mechanical, and optoelectronic properties. They are potential candidates for energy storage and supply, particularly in lithium ion batteries as electrode material. The high thermal conductivity of graphene and graphene-like materials can play a significant role in thermal management of batteries. However, defects always exist in nano-materials since there is no ideal fabrication process. One of the most important defects in materials are nano-crack which can dramatically weaken the mechanical properties of the materials. Newly synthesized crystalline carbon nitride with the stoichiometry of C3N have attracted many attentions due to its extraordinary mechanical and thermal properties. The other nano-material is phagraphene which shows anisotropic mechanical characteristics which is ideal in production of nanocomposite.
It shows ductile fracture behavior when subjected under uniaxial loadings. It is worth to investigate their thermo-mechanical properties in its pristine and defective states. We hope that the findings of our work not only be useful for both experimental and theoretical researches but also help to design advanced electrodes for LIBs.
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.
Compactly, this thesis encompasses two major parts to examine mechanical responses of polymer compounds and two dimensional materials:
1- Molecular dynamics approach is investigated to study transverse impact behavior of polymers, polymer compounds and two dimensional materials.
2- Large deflection of circular and rectangular membranes is examined by employing continuum mechanics approach.
Two dimensional materials (2D), including, Graphene and molybdenum disulfide (MoS2), exhibited new and promising physical and chemical properties, opening new opportunities to be utilized alone or to enhance the performance of conventional materials. These 2D materials have attracted tremendous attention owing to their outstanding physical properties, especially concerning transverse impact loading.
Polymers, with the backbone of carbon (organic polymers) or do not include carbon atoms in the backbone (inorganic polymers) like polydimethylsiloxane (PDMS), have extraordinary characteristics particularly their flexibility leads to various easy ways of forming and casting. These simple shape processing label polymers as an excellent material often used as a matrix in composites (polymer compounds).
In this PhD work, Classical Molecular Dynamics (MD) is implemented to calculate transverse impact loading of 2D materials as well as polymer compounds reinforced with graphene sheets. In particular, MD was adopted to investigate perforation of the target and impact resistance force . By employing MD approach, the minimum velocity of the projectile that could create perforation and passes through the target is obtained. The largest investigation was focused on how graphene could enhance the impact properties of the compound. Also the purpose of this work was to discover the effect of the atomic arrangement of 2D materials on the impact problem. To this aim, the impact properties of two different 2D materials, graphene and MoS2, are studied. The simulation of chemical functionalization was carried out systematically, either with covalently bonded molecules or with non-bonded ones, focusing the following efforts on the covalently bounded species, revealed as the most efficient linkers.
To study transverse impact behavior by using classical MD approach , Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software, that is well-known among most researchers, is employed. The simulation is done through predefined commands in LAMMPS. Generally these commands (atom style, pair style, angle style, dihedral style, improper style, kspace style, read data, fix, run, compute and so on) are used to simulate and run the model for the desired outputs. Depends on the particles and model types, suitable inter-atomic potentials (force fields) are considered. The ensembles, constraints and boundary conditions are applied depends upon the problem definition. To do so, atomic creation is needed. Python codes are developed to generate particles which explain atomic arrangement of each model. Each atomic arrangement introduced separately to LAMMPS for simulation. After applying constraints and boundary conditions, LAMMPS also include integrators like velocity-Verlet integrator or Brownian dynamics or other types of integrator to run the simulation and finally the outputs are emerged. The outputs are inspected carefully to appreciate the natural behavior of the problem. Appreciation of natural properties of the materials assist us to design new applicable materials.
In investigation on the large deflection of circular and rectangular membranes, which is related to the second part of this thesis, continuum mechanics approach is implemented. Nonlinear Föppl membrane theory, which carefully release nonlinear governing equations of motion, is considered to establish the non-linear partial differential equilibrium equations of the membranes under distributed and centric point loads. The Galerkin and energy methods are utilized to solve non-linear partial differential equilibrium equations of circular and rectangular plates respectively. Maximum deflection as well as stress through the film region, which are kinds of issue in many industrial applications, are obtained.
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.
Das Ziel der Arbeit ist, eine mögliche Verbesserung der Güte der Lebensdauervorhersage für Gusseisenwerkstoffe mit Kugelgraphit zu erreichen, wobei die Gießprozesse verschiedener Hersteller berücksichtigt werden.
Im ersten Schritt wurden Probenkörper aus GJS500 und GJS600 von mehreren Gusslieferanten gegossen und daraus Schwingproben erstellt.
Insgesamt wurden Schwingfestigkeitswerte der einzelnen gegossenen Proben sowie der Proben des Bauteils von verschiedenen Gussherstellern weltweit entweder durch direkte Schwingversuche oder durch eine Sammlung von Betriebsfestigkeitsversuchen bestimmt.
Dank der metallografischen Arbeit und Korrelationsanalyse konnten drei wesentliche Parameter zur Bestimmung der lokalen Dauerfestigkeit festgestellt werden: 1. statische Festigkeit, 2. Ferrit- und Perlitanteil der Mikrostrukturen und 3. Kugelgraphitanzahl pro Flächeneinheit.
Basierend auf diesen Erkenntnissen wurde ein neues Festigkeitsverhältnisdiagramm (sogenanntes Sd/Rm-SG-Diagramm) entwickelt.
Diese neue Methodik sollte vor allem ermöglichen, die Bauteildauerfestigkeit auf der Grundlage der gemessenen oder durch eine Gießsimulation vorhersagten lokalen Zugfestigkeitswerte sowie Mikrogefügenstrukturen besser zu prognostizieren.
Mithilfe der Versuche sowie der Gießsimulation ist es gelungen, unterschiedliche Methoden der Lebensdauervorhersage unter Berücksichtigung der Herstellungsprozesse weiterzuentwickeln.
This thesis addresses an adaptive higher-order method based on a Geometry Independent Field approximatTion(GIFT) of polynomial/rationals plines over hierarchical T-meshes(PHT/RHT-splines).
In isogeometric analysis, basis functions used for constructing geometric models in computer-aided design(CAD) are also employed to discretize the partial differential equations(PDEs) for numerical analysis. Non-uniform rational B-Splines(NURBS) are the most commonly used basis functions in CAD. However, they may not be ideal for numerical analysis where local refinement is required.
The alternative method GIFT deploys different splines for geometry and numerical analysis. NURBS are utilized for the geometry representation, while for the field solution, PHT/RHT-splines are used. PHT-splines not only inherit the useful properties of B-splines and NURBS, but also possess the capabilities of local refinement and hierarchical structure. The smooth basis function properties of PHT-splines make them suitable for analysis purposes. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial problems have rough solutions. For example, this can be caused by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis (as in the case of NURBS) is less suitable for resolving the singularities that appear since refinement propagates throughout the computational domain. Hierarchical bases and local refinement (as in the case of PHT-splines) allow for a more efficient way to resolve these singularities by adding more degrees of freedom where they are necessary. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this thesis. The estimator produces a recovery solution which is a more accurate approximation than the computed numerical solution. Several two- and three-dimensional numerical investigations with PHT-splines of higher order and continuity prove that the proposed method is capable of obtaining results with higher accuracy, better convergence, fewer degrees of freedom and less computational cost than NURBS for smooth solution problems. The adaptive GIFT method utilizing PHT-splines with the recovery-based error estimator is used for solutions with discontinuities or singularities where adaptive local refinement in particular domains of interest achieves higher accuracy with fewer degrees of freedom. This method also proves that it can handle complicated multi-patch domains for two- and three-dimensional problems outperforming uniform refinement in terms of degrees of freedom and computational cost.
Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics.
An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries.
Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations.
The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels.
Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target
displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams.
Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed .
The gradual digitization in the architecture, engineering, and construction industry over the past fifty years led to an extremely heterogeneous software environment, which today is embodied by the multitude of different digital tools and proprietary data formats used by the many specialists contributing to the design process in a construction project. Though these projects become increasingly complex, the demands on financial efficiency and the completion within a tight schedule grow at the same time. The digital collaboration of project partners has been identified as one key issue in successfully dealing with these challenges. Yet currently, the numerous software applications and their respective individual views on the design process severely impede that collaboration.
An approach to establish a unified basis for the digital collaboration, regardless of the existing software heterogeneity, is a comprehensive digital building model contributed to by all projects partners. This type of data management known as building information modeling (BIM) has many benefits, yet its adoption is associated with many difficulties and thus, proceeds only slowly. One aspect in the field of conflicting requirements on such a digital model is the cooperation of architects and structural engineers. Traditionally, these two disciplines use different abstractions of reality for their models that in consequence lead to incompatible digital representations thereof.
The onset of isogeometric analysis (IGA) promised to ease the discrepancy in design and analysis model representations. Yet, that initial focus quickly shifted towards using these methods as a more powerful basis for numerical simulations. Furthermore, the isogeometric representation alone is not capable of solving the model abstraction problem. It is thus the intention of this work to contribute to an improved digital collaboration of architects and engineers by exploring an integrated analysis approach on the basis of an unified digital model and solid geometry expressed by splines. In the course of this work, an analysis framework is developed that utilizes such models to automatically conduct numerical simulations commonly required in construction projects. In essence, this allows to retrieve structural analysis results from BIM models in a fast and simple manner, thereby facilitating rapid design iterations and profound design feedback.
The BIM implementation Industry Foundation Classes (IFC) is reviewed with regard to its capabilities of representing the unified model. The current IFC schema strongly supports the use of redundant model data, a major pitfall in digital collaboration. Additionally, it does not allow to describe the geometry by volumetric splines. As the pursued approach builds upon a unique model for both, architectural and structural design, and furthermore requires solid geometry, necessary schema modifications are suggested.
Structural entities are modeled by volumetric NURBS patches, each of which constitutes an individual subdomain that, with regard to the analysis, is incompatible with the remaining full model. The resulting consequences for numerical simulation are elaborated in this work. The individual subdomains have to be weakly coupled, for which the mortar method is used. Different approaches to discretize the interface traction fields are implemented and their respective impact on the analysis results is evaluated. All necessary coupling conditions are automatically derived from the related geometry model.
The weak coupling procedure leads to a linear system of equations in saddle point form, which, owed to the volumetric modeling, is large in size and, the associated coefficient matrix has, due to the use of higher degree basis functions, a high bandwidth. The peculiarities of the system require adapted solution methods that generally cause higher numerical costs than the standard procedures for symmetric, positive-definite systems do. Different methods to solve the specific system are investigated and an efficient parallel algorithm is finally proposed.
When the structural analysis model is derived from the unified model in the BIM data, it does in general initially not meet the requirements on the discretization that are necessary to obtain sufficiently accurate analysis results. The consequently necessary patch refinements must be controlled automatically to allowfor an entirely automatic analysis procedure. For that purpose, an empirical refinement scheme based on the geometrical and possibly mechanical properties of the specific entities is proposed. The level of refinement may be selectively manipulated by the structural engineer in charge. Furthermore, a Zienkiewicz-Zhu type error estimator is adapted for the use with isogeometric analysis results. It is shown that also this estimator can be used to steer an adaptive refinement procedure.
Although it is impractical to avert subsequent natural disasters, advances in simulation science and seismological studies make it possible to lessen the catastrophic damage. There currently exists in many urban areas a large number of structures, which are prone to damage by earthquakes. These were constructed without the guidance of a national seismic code, either before it existed or before it was enforced. For instance, in Istanbul, Turkey, as a high seismic area, around 90% of buildings are substandard, which can be generalized into other earthquakeprone regions in Turkey. The reliability of this building stock resulting from earthquake-induced collapse is currently uncertain. Nonetheless, it is also not feasible to perform a detailed seismic vulnerability analysis on each building as a solution to the scenario, as it will be too complicated and expensive. This indicates the necessity of a reliable, rapid, and computationally easy method for seismic vulnerability assessment, commonly known as Rapid Visual Screening (RVS). In RVS methodology, an observational survey of buildings is performed, and according to the data collected during the visual inspection, a structural score is calculated without performing any structural calculations to determine the expected damage of a building and whether the building needs detailed assessment. Although this method might save time and resources due to the subjective/qualitative judgments of experts who performed the inspection, the evaluation process is dominated by vagueness and uncertainties, where the vagueness can be handled adequately through the fuzzy set theory but do not cover all sort of uncertainties due to its crisp membership functions. In this study, a novel method of rapid visual hazard safety assessment of buildings against earthquake is introduced in which an interval type-2 fuzzy logic system (IT2FLS) is used to cover uncertainties. In addition, the proposed method provides the possibility to evaluate the earthquake risk of the building by considering factors related to the building importance and exposure. A smartphone app prototype of the method has been introduced. For validation of the proposed method, two case studies have been selected, and the result of the analysis presents the robust efficiency of the proposed method.
The thesis investigates at the computer aided simulation process for operational vibration analysis of complex coupled systems. As part of the internal methods project “Absolute Values” of the BMW Group, the thesis deals with the analysis of the structural dynamic interactions and excitation interactions. The overarching aim of the methods project is to predict the operational vibrations of engines.
Simulations are usually used to analyze technical aspects (e. g. operational vibrations, strength, ...) of single components in the industrial development. The boundary conditions of submodels are mostly based on experiences. So the interactions with neighboring components and systems are neglected. To get physically more realistic results but still efficient simulations, this work wants to support the engineer during the preprocessing phase by useful criteria.
At first suitable abstraction levels based on the existing literature are defined to identify structural dynamic interactions and excitation interactions of coupled systems. So it is possible to separate different effects of the coupled subsystems. On this basis, criteria are derived to assess the influence of interactions between the considered systems. These criteria can be used during the preprocessing phase and help the engineer to build up efficient models with respect to the interactions with neighboring systems. The method was developed by using several models with different complexity levels. Furthermore, the method is proved for the application in the industrial environment by using the example of a current combustion engine.
Modern digital material approaches for the visualization and simulation of heterogeneous materials allow to investigate the behavior of complex multiphase materials with their physical nonlinear material response at various scales. However, these computational techniques require extensive hardware resources with respect to computing power and main memory to solve numerically large-scale discretized models in 3D. Due to a very high number of degrees of freedom, which may rapidly be increased to the two-digit million range, the limited hardware ressources are to be utilized in a most efficient way to enable an execution of the numerical algorithms in minimal computation time. Hence, in the field of computational mechanics, various methods and algorithms can lead to an optimized runtime behavior of nonlinear simulation models, where several approaches are proposed and investigated in this thesis.
Today, the numerical simulation of damage effects in heterogeneous materials is performed by the adaption of multiscale methods. A consistent modeling in the three-dimensional space with an appropriate discretization resolution on each scale (based on a hierarchical or concurrent multiscale model), however, still contains computational challenges in respect to the convergence behavior, the scale transition or the solver performance of the weak coupled problems. The computational efficiency and the distribution among available hardware resources (often based on a parallel hardware architecture) can significantly be improved. In the past years, high-performance computing (HPC) and graphics processing unit (GPU) based computation techniques were established for the investigationof scientific objectives. Their application results in the modification of existing and the development of new computational methods for the numerical implementation, which enables to take advantage of massively clustered computer hardware resources. In the field of numerical simulation in material science, e.g. within the investigation of damage effects in multiphase composites, the suitability of such models is often restricted by the number of degrees of freedom (d.o.f.s) in the three-dimensional spatial discretization. This proves to be difficult for the type of implementation method used for the nonlinear simulation procedure and, simultaneously has a great influence on memory demand and computational time.
In this thesis, a hybrid discretization technique has been developed for the three-dimensional discretization of a three-phase material, which is respecting the numerical efficiency of nonlinear (damage) simulations of these materials. The increase of the computational efficiency is enabled by the improved scalability of the numerical algorithms. Consequently, substructuring methods for partitioning the hybrid mesh were implemented, tested and adapted to the HPC computing framework using several hundred CPU (central processing units) nodes for building the finite element assembly. A memory-efficient iterative and parallelized equation solver combined with a special preconditioning technique for solving the underlying equation system was modified and adapted to enable combined CPU and GPU based computations.
Hence, it is recommended by the author to apply the substructuring method for hybrid meshes, which respects different material phases and their mechanical behavior and which enables to split the structure in elastic and inelastic parts. However, the consideration of the nonlinear material behavior, specified for the corresponding phase, is limited to the inelastic domains only, and by that causes a decreased computing time for the nonlinear procedure. Due to the high numerical effort for such simulations, an alternative approach for the nonlinear finite element analysis, based on the sequential linear analysis, was implemented in respect to scalable HPC. The incremental-iterative procedure in finite element analysis (FEA) during the nonlinear step was then replaced by a sequence of linear FE analysis when damage in critical regions occured, known in literature as saw-tooth approach. As a result, qualitative (smeared) crack initiation in 3D multiphase specimens has efficiently been simulated.
The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high-resolution analysis reaches the limits of today's computational power, in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid-based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid-based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid, which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program, called Mulgrido, was just developed to realize this concept consistently and to test the proposed methods. Several disadvantages which generally result from grid discretizations are selectively corrected by modified methods. The present work is structured into a geometrical model, a mechanical model and a numerical model. The geometrical model includes digital image-based modeling and in particular several methods for the theory-based generation of inclusion-matrix models. Essential contributions refer to variable shape, size distribution, separation checks and placement procedures of inclusions. The mechanical model prepares the fundamentals of continuum mechanics, homogenization and damage modeling for the following numerical methods. The first topic of the numerical model introduces to a special version of B-spline finite elements. These finite elements are entirely variable in the order k of B-splines. For homogeneous bodies this means that the approximation quality can arbitrarily be scaled. In addition, the multiphase finite element concept in combination with transition zones along material interfaces yields a valuable solution for heterogeneous bodies. As the formulation is element-based, the storage of a global stiffness matrix is superseded such that the memory demand can essentially be reduced. This is possible in combination with iterative solver methods which represent the second topic of the numerical model. Here, the focus lies on multigrid methods where the number of required operations to solve a linear equation system only increases linearly with problem size. Moreover, for badly conditioned problems quite an essential improvement is achieved by preconditioning. The third part of the numerical model discusses certain aspects of damage simulation which are closely related to the proposed grid discretization. The strong efficiency of the linear analysis can be maintained for damage simulation. This is achieved by a damage-controlled sequentially linear iteration scheme. Finally a study on the effective material behavior of heterogeneous bodies is presented. Especially the influence of inclusion shapes is examined. By means of altogether more than one hundred thousand random geometrical arrangements, the effective material behavior is statistically analyzed and assessed.
In recent years, substantial attention has been devoted to thermoelastic multifield problems and their numerical analysis. Thermoelasticity is one of the important categories of multifield problems which deals with the effect of mechanical and thermal disturbances on an elastic body. In other words, thermoelasticity encompasses the phenomena that describe the elastic and thermal behavior of solids and their interactions under thermo-mechanical loadings. Since providing an analytical solution for general coupled thermoelasticity problems is mathematically complicated, the development of alternative numerical solution techniques seems essential.
Due to the nature of numerical analysis methods, presence of error in results is inevitable, therefore in any numerical simulation, the main concern is the accuracy of the approximation. There are different error estimation (EE) methods to assess the overall quality of numerical approximation. In many real-life numerical simulations, not only the overall error, but also the local error or error in a particular quantity of interest is of main interest. The error estimation techniques which are developed to evaluate the error in the quantity of interest are known as “goal-oriented” error estimation (GOEE) methods.
This project, for the first time, investigates the classical a posteriori error estimation and goal-oriented a posteriori error estimation in 2D/3D thermoelasticity problems. Generally, the a posteriori error estimation techniques can be categorized into two major branches of recovery-based and residual-based error estimators. In this research, application of both recovery- and residual-based error estimators in thermoelasticity are studied. Moreover, in order to reduce the error in the quantity of interest efficiently and optimally in 2D and 3D thermoelastic problems, goal-oriented adaptive mesh refinement is performed.
As the first application category, the error estimation in classical Thermoelasticity (CTE) is investigated. In the first step, a rh-adaptive thermo-mechanical formulation based on goal-oriented error estimation is proposed.The developed goal-oriented error estimation relies on different stress recovery techniques, i.e., the superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR), and weighted superconvergent patch recovery (WSPR). Moreover, a new adaptive refinement strategy (ARS) is presented that minimizes the error in a quantity of interest and refines the discretization such that the error is equally distributed in the refined mesh. The method is validated by numerous numerical examples where an analytical solution or reference solution is available.
After investigating error estimation in classical thermoelasticity and evaluating the quality of presented error estimators, we extended the application of the developed goal-oriented error estimation and the associated adaptive refinement technique to the classical fully coupled dynamic thermoelasticity. In this part, we present an adaptive method for coupled dynamic thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark-_ method. In this part, the SPR, L2-PR, and WSPR recovery methods are exploited to estimate the error in the quantity of interest (QoI). By using
adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed in the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.
After studying the recovery-based error estimators, we investigated the residual-based error estimation in thermoelasticity. In the last part of this research, we present a 3D adaptive method for thermoelastic problems based on goal-oriented error estimation where the error is measured with respect to a pointwise quantity of interest. We developed a method for a posteriori error estimation and mesh adaptation based on dual weighted residual (DWR) method relying on the duality principles and consisting of an adjoint problem solution. Here, we consider the application of the derived estimator and mesh refinement to two-/three-dimensional (2D/3D) thermo-mechanical multifield problems. In this study, the goal is considered to be given by singular pointwise functions, such as the point value or point value derivative at a specific point of interest (PoI). An adaptive algorithm has been adopted to refine the mesh to minimize the goal in the quantity of interest.
The mesh adaptivity procedure based on the DWR method is performed by adaptive local h-refinement/coarsening with allowed hanging nodes. According to the proposed DWR method, the error contribution of each element is evaluated. In the refinement process, the contribution of each element to the goal error is considered as the mesh refinement criterion.
In this study, we substantiate the accuracy and performance of this method by several numerical examples with available analytical solutions. Here, 2D and 3D problems under thermo-mechanical loadings are considered as benchmark problems. To show how accurately the derived estimator captures the exact error in the evaluation of the pointwise quantity of interest, in all examples, considering the analytical solutions, the goal error effectivity index as a standard measure of the quality of an estimator is calculated. Moreover, in order to demonstrate the efficiency of the proposed method and show the optimal behavior of the employed refinement method, the results of different conventional error estimators and refinement techniques (e.g., global uniform refinement, Kelly, and weighted Kelly techniques) are used for comparison.
In the last two decades, Peridynamics (PD) attracts much attention in the field of fracture mechanics. One key feature of PD is the nonlocality, which is quite different from the ideas in conventional methods such as FEM and meshless method. However, conventional PD suffers from problems such as constant horizon, explicit algorithm, hourglass mode. In this thesis, by examining the nonlocality with scrutiny, we proposed several new concepts such as dual-horizon (DH) in PD, dual-support (DS) in smoothed particle hydrodynamics (SPH), nonlocal operators and operator energy functional. The conventional PD (SPH) is incorporated in the DH-PD (DS-SPH), which can adopt an inhomogeneous discretization and inhomogeneous support domains. The DH-PD (DS-SPH) can be viewed as some fundamental improvement on the conventional PD (SPH). Dual formulation of PD and SPH allows h-adaptivity while satisfying the conservations of linear momentum, angular momentum and energy. By developing the concept of nonlocality further, we introduced the nonlocal operator method as a generalization of DH-PD. Combined with energy functional of various physical models, the nonlocal forms based on dual-support concept are derived. In addition, the variation of the energy functional allows implicit formulation of the nonlocal theory. At last, we developed the higher order nonlocal operator method which is capable of solving higher order partial differential equations on arbitrary domain in higher dimensional space. Since the concepts are developed gradually, we described our findings chronologically.
In chapter 2, we developed a DH-PD formulation that includes varying horizon sizes and solves the "ghost force" issue. The concept of dual-horizon considers the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly with arbitrary particle discretization. All three peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based peridynamics can be implemented within the DH-PD framework. A simple adaptive refinement procedure (h-adaptivity) is proposed reducing the computational cost. Both two- and three- dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method.
In chapter 3, a nonlocal operator method (NOM) based on the variational principle is proposed for the solution of waveguide problem in computational electromagnetic field. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease, which is necessary for the eigenvalue analysis of the waveguide problem. The present formulation is applied to solve 1D Schrodinger equation, 2D electrostatic problem and the differential electromagnetic vector wave equations based on electric fields.
In chapter 4, a general nonlocal operator method is proposed which is applicable for solving partial differential equations (PDEs) of mechanical problems. The nonlocal operator can be regarded as the integral form, ``equivalent'' to the differential form in the sense of a nonlocal interaction model. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method. Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. A highlight of the present method is the functional derived based on the nonlocal operator can convert the construction of residual and stiffness matrix into a series of matrix multiplications using the predefined nonlocal operators. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support. Several numerical examples of different types of PDEs are presented.
In chapter 5, we extended the NOM to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original NOM in chapter 3 and chapter 4, which can only achieve one-order convergence. The higher order NOM obtains all partial derivatives with specified maximal order simultaneously without resorting to shape functions. The functional based on the nonlocal operators converts the construction of residual and stiffness matrix into a series of matrix multiplication on the nonlocal operator matrix. Several numerical examples solved by strong form or weak form are presented to show the capabilities of this method.
In chapter 6, the NOM proposed as a particle-based method in chapter 3,4,5, has difficulty in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with interpolation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed a special case of NOM with interpolation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method, as a consequence, the operator energy functional in particle-based NOM is not required. We demonstrated the capabilities of current method by solving the gradient solid problems and comparing the numerical results with the available exact solutions.
In chapter 7, we derived the DS-SPH in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We proposed an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is {involved} in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method.
The aim of this study is controlling of spurious oscillations developing around discontinuous solutions of both linear and non-linear wave equations or hyperbolic partial differential equations (PDEs). The equations include both first-order and second-order (wave) hyperbolic systems. In these systems even smooth initial conditions, or smoothly varying source (load) terms could lead to discontinuous propagating solutions (fronts). For the first order hyperbolic PDEs, the concept of central high resolution schemes is integrated with the multiresolution-based adaptation to capture properly both discontinuous propagating fronts and effects of fine-scale responses on those of larger scales in the multiscale manner. This integration leads to using central high resolution schemes on non-uniform grids; however, such simulation is unstable, as the central schemes are originally developed to work properly on uniform cells/grids. Hence, the main concern is stable collaboration of central schemes and multiresoltion-based cell adapters. Regarding central schemes, the considered approaches are: 1) Second order central and central-upwind schemes; 2) Third order central schemes; 3) Third and fourth order central weighted non-oscillatory schemes (central-WENO or CWENO); 4) Piece-wise parabolic methods (PPMs) obtained with two different local stencils. For these methods, corresponding (nonlinear) stability conditions are studied and modified, as well. Based on these stability conditions several limiters are modified/developed as follows: 1) Several second-order limiters with total variation diminishing (TVD) feature, 2) Second-order uniformly high order accurate non-oscillatory (UNO) limiters, 3) Two third-order nonlinear scaling limiters, 4) Two new limiters for PPMs. Numerical results show that adaptive solvers lead to cost-effective computations (e.g., in some 1-D problems, number of adapted grid points are less than 200 points during simulations, while in the uniform-grid case, to have the same accuracy, using of 2049 points is essential). Also, in some cases, it is confirmed that fine scale responses have considerable effects on higher scales.
In numerical simulation of nonlinear first order hyperbolic systems, the two main concerns are: convergence and uniqueness. The former is important due to developing of the spurious oscillations, the numerical dispersion and the numerical dissipation. Convergence in a numerical solution does not guarantee that it is the physical/real one (the uniqueness feature). Indeed, a nonlinear systems can converge to several numerical results (which mathematically all of them are true). In this work, the convergence and uniqueness are directly studied on non-uniform grids/cells by the concepts of local numerical truncation error and numerical entropy production, respectively. Also, both of these concepts have been used for cell/grid adaptations. So, the performance of these concepts is also compared by the multiresolution-based method. Several 1-D and 2-D numerical examples are examined to confirm the efficiency of the adaptive solver. Examples involve problems with convex and non-convex fluxes. In the latter case, due to developing of complex waves, proper capturing of real answers needs more attention. For this purpose, using of method-adaptation seems to be essential (in parallel to the cell/grid adaptation). This new type of adaptation is also performed in the framework of the multiresolution analysis.
Regarding second order hyperbolic PDEs (mechanical waves), the regularization concept is used to cure artificial (numerical) oscillation effects, especially for high-gradient or discontinuous solutions. There, oscillations are removed by the regularization concept acting as a post-processor. Simulations will be performed directly on the second-order form of wave equations. It should be mentioned that it is possible to rewrite second order wave equations as a system of first-order waves, and then simulated the new system by high resolution schemes. However, this approach ends to increasing of variable numbers (especially for 3D problems).
The numerical discretization is performed by the compact finite difference (FD) formulation with desire feature; e.g., methods with spectral-like or optimized-error properties. These FD methods are developed to handle high frequency waves (such as waves near earthquake sources). The performance of several regularization approaches is studied (both theoretically and numerically); at last, a proper regularization approach controlling the Gibbs phenomenon is recommended.
At the end, some numerical results are provided to confirm efficiency of numerical solvers enhanced by the regularization concept. In this part, shock-like responses due to local and abrupt changing of physical properties, and also stress wave propagation in stochastic-like domains are studied.
Isogeometric analysis (IGA) is a numerical method for solving partial differential equations (PDEs), which was introduced with the aim of integrating finite element analysis with computer-aided design systems. The main idea of the method is to use the same spline basis functions which describe the geometry in CAD systems for the approximation of solution fields in the finite element method (FEM). Originally, NURBS which is a standard technology employed in CAD systems was adopted as basis functions in IGA but there were several variants of IGA using other technologies such as T-splines, PHT splines, and subdivision surfaces as basis functions. In general, IGA offers two key advantages over classical FEM: (i) by describing the CAD geometry exactly using smooth, high-order spline functions, the mesh generation process is simplified and the interoperability between CAD and FEM is improved, (ii) IGA can be viewed as a high-order finite element method which offers basis functions with high inter-element continuity and therefore can provide a primal variational formulation of high-order PDEs in a straightforward fashion. The main goal of this thesis is to further advance isogeometric analysis by exploiting these major advantages, namely precise geometric modeling and the use of smooth high-order splines as basis functions, and develop robust computational methods for problems with complex geometry and/or complex multi-physics.
As the first contribution of this thesis, we leverage the precise geometric modeling of isogeometric analysis and propose a new method for its coupling with meshfree discretizations. We exploit the strengths of both methods by using IGA to provide a smooth, geometrically-exact surface discretization of the problem domain boundary, while the Reproducing Kernel Particle Method (RKPM) discretization is used to provide the volumetric discretization of the domain interior. The coupling strategy is based upon the higher-order consistency or reproducing conditions that are directly imposed in the physical domain. The resulting coupled method enjoys several favorable features: (i) it preserves the geometric exactness of IGA, (ii) it circumvents the need for global volumetric parameterization of the problem domain, (iii) it achieves arbitrary-order approximation accuracy while preserving higher-order smoothness of the discretization. Several numerical examples are solved to show the optimal convergence properties of the coupled IGA–RKPM formulation, and to demonstrate its effectiveness in constructing volumetric discretizations for complex-geometry objects.
As for the next contribution, we exploit the use of smooth, high-order spline basis functions in IGA to solve high-order surface PDEs governing the morphological evolution of vesicles. These governing equations are often consisted of geometric PDEs, high-order PDEs on stationary or evolving surfaces, or a combination of them. We propose an isogeometric formulation for solving these PDEs. In the context of geometric PDEs, we consider phase-field approximations of mean curvature flow and Willmore flow problems and numerically study the convergence behavior of isogeometric analysis for these problems. As a model problem for high-order PDEs on stationary surfaces, we consider the Cahn–Hilliard equation on a sphere, where the surface is modeled using a phase-field approach. As for the high-order PDEs on evolving surfaces, a phase-field model of a deforming multi-component vesicle, which consists of two fourth-order nonlinear PDEs, is solved using the isogeometric analysis in a primal variational framework. Through several numerical examples in 2D, 3D and axisymmetric 3D settings, we show the robustness of IGA for solving the considered phase-field models.
Finally, we present a monolithic, implicit formulation based on isogeometric analysis and generalized-alpha time integration for simulating hydrodynamics of vesicles according to a phase-field model. Compared to earlier works, the number of equations of the phase-field model which need to be solved is reduced by leveraging high continuity of NURBS functions, and the algorithm is extended to 3D settings. We use residual-based variational multi-scale method (RBVMS) for solving Navier–Stokes equations, while the rest of PDEs in the phase-field model are treated using a standard Galerkin-based IGA. We introduce the resistive immersed surface (RIS) method into the formulation which can be employed for an implicit description of complex geometries using a diffuse-interface approach. The implementation highlights the robustness of the RBVMS method for Navier–Stokes equations of incompressible flows with non-trivial localized forcing terms including bending and tension forces of the vesicle. The potential of the phase-field model and isogeometric analysis for accurate simulation of a variety of fluid-vesicle interaction problems in 2D and 3D is demonstrated.
This dissertation is devoted to the theoretical development and experimental laboratory verification of a new damage localization method: The state projection estimation error (SP2E). This method is based on the subspace identification of mechanical structures, Krein space based H-infinity estimation and oblique projections. To explain method SP2E, several theories are discussed and laboratory experiments have been conducted and analysed.
A fundamental approach of structural dynamics is outlined first by explaining mechanical systems based on first principles. Following that, a fundamentally different approach, subspace identification, is comprehensively explained. While both theories, first principle and subspace identification based mechanical systems, may be seen as widespread methods, barely known and new techniques follow up. Therefore, the indefinite quadratic estimation theory is explained. Based on a Popov function approach, this leads to the Krein space based H-infinity theory. Subsequently, a new method for damage identification, namely SP2E, is proposed. Here, the introduction of a difference process, the analysis by its average process power and the application of oblique projections is discussed in depth.
Finally, the new method is verified in laboratory experiments. Therefore, the identification of a laboratory structure at Leipzig University of Applied Sciences is elaborated. Then structural alterations are experimentally applied, which were localized by SP2E afterwards. In the end four experimental sensitivity studies are shown and discussed. For each measurement series the structural alteration was increased, which was successfully tracked by SP2E. The experimental results are plausible and in accordance with the developed theories. By repeating these experiments, the applicability of SP2E for damage localization is experimentally proven.
Identification of flaws in structures is a critical element in the management of maintenance and quality assurance processes in engineering. Nondestructive testing (NDT) techniques based on a wide range of physical principles have been developed and are used in common practice for structural health monitoring. However, basic NDT techniques are usually limited in their ability to provide the accurate information on locations, dimensions and shapes of flaws. One alternative to extract additional information from the results of NDT is to append it with a computational model that provides detailed analysis of the physical process involved and enables the accurate identification of the flaw parameters. The aim here is to develop the strategies to uniquely identify cracks in two-dimensional 2D) structures under dynamic loadings.
A local NDT technique combined eXtended Finite Element Method (XFEM) with dynamic loading in order to identify the cracks in the structures quickly and accurately is developed in this dissertation. The Newmark-b time integration method with Rayleigh damping is used for the time integration. We apply Nelder-Mead (NM)and Quasi-Newton (QN) methods for identifying the crack tip in plate. The inverse problem is solved iteratively, in which XFEM is used for solving the forward problem in each iteration. For a timeharmonic excitation with a single frequency and a short-duration signal measured along part of the external boundary, the crack is detected through the solution of an inverse time-dependent problem. Compared to the static load, we show that the dynamic loads are more effective for crack detection problems. Moreover, we tested different dynamic loads and find that NM method works more efficient under the harmonic load than the pounding load while the QN method achieves almost the same results for both load types.
A global strategy, Multilevel Coordinate Search (MCS) with XFEM (XFEM-MCS) methodology under the dynamic electric load, to detect multiple cracks in 2D piezoelectric plates is proposed in this dissertation. The Newmark-b method is employed for the time integration and in each iteration the forward problem is solved by XFEM for various cracks. The objective functional is minimized by using a global search algorithm MCS. The test problems show that the XFEM-MCS algorithm under the dynamic electric load can be effectively employed for multiple cracks detection in piezoelectric materials, and it proves to be robust in identifying defects in piezoelectric structures. Fiber-reinforced composites (FRCs) are extensively applied in practical engineering since they have high stiffness and strength. Experiments reveal a so-called interphase zone, i.e. the space between the outside interface of the fiber and the inside interface of the matrix. The interphase strength between the fiber and the matrix strongly affects the mechanical properties as a result of the large ratio of interface/volume. For the purpose of understanding the mechanical properties of FRCs with functionally graded interphase (FGI), a closed-form expression of the interface strength between a fiber and a matrix is obtained in this dissertation using a continuum modeling approach according to the ver derWaals (vdW) forces. Based on the interatomic potential, we develop a new modified nonlinear cohesive law, which is applied to study the interface delamination of FRCs with FGI under different loadings. The analytical solutions show that the delamination behavior strongly depends on the interphase thickness, the fiber radius, the Young’s moduli and Poisson’s ratios of the fiber and the matrix. Thermal conductivity is the property of a material to conduct heat. With the development and deep research of 2D materials, especially graphene and molybdenum disulfide (MoS2), the thermal conductivity of 2D materials attracts wide attentions. The thermal conductivity of graphene nanoribbons (GNRs) is found to appear a tendency of decreasing under tensile strain by classical molecular dynamics (MD) simulations. Hence, the strain effects of graphene can play a key role in the continuous tunability and applicability of its thermal conductivity property at nanoscale, and the dissipation of thermal conductivity is an obstacle for the applications of thermal management. Up to now, the thermal conductivity of graphene under shear deformation has not been investigated yet. From a practical point of view, good thermal managements of GNRs have significantly potential applications of future GNR-based thermal nanodevices, which can greatly improve performances of the nanosized devices due to heat dissipations. Meanwhile, graphene is a thin membrane structure, it is also important to understand the wrinkling behavior under shear deformation. MoS2 exists in the stable semiconducting 1H phase (1H-MoS2) while the metallic 1T phase (1T-MoS2) is unstable at ambient conditions. As it’s well known that much attention has been focused on studying the nonlinear optical properties of the 1H-MoS2. In a very recent research, the 1T-type monolayer crystals of TMDCs, MX2 (MoS2, WS2 ...) was reported having an intrinsic in-plane negative Poisson’s ratio. Luckily, nearly at the same time, unprecedented long-term (>3months) air stability of the 1T-MoS2 can be achieved by using the donor lithium hydride (LiH). Therefore, it’s very important to study the thermal conductivity of 1T-MoS2.
The thermal conductivity of graphene under shear strain is systematically studied in this dissertation by MD simulations. The results show that, in contrast to the dramatic decrease of thermal conductivity of graphene under uniaxial tensile, the thermal conductivity of graphene is not sensitive to the shear strain, and the thermal conductivity decreases only 12-16%. The wrinkle evolves when the shear strain is around 5%-10%, but the thermal conductivity barely changes.
The thermal conductivities of single-layer 1H-MoS2(1H-SLMoS2) and single-layer 1T-MoS2 (1T-SLMoS2) with different sample sizes, temperatures and strain rates have been studied systematically in this dissertation. We find that the thermal conductivities of 1H-SLMoS2 and 1T-SLMoS2 in both the armchair and the zigzag directions increase with the increasing of the sample length, while the increase of the width of the sample has minor effect on the thermal conductions of these two structures. The thermal conductivity of 1HSLMoS2 is smaller than that of 1T-SLMoS2 under size effect. Furthermore, the temperature effect results show that the thermal conductivities of both 1H-SLMoS2 and 1T-SLMoS2 decrease with the increasing of the temperature. The thermal conductivities of 1HSLMoS2 and 1T-SLMoS2 are nearly the same (difference <6%) in both of the chiral orientations under corresponding temperatures, especially in the armchair direction (difference <2.8%). Moreover, we find that the strain effects on the thermal conductivity of 1HSLMoS2 and 1T-SLMoS2 are different. More specifically, the thermal conductivity decreases with the increasing tensile strain rate for
1T-SLMoS2, while fluctuates with the growth of the strain for 1HSLMoS2. Finally, we find that the thermal conductivity of same sized 1H-SLMoS2 is similar with that of the strained 1H-SLMoS2 structure.
In recent years increasingly consideration has been given to the lifetime extension of existing structures. This is based on the fact that a growing percentage of civil infrastructure as well as buildings is threatened by obsolescence and that due to simple monetary reasons this can no longer be countered by simply re-building everything anew. Hence maintenance interventions are required which allow partial or complete structural rehabilitation. However, maintenance interventions have to be economically reasonable, that is, maintenance expenditures have to be outweighed by expected future benefits. Is this not the case, then indeed the structure is obsolete - at least in its current functional, economic, technical, or social configuration - and innovative alternatives have to be evaluated. An optimization formulation for planning maintenance interventions based on cost-benefit criteria is proposed herein. The underlying formulation is as follows: (a) between maintenance interventions structural deterioration is described as a random process; (b) maintenance interventions can take place anytime throughout lifetime and comprise the rehabilitation of all deterioration states above a certain minimum level; and (c) maintenance interventions are optimized by taking into account all expected life-cycle costs (construction, failure, inspection and state-dependent repair costs) as well as state- or time-dependent benefit rates. The optimization is performed by an evolutionary algorithm. The proposed approach also allows to determine optimal lifetimes and acceptable failure rates. Numerical examples demonstrate the importance of defining benefit rates explicitly. It is shown, that the optimal solution to maintenance interventions requires to take action before reaching the acceptable failure rate or the zero expected net benefit rate level. Deferring decisions with respect to maintenance not only results, in general, in higher losses, but also results in overly hazardous structures.