@phdthesis{Hanna,
  author    = {Hanna, John},
  title     = {Computational Fracture Modeling and Design of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique},
  doi       = {10.25643/bauhaus-universitaet.4746},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221124-47467},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {125},
  abstract  = {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.},
  subject      = {Beton},
  language  = {en}
}
@phdthesis{Zacharias,
  author    = {Zacharias, Christin},
  title     = {Numerical Simulation Models for Thermoelastic Damping Effects},
  doi       = {10.25643/bauhaus-universitaet.4735},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221116-47352},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {191},
  abstract  = {Finite Element Simulations of dynamically excited structures are mainly influenced by the mass, stiffness, and damping properties of the system, as well as external loads. The prediction quality of dynamic simulations of vibration-sensitive components depends significantly on the use of appropriate damping models. Damping phenomena have a decisive influence on the vibration amplitude and the frequencies of the vibrating structure. However, developing realistic damping models is challenging due to the multiple sources that cause energy dissipation, such as material damping, different types of friction, or various interactions with the environment. This thesis focuses on thermoelastic damping, which is the main cause of material damping in homogeneous materials. The effect is caused by temperature changes due to mechanical strains. In vibrating structures, temperature gradients arise in adjacent tension and compression areas. Depending on the vibration frequency, they result in heat flows, leading to increased entropy and the irreversible transformation of mechanical energy into thermal energy. The central objective of this thesis is the development of efficient simulation methods to incorporate thermoelastic damping in finite element analyses based on modal superposition. The thermoelastic loss factor is derived from the structure's mechanical mode shapes and eigenfrequencies. In subsequent analyses that are performed in the time and frequency domain, it is applied as modal damping. Two approaches are developed to determine the thermoelastic loss in thin-walled plate structures, as well as three-dimensional solid structures. The realistic representation of the dissipation effects is verified by comparing the simulation results with experimentally determined data. Therefore, an experimental setup is developed to measure material damping, excluding other sources of energy dissipation. The three-dimensional solid approach is based on the determination of the generated entropy and therefore the generated heat per vibration cycle, which is a measure for thermoelastic loss in relation to the total strain energy. For thin plate structures, the amount of bending energy in a modal deformation is calculated and summarized in the so-called Modal Bending Factor (MBF). The highest amount of thermoelastic loss occurs in the state of pure bending. Therefore, the MBF enables a quantitative classification of the mode shapes concerning the thermoelastic damping potential. The results of the developed simulations are in good agreement with the experimental results and are appropriate to predict thermoelastic loss factors. Both approaches are based on modal superposition with the advantage of a high computational efficiency. Overall, the modeling of thermoelastic damping represents an important component in a comprehensive damping model, which is necessary to perform realistic simulations of vibration processes.},
  subject      = {Werkstoffd{\"a}mpfung},
  language  = {en}
}
@phdthesis{LopezZermeno,
  author    = {L{\´o}pez Zerme{\~n}o, Jorge Alberto},
  title     = {Isogeometric and CAD-based methods for shape and topology optimization: Sensitivity analysis, B{\´e}zier elements and phase-field approaches},
  doi       = {10.25643/bauhaus-universitaet.4710},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220831-47102},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The Finite Element Method (FEM) is widely used in engineering for solving Partial Differential Equations (PDEs) over complex geometries. To this end, it is required to provide the FEM software with a geometric model that is typically constructed in a Computer-Aided Design (CAD) software. However, FEM and CAD use different approaches for the mathematical description of the geometry. Thus, it is required to generate a mesh, which is suitable for FEM, based on the CAD model. Nonetheless, this procedure is not a trivial task and it can be time consuming. This issue becomes more significant for solving shape and topology optimization problems, which consist in evolving the geometry iteratively. Therefore, the computational cost associated to the mesh generation process is increased exponentially for this type of applications. The main goal of this work is to investigate the integration of CAD and CAE in shape and topology optimization. To this end, numerical tools that close the gap between design and analysis are presented. The specific objectives of this work are listed below: • Automatize the sensitivity analysis in an isogeometric framework for applications in shape optimization. Applications for linear elasticity are considered. • A methodology is developed for providing a direct link between the CAD model and the analysis mesh. In consequence, the sensitivity analysis can be performed in terms of the design variables located in the design model. • The last objective is to develop an isogeometric method for shape and topological optimization. This method should take advantage of using Non-Uniform Rational B-Splines (NURBS) with higher continuity as basis functions. Isogeometric Analysis (IGA) is a framework designed to integrate the design and analysis in engineering problems. The fundamental idea of IGA is to use the same basis functions for modeling the geometry, usually NURBS, for the approximation of the solution fields. The advantage of integrating design and analysis is two-fold. First, the analysis stage is more accurate since the system of PDEs is not solved using an approximated geometry, but the exact CAD model. Moreover, providing a direct link between the design and analysis discretizations makes possible the implementation of efficient sensitivity analysis methods. Second, the computational time is significantly reduced because the mesh generation process can be avoided. Sensitivity analysis is essential for solving optimization problems when gradient-based optimization algorithms are employed. Automatic differentiation can compute exact gradients, automatically by tracking the algebraic operations performed on the design variables. For the automation of the sensitivity analysis, an isogeometric framework is used. Here, the analysis mesh is obtained after carrying out successive refinements, while retaining the coarse geometry for the domain design. An automatic differentiation (AD) toolbox is used to perform the sensitivity analysis. The AD toolbox takes the code for computing the objective and constraint functions as input. Then, using a source code transformation approach, it outputs a code for computing the objective and constraint functions, and their sensitivities as well. The sensitivities obtained from the sensitivity propagation method are compared with analytical sensitivities, which are computed using a full isogeometric approach. The computational efficiency of AD is comparable to that of analytical sensitivities. However, the memory requirements are larger for AD. Therefore, AD is preferable if the memory requirements are satisfied. Automatic sensitivity analysis demonstrates its practicality since it simplifies the work of engineers and designers. Complex geometries with sharp edges and/or holes cannot easily be described with NURBS. One solution is the use of unstructured meshes. Simplex-elements (triangles and tetrahedra for two and three dimensions respectively) are particularly useful since they can automatically parameterize a wide variety of domains. In this regard, unstructured B{\´e}zier elements, commonly used in CAD, can be employed for the exact modelling of CAD boundary representations. In two dimensions, the domain enclosed by NURBS curves is parameterized with B{\´e}zier triangles. To describe exactly the boundary of a two-dimensional CAD model, the continuity of a NURBS boundary representation is reduced to C^0. Then, the control points are used to generate a triangulation such that the boundary of the domain is identical to the initial CAD boundary representation. Thus, a direct link between the design and analysis discretizations is provided and the sensitivities can be propagated to the design domain. In three dimensions, the initial CAD boundary representation is given as a collection of NURBS surfaces that enclose a volume. Using a mesh generator (Gmsh), a tetrahedral mesh is obtained. The original surface is reconstructed by modifying the location of the control points of the tetrahedral mesh using B{\´e}zier tetrahedral elements and a point inversion algorithm. This method offers the possibility of computing the sensitivity analysis using the analysis mesh. Then, the sensitivities can be propagated into the design discretization. To reuse the mesh originally generated, a moving B{\´e}zier tetrahedral mesh approach was implemented. A gradient-based optimization algorithm is employed together with a sensitivity propagation procedure for the shape optimization cases. The proposed shape optimization approaches are used to solve some standard benchmark problems in structural mechanics. The results obtained show that the proposed approach can compute accurate gradients and evolve the geometry towards optimal solutions. In three dimensions, the moving mesh approach results in faster convergence in terms of computational time and avoids remeshing at each optimization step. For considering topological changes in a CAD-based framework, an isogeometric phase-field based shape and topology optimization is developed. In this case, the diffuse interface of a phase-field variable over a design domain implicitly describes the boundaries of the geometry. The design variables are the local values of the phase-field variable. The descent direction to minimize the objective function is found by using the sensitivities of the objective function with respect to the design variables. The evolution of the phase-field is determined by solving the time dependent Allen-Cahn equation. Especially for topology optimization problems that require C^1 continuity, such as for flexoelectric structures, the isogeometric phase field method is of great advantage. NURBS can achieve the desired continuity more efficiently than the traditional employed functions. The robustness of the method is demonstrated when applied to different geometries, boundary conditions, and material configurations. The applications illustrate that compared to piezoelectricity, the electrical performance of flexoelectric microbeams is larger under bending. In contrast, the electrical power for a structure under compression becomes larger with piezoelectricity.},
  subject      = {CAD},
  language  = {en}
}
@phdthesis{Habtemariam,
  author    = {Habtemariam, Abinet Kifle},
  title     = {Generalized Beam Theory for the analysis of thin-walled circular pipe members},
  doi       = {10.25643/bauhaus-universitaet.4572},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220127-45723},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {188},
  abstract  = {The detailed structural analysis of thin-walled circular pipe members often requires the use of a shell or solid-based finite element method. Although these methods provide a very good approximation of the deformations, they require a higher degree of discretization which causes high computational costs. On the other hand, the analysis of thin-walled circular pipe members based on classical beam theories is easy to implement and needs much less computation time, however, they are limited in their ability to approximate the deformations as they cannot consider the deformation of the cross-section. This dissertation focuses on the study of the Generalized Beam Theory (GBT) which is both accurate and efficient in analyzing thin-walled members. This theory is based on the separation of variables in which the displacement field is expressed as a combination of predetermined deformation modes related to the cross-section, and unknown amplitude functions defined on the beam's longitudinal axis. Although the GBT was initially developed for long straight members, through the consideration of complementary deformation modes, which amend the null transverse and shear membrane strain assumptions of the classical GBT, problems involving short members, pipe bends, and geometrical nonlinearity can also be analyzed using GBT. In this dissertation, the GBT formulation for the analysis of these problems is developed and the application and capabilities of the method are illustrated using several numerical examples. Furthermore, the displacement and stress field results of these examples are verified using an equivalent refined shell-based finite element model. The developed static and dynamic GBT formulations for curved thin-walled circular pipes are based on the linear kinematic description of the curved shell theory. In these formulations, the complex problem in pipe bends due to the strong coupling effect of the longitudinal bending, warping and the cross-sectional ovalization is handled precisely through the derivation of the coupling tensors between the considered GBT deformation modes. Similarly, the geometrically nonlinear GBT analysis is formulated for thin-walled circular pipes based on the nonlinear membrane kinematic equations. Here, the initial linear and quadratic stress and displacement tangent stiffness matrices are built using the third and fourth-order GBT deformation mode coupling tensors. Longitudinally, the formulation of the coupled GBT element stiffness and mass matrices are presented using a beam-based finite element formulation. Furthermore, the formulated GBT elements are tested for shear and membrane locking problems and the limitations of the formulations regarding the membrane locking problem are discussed.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@article{KrausCrişanWittor,
  author    = {Kraus, Matthias and Cri{\c{s}}an, Nicolae-Andrei and Wittor, Bj{\"o}rn},
  title     = {Stability Study of Cantilever-Beams - Numerical Analysis and Analytical Calculation (LTB)},
  series = {ce/papers},
  volume    = {2021},
  journal   = {ce/papers},
  number    = {Volume 4, issue 2-4},
  publisher = {Ernst \& Sohn, a Wiley brand},
  address   = {Berlin},
  doi       = {10.1002/cepa.1539},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220112-45637},
  pages     = {2199 -- 2206},
  abstract  = {According to Eurocode, the computation of bending strength for steel cantilever beams is a straightforward process. The approach is based on an Ayrton-Perry formula adaptation of buckling curves for steel members in compression, which involves the computation of an elastic critical buckling load for considering the instability. NCCI documents offer a simplified formula to determine the critical bending moment for cantilevers beams with symmetric cross-section. Besides the NCCI recommendations, other approaches, e.g. research literature or Finite-Element-Analysis, may be employed to determine critical buckling loads. However, in certain cases they render different results. Present paper summarizes and compares the abovementioned analytical and numerical approaches for determining critical loads and it exemplarily analyses corresponding cantilever beam capacities using numerical approaches based on plastic zones theory (GMNIA).},
  subject      = {Tr{\"a}ger},
  language  = {en}
}
@article{IbanezKraus,
  author    = {Ibanez, Stalin and Kraus, Matthias},
  title     = {A Numerical Approach for Plastic Cross Cross-Sectional Analyses of Steel Members},
  series = {ce/papers},
  volume    = {2021},
  journal   = {ce/papers},
  number    = {Volume 4, issue 2-4},
  publisher = {Ernst \& Sohn, a Wiley brand},
  address   = {Berlin},
  doi       = {10.1002/cepa.1527},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220112-45622},
  pages     = {2098 -- 2106},
  abstract  = {Global structural analyses in civil engineering are usually performed considering linear-elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three-dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time-consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one-dimensional) combined with cross-sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed.},
  subject      = {Stahlkonstruktion},
  language  = {en}
}
@article{LegatiukWeiszPatrault,
  author    = {Legatiuk, Dmitrii and Weisz-Patrault, Daniel},
  title     = {Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann-Hilbert Problem},
  series = {Computational Methods and Function Theory},
  volume    = {2021},
  journal   = {Computational Methods and Function Theory},
  publisher = {Springer},
  address   = {Heidelberg},
  doi       = {10.1007/s40315-021-00403-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210805-44763},
  pages     = {1 -- 23},
  abstract  = {In this paper we present a theoretical background for a coupled analytical-numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical-numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann-Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ReichertOlneyLahmer,
  author    = {Reichert, Ina and Olney, Peter and Lahmer, Tom},
  title     = {Combined approach for optimal sensor placement and experimental verification in the context of tower-like structures},
  series = {Journal of Civil Structural Health Monitoring},
  volume    = {2021},
  journal   = {Journal of Civil Structural Health Monitoring},
  number    = {volume 11},
  publisher = {Heidelberg},
  address   = {Springer},
  doi       = {10.1007/s13349-020-00448-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44701},
  pages     = {223 -- 234},
  abstract  = {When it comes to monitoring of huge structures, main issues are limited time, high costs and how to deal with the big amount of data. In order to reduce and manage them, respectively, methods from the field of optimal design of experiments are useful and supportive. Having optimal experimental designs at hand before conducting any measurements is leading to a highly informative measurement concept, where the sensor positions are optimized according to minimal errors in the structures' models. For the reduction of computational time a combined approach using Fisher Information Matrix and mean-squared error in a two-step procedure is proposed under the consideration of different error types. The error descriptions contain random/aleatoric and systematic/epistemic portions. Applying this combined approach on a finite element model using artificial acceleration time measurement data with artificially added errors leads to the optimized sensor positions. These findings are compared to results from laboratory experiments on the modeled structure, which is a tower-like structure represented by a hollow pipe as the cantilever beam. Conclusively, the combined approach is leading to a sound experimental design that leads to a good estimate of the structure's behavior and model parameters without the need of preliminary measurements for model updating.},
  subject      = {Strukturmechanik},
  language  = {en}
}
@misc{Habtemariam,
  type      = {Master Thesis},
  author    = {Habtemariam, Abinet Kifle},
  title     = {Numerical Demolition Analysis of a Slender Guyed Antenna Mast},
  doi       = {10.25643/bauhaus-universitaet.4460},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210723-44609},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {75},
  abstract  = {The main purpose of the thesis is to ensure the safe demolition of old guyed antenna masts that are located in different parts of Germany. The major problem in demolition of this masts is the falling down of the masts in unexpected direction because of buckling problem. The objective of this thesis is development of a numerical models using finite element method (FEM) and assuring a controlled collapse by coming up with different time setups for the detonation of explosives which are responsible for cutting down the cables. The result of this thesis will avoid unexpected outcomes during the demolition processes and prevent risk of collapsing of the mast over near by structures.},
  subject      = {Abbruch},
  language  = {en}
}
@phdthesis{Hossain,
  author    = {Hossain, Md Naim},
  title     = {Isogeometric analysis based on Geometry Independent Field approximaTion (GIFT) and Polynomial Splines over Hierarchical T-meshes},
  doi       = {10.25643/bauhaus-universitaet.4037},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20191129-40376},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {157},
  abstract  = {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.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}