@misc{CicekCancino,
  type      = {Master Thesis},
  author    = {Cicek, Burhan and Cancino, Pamela},
  title     = {K{\"u}reken 2013. Entwerfen eines Dorfes aus Lehm},
  doi       = {10.25643/bauhaus-universitaet.6356},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20240507-63568},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {107},
  abstract  = {Die Diskussionen in der Politik und in der Gesellschaft {\"u}ber Klimawandel, globale Erw{\"a}rmung oder Nachhaltigkeit, die schon noch l{\"a}nger anh{\"a}lt, werden nie ein Ende finden, solange die Probleme, auf denen sie basiert, unl{\"o}sbar bleiben. Vorgeschlagene L{\"o}sungen werden meist nicht richtig umgesetzt. Im Zusammenhang mit dieser Problematik steigt aber das Verantwortungsgef{\"u}hl f{\"u}r bessere Zukunftsstrategien immer mehr. Die in den letzten Jahren vorgekommenen Umweltkatastrophen, wie im Golf von Mexiko (April 2010) oder im Fukushima (M{\"a}rz 2011) die noch aktuell sind, zeigen, dass der Prim{\"a}renergieeinsatz oder die Transportproblematik nicht mehr nur die Sorge der Entwicklungsl{\"a}nder, sondern auch der Industriel{\"a}nder ist. Die Bauwelt mit ihrem erheblichen Energiebedarf spielt bei der Festlegung der Zukunftsstrategien eine große Rolle. Vor allem sind die Forschungen nach umweltfreundlichen Materialien, der Recyclebarkeit der eingesetzten Baumaterialien oder dem vern{\"u}nftigen Nutzen der Naturressourcen die wichtigsten Schwerpunkte. In dieser Hinsicht bringt Lehm als Baumaterial viele Vorteile mit sich. Bei einem Artikel sagt der Lehmbauexperte Martin Rauch: "In heutiger Zeit und einem Kulturkreis, in dem Baugrund und Arbeitszeit unsere großen Kosten verursachen, findet der tradierte Lehmbau mit dem verbundenen großen Aufwand an menschlicher Arbeitszeit nur schwer seinen Platz. {\"U}ber die Art der Bauweise wird auch die Entscheidung gef{\"a}llt, wie und wo die Wertsch{\"o}pfung erfolgt und ob der Einsatz des Budgets einen gesellschaftlichen Nutzen mit sich bringt. Im Vergleich zu einem Sichtbetonhaus k{\"o}nnen bei einem Stampflehmhaus 40\% der Prim{\"a}renergie ein gespart und daf{\"u}r mehr lokale Arbeitsressourcen gebunden werden. Davon profitieren vor allem die lokalen Handwerker und mittelst{\"a}ndischen Betriebe" Anatolien ist der Ort, wo man immer noch die tiefsten Wurzeln der Baukultur menschlicher Geschichte findet. Diese Baukultur, die in den vergangenen Jahrzehnten fast verlorengegangen ist, ist die Lehmbaukultur. In dieser Hinsicht beabsichtigt dieser Entwurf die W{\"u}rde des Lehms in Anatolien wieder herzustellen und dadurch dessen Glaubw{\"u}rdigkeit zur{\"u}ckzubringen.},
  subject      = {Lehm},
  language  = {de}
}
@misc{Piethe,
  type      = {Master Thesis},
  author    = {Piethe, Vivienne},
  title     = {Konfektionierung eines Calciumsulfat-Bindemittelsystems zur Herstellung volumenstabiler Fließestrichm{\"o}rtel},
  doi       = {10.25643/bauhaus-universitaet.3944},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190902-39445},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {107},
  abstract  = {Bei einem markt{\"u}blichen Calciumsulfat-Fließestrich wurden in der Praxis sch{\"a}digende Volu-menexpansionen festgestellt. Diese sind ein Resultat aus dem Zusammenwirken des einge-setzten Bindemittel-Compounds und einer kritischen Gesteinsk{\"o}rnung. Das Ziel dieser Arbeit ist es, ein Calciumsulfat-Bindemittelsystem zu konfektionieren, welches in der Lage ist, die im M{\"o}rtel festgestellten Volumenexpansionen zu unterbinden. Es sollen verschiedene Bindemittel- und Additivzusammensetzungen untersucht werden, welche in Verbindung mit der kritischen Gesteinsk{\"o}rnung die Herstellung eines volumenstabilen Fließestrichs erm{\"o}glichen. Dazu soll folgende Fragestellung beantwortet werden: Welche Ursachen hat die Volumenzunahme und wie ist diese zu minimieren bzw. unterbinden? Dabei werden unterschiedliche Bindemittelrezepturen aus α-Halbhydrat, Thermoanhydrit und Naturanhydrit, sowie verschiedene Additivzusammensetzungen hergestellt und untersucht. Durch L{\"a}ngen{\"a}nderungsmessungen in der Schwindrinne werden die Einfl{\"u}sse der Binde-mittel, der Additivzusammensetzungen und der Wasser/Bindemittel-Werte auf das L{\"a}n-gen{\"a}nderungsverhalten untersucht. Mittels Variation der einzelnen Compound-Bestandteile kann festgestellt werden, dass der Stabilisierer die L{\"a}ngen{\"a}nderung negativ beeinflusst. Dieser bindet freies Wasser, welches f{\"u}r eine Reaktion zwischen Bindemittel und Gesteins-k{\"o}rnung im plastischen Zustand nicht mehr zur Verf{\"u}gung steht. Diese Reaktion kann folglich erst im erh{\"a}rteten Zustand ablaufen und verursacht die sch{\"a}digende Volumenexpansion. Abschließend wurde ein Bindemittel-Compound konfektioniert, welcher ohne Zusatz von Stabilisierern in Zusammenhang mit der kritischen Gesteinsk{\"o}rnung volumenstabil ist und keine Sch{\"a}den ausl{\"o}st.},
  subject      = {Calciumsulfat},
  language  = {de}
}
@unpublished{RadmardRahmaniKoenke,
  author    = {Radmard Rahmani, Hamid and K{\"o}nke, Carsten},
  title     = {Passive Control of Tall Buildings Using Distributed Multiple Tuned Mass Dampers},
  doi       = {10.25643/bauhaus-universitaet.3859},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190311-38597},
  pages     = {43},
  abstract  = {The vibration control of the tall building during earthquake excitations is a challenging task due to their complex seismic behavior. This paper investigates the optimum placement and properties of the Tuned Mass Dampers (TMDs) in tall buildings, which are employed to control the vibrations during earthquakes. An algorithm was developed to spend a limited mass either in a single TMD or in multiple TMDs and distribute them optimally over the height of the building. The Non-dominated Sorting Genetic Algorithm (NSGA - II) method was improved by adding multi-variant genetic operators and utilized to simultaneously study the optimum design parameters of the TMDs and the optimum placement. The results showed that under earthquake excitations with noticeable amplitude in higher modes, distributing TMDs over the height of the building is more effective in mitigating the vibrations compared to the use of a single TMD system. From the optimization, it was observed that the locations of the TMDs were related to the stories corresponding to the maximum modal displacements in the lower modes and the stories corresponding to the maximum modal displacements in the modes which were highly activated by the earthquake excitations. It was also noted that the frequency content of the earthquake has significant influence on the optimum location of the TMDs.},
  subject      = {Schwingungsd{\"a}mpfer},
  language  = {en}
}
@phdthesis{Zhang,
  author    = {Zhang, Yongzheng},
  title     = {A Nonlocal Operator Method for Quasi-static and Dynamic Fracture Modeling},
  doi       = {10.25643/bauhaus-universitaet.4732},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221026-47321},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Material failure can be tackled by so-called nonlocal models, which introduce an intrinsic length scale into the formulation and, in the case of material failure, restore the well-posedness of the underlying boundary value problem or initial boundary value problem. Among nonlocal models, peridynamics (PD) has attracted a lot of attention as it allows the natural transition from continuum to discontinue and thus allows modeling of discrete cracks without the need to describe and track the crack topology, which has been a major obstacle in traditional discrete crack approaches. This is achieved by replacing the divergence of the Cauchy stress tensor through an integral over so-called bond forces, which account for the interaction of particles. A quasi-continuum approach is then used to calibrate the material parameters of the bond forces, i.e., equating the PD energy with the energy of a continuum. One major issue for the application of PD to general complex problems is that they are limited to fairly simple material behavior and pure mechanical problems based on explicit time integration. PD has been extended to other applications but losing simultaneously its simplicity and ease in modeling material failure. Furthermore, conventional PD suffers from instability and hourglass modes that require stabilization. It also requires the use of constant horizon sizes, which drastically reduces its computational efficiency. The latter issue was resolved by the so-called dual-horizon peridynamics (DH-PD) formulation and the introduction of the duality of horizons. Within the nonlocal operator method (NOM), the concept of nonlocality is further extended and can be considered a generalization of DH-PD. Combined with the energy functionals of various physical models, the nonlocal forms based on the dual-support concept can be derived. In addition, the variation of the energy functional allows implicit formulations of the nonlocal theory. While traditional integral equations are formulated in an integral domain, the dual-support approaches are based on dual integral domains. One prominent feature of NOM is its compatibility with variational and weighted residual methods. The NOM yields a direct numerical implementation based on the weighted residual method for many physical problems without the need for shape functions. Only the definition of the energy or boundary value problem is needed to drastically facilitate the implementation. The nonlocal operator plays an equivalent role to the derivatives of the shape functions in meshless methods and finite element methods (FEM). Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease by a series of matrix multiplications. In addition, NOM can be used to derive many nonlocal models in strong form. The principal contributions of this dissertation are the implementation and application of NOM, and also the development of approaches for dealing with fractures within the NOM, mostly for dynamic fractures. The primary coverage and results of the dissertation are as follows: -The first/higher-order implicit NOM and explicit NOM, including a detailed description of the implementation, are presented. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combining with the method of weighted residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. For the sake of conciseness, the implementation in this chapter is focused on linear elastic solids only, though the NOM can handle more complex nonlinear problems. An explicit nonlocal operator method for the dynamic analysis of elasticity solid problems is also presented. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The explicit scheme comprises the Verlet-velocity algorithm. The NOM can be very flexible and efficient for solving partial differential equations (PDEs). It's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Several numerical examples are presented to show the capabilities of this method. -A nonlocal operator method for the dynamic analysis of (thin) Kirchhoff plates is proposed. The nonlocal Hessian operator is derived from a second-order Taylor series expansion. NOM is higher-order continuous, which is exploited for thin plate analysis that requires \$C^1\$ continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation. -A nonlocal fracture modeling is developed and applied to the simulation of quasi-static and dynamic fractures using the NOM. The phase field's nonlocal weak and associated strong forms are derived from a variational principle. The NOM requires only the definition of energy. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems, while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.},
  subject      = {Variationsprinzip},
  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{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{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}
}
@phdthesis{Valizadeh,
  author    = {Valizadeh, Navid},
  title     = {Developments in Isogeometric Analysis and Application to High-Order Phase-Field Models of Biomembranes},
  doi       = {10.25643/bauhaus-universitaet.4565},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220114-45658},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {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.},
  subject      = {Phasenfeldmodell},
  language  = {en}
}
@phdthesis{ShaabanMohamed,
  author    = {Shaaban Mohamed, Ahmed Mostafa},
  title     = {Isogeometric boundary element analysis and structural shape optimization for Helmholtz acoustic problems},
  doi       = {10.25643/bauhaus-universitaet.4703},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220816-47030},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {In this thesis, a new approach is developed for applications of shape optimization on the time harmonic wave propagation (Helmholtz equation) for acoustic problems. This approach is introduced for different dimensional problems: 2D, 3D axi-symmetric and fully 3D problems. The boundary element method (BEM) is coupled with the isogeometric analysis (IGA) forming the so-called (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. BEM is superior for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM) since BEM solutions satisfy the Sommerfeld radiation condition automatically. Moreover, BEM reduces the space dimension by one from a volumetric three-dimensional problem to a surface two-dimensional problem, or from a surface two-dimensional problem to a perimeter one-dimensional problem. Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields. IGABEM is coupled with one of the gradient-free optimization methods, the Particle Swarm Optimization (PSO) for structural shape optimization problems. PSO is a straightforward method since it does not require any sensitivity analysis but it has some trade-offs with regard to the computational cost. Coupling IGA with optimization problems enables the NURBS basis functions to represent the three models: shape design, analysis and optimization models, by a definition of a set of control points to be the control variables and the optimization parameters as well which enables an easy transition between the three models. Acoustic shape optimization for various frequencies in different mediums is performed with PSO and the results are compared with the benchmark solutions from the literature for different dimensional problems proving the efficiency of the proposed approach with the following remarks: - In 2D problems, two BEM methods are used: the conventional isogeometric boundary element method (IGABEM) and the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves, where the results are generally in good agreement with the linterature with some computation advantage to XIBEM which allows coarser meshes. -In 3D axi-symmetric problems, the three-dimensional problem is simplified in BEM from a surface integral to a combination of two 1D integrals. The first is the line integral similar to a two-dimensional BEM problem. The second integral is performed over the angle of revolution. The discretization is applied only to the former integration. This leads to significant computational savings and, consequently, better treatment for higher frequencies over the full three-dimensional models. - In fully 3D problems, a detailed comparison between two BEM methods: the conventional boundary integral equation (CBIE) and Burton-Miller (BM) is provided including the computational cost. The proposed models are enhanced with a modified collocation scheme with offsets to Greville abscissae to avoid placing collocation points at the corners. Placing collocation points on smooth surface enables accurate evaluation of normals for BM formulation in addition to straightforward prediction of jump-terms and avoids singularities in \$\mathcal{O} (1/r)\$ integrals eliminating the need for polar integration. Furthermore, no additional special treatment is required for the hyper-singular integral while collocating on highly distorted elements, such as those containing sphere poles. The obtained results indicate that, CBIE with PSO is a feasible alternative (except for a small number of fictitious frequencies) which is easier to implement. Furthermore, BM presents an outstanding treatment of the complicated geometry of mufflers with internal extended inlet/outlet tube as an interior 3D Helmholtz acoustic problem instead of using mixed or dual BEM.},
  subject      = {Randelemente-Methode},
  language  = {en}
}