@phdthesis{Winkel,
  author    = {Winkel, Benjamin},
  title     = {A three-dimensional model of skeletal muscle for physiological, pathological and experimental mechanical simulations},
  doi       = {10.25643/bauhaus-universitaet.4300},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20201211-43002},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {In recent decades, a multitude of concepts and models were developed to understand, assess and predict muscular mechanics in the context of physiological and pathological events. Most of these models are highly specialized and designed to selectively address fields in, e.g., medicine, sports science, forensics, product design or CGI; their data are often not transferable to other ranges of application. A single universal model, which covers the details of biochemical and neural processes, as well as the development of internal and external force and motion patterns and appearance could not be practical with regard to the diversity of the questions to be investigated and the task to find answers efficiently. With reasonable limitations though, a generalized approach is feasible. The objective of the work at hand was to develop a model for muscle simulation which covers the phenomenological aspects, and thus is universally applicable in domains where up until now specialized models were utilized. This includes investigations on active and passive motion, structural interaction of muscles within the body and with external elements, for example in crash scenarios, but also research topics like the verification of in vivo experiments and parameter identification. For this purpose, elements for the simulation of incompressible deformations were studied, adapted and implemented into the finite element code SLang. Various anisotropic, visco-elastic muscle models were developed or enhanced. The applicability was demonstrated on the base of several examples, and a general base for the implementation of further material models was developed and elaborated.},
  subject      = {Biomechanik},
  language  = {en}
}
@phdthesis{Schrader,
  author    = {Schrader, Kai},
  title     = {Hybrid 3D simulation methods for the damage analysis of multiphase composites},
  doi       = {10.25643/bauhaus-universitaet.2059},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20131021-20595},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {174},
  abstract  = {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.},
  subject      = {high-performance computing},
  language  = {en}
}
@phdthesis{NguyenThanh,
  author    = {Nguyen-Thanh, Nhon},
  title     = {Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis},
  issn      = {1610-7381},
  doi       = {10.25643/bauhaus-universitaet.2078},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20131125-20781},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {196},
  abstract  = {This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements. The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results.},
  subject      = {Isogeometric analysis},
  language  = {en}
}
@misc{Kessel2005,
  type      = {Master Thesis},
  author    = {Kessel, Marco},
  title     = {Implementierung rechteckiger Scheibenelemente mit B-Spline Ans{\"a}tzen n-ter Ordnung},
  doi       = {10.25643/bauhaus-universitaet.682},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6822},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2005},
  abstract  = {Diese Arbeit stellt die Implementierung von Scheibenelementen mit B-Spline Ans{\"a}tzen n-ter Ordnung speziell f{\"u}r rechteckige Gebiete mit orthogonaler Vernetzung vor. Dabei kam insbesondere eine spezielle elementbasierte Formulierung auf Grundlage der einzelnen B-Spline Segmente zum Einsatz, die zur Aufbringung von Randbedingungen an den R{\"a}ndern modifizierte B-Splines benutzt. In der Folge entstehen verschiedene Elementtypen zur Diskretisierung von rechteckigen Gebieten, deren Erzeugung, Speicherung und Anwendung im Zusammenhang mit der Finiten Elemente Methode Gegenstand der Arbeit sind. Anhand von untersuchten Beispielen werden die erfolgreiche Implementierung nachgewiesen und verschiedene Eigenschaften der Methode herausgestellt.},
  subject      = {B-Splines},
  language  = {de}
}
@misc{Arnold2005,
  type      = {Master Thesis},
  author    = {Arnold, Daniel},
  title     = {Implementierung eines vierknotigen Schalenelementes f{\"u}r geometrisch und physikalisch nichtlineare Berechnungen in das Programmsystem SLang},
  doi       = {10.25643/bauhaus-universitaet.731},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-7315},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2005},
  abstract  = {Die Finite-Elemente-Methode entwickelte sich in den letzten beiden Jahrzehnten zu einem wichtigen und m{\"a}chtigen Werkzeug f{\"u}r Berechnungen im Ingenieurwesen. Waren zu Beginn dieser Entwicklung nur kleine Probleme l{\"o}sbar, sind mit der heutigen Rechentechnik Systeme mit vielen Tausend Freiheitsgraden berechenbar. Durch diese Entwicklung werden Berechnungen von sehr komplizierten Strukturen m{\"o}glich. Besonders in der Automobilindustrie kann mit einem solchen Verfahren die Konstruktion von Strukturen verbessert und optimiert werden. Um gute Ergebnisse bei den Berechnungen erzielen zu k{\"o}nnen m{\"u}ssen Programme entwickelt werden, die entsprechende mathematische Methoden enthalten. Besonders im Maschinenbau, aber auch in anderen Ingenieurbereichen wie dem Bauwesen, werden h{\"a}ufig gekr{\"u}mmte d{\"u}nne Schalenstrukturen untersucht. Eine effiziente und logische Konsequenz daraus ist die Nutzung von Schalenelementen innerhalb der FE-Berechnungen. Wird nun noch Wert auf eine realit{\"a}tsnahe Modellierung gelegt, dann l{\"a}sst es sich oft nicht vermeiden von der im Bauwesen {\"u}blichen Theorie erster Ordnung in eine nichtlineare Berechnungstheorie zu wechseln. Hierf{\"u}r sind Methoden notwendig, die es verm{\"o}gen diese Theorie abzubilden. Sollen Schalenstrukturen mit großen Verschiebungen betrachtet werden, ist es notwendig, die linearen Elementformulierungen um die nichtlinearen Ans{\"a}tze der Strukturmechanik zu erweitern. Die Grundlage dieser Formulierung stellt oft die Lagrange'sche Betrachtungsweise dar, die Berechnungen an Strukturen mit großen Verformungen zul{\"a}sst. Die Inhalte dieser Formulierung werden in Abschnitt 1.5 dieser Arbeit betrachtet. R{\"a}umlich ver{\"a}nderlichen Strukturen, also solche mit großen Verformungen, sind im Allgemeinen mit großen Rotationen verkn{\"u}pft. Diese Rotationen werden bei Volumenelementen durch die unterschiedliche Verschiebung zweier benachbarter Elementknoten realisiert. Bei der Formulierung von d{\"u}nnen Schalenelementen wird hingegen die Struktur als gekr{\"u}mmte Raumfl{\"a}che betrachtet. Da in Dickenrichtung nur ein Elementknoten zur Verf{\"u}gung steht, muss die Rotation {\"u}ber eine andere Formulierung in die Berechnung einfließen. Ans{\"a}tze zu allgemeinen großen Rotationen werden im Kapitel 2 betrachtet und f{\"u}r den Einsatz in einer Elementformulierung vorbereitet. F{\"u}r die beschriebenen Schalenstrukturen werden h{\"a}ufig vierknotige Elemente genutzt, da mit ihnen Strukturen in einfacher Weise abgebildet werden k{\"o}nnen. Ein weiterer Vorteil besteht in der sich ergebenden geringen Bandbreite der Elementmatrizen. Diese Elementgruppe besitzt jedoch bei der klassischen isoparametrischen Formulierung einen großen Nachteil, der in der Erzeugung von parasit{\"a}ren Steifigkeitsanteilen besteht. Um dieses Sperrverhalten, was auch als 'Locking' bekannt ist, zu minimieren wurden in der Vergangenheit verschiedene Ans{\"a}tze entwickelt. Ein sehr effizienter Ansatz zur Minimierung des Transversalschublockings bei bilinearen Schalenelementen stellt das Verfahren der ver{\"a}nderten Verzerrungsverl{\"a}ufe auf Elementebene dar. Dieses Verfahren wird vielfach in der Literatur aufgegriffen und als 'Assumed-Natural-Strain'-Ansatz oder als 'Mixed Interpolation of Tensorial Components' bezeichnet. Dieses Verfahren wird im Abschnitt 1.6 vorgestellt. Das Programmsystem SLang erm{\"o}glicht eine Berechnung von Strukturen mittels der Finite-Elemente-Methode. Um mit diesem Programm auch nichtlineare Probleme an Schalentragwerken berechnen zu k{\"o}nnen, wird im Rahmen dieser Diplomarbeit ein vierknotiges nichtlineares Schalenelement implementiert, das die genannten Ans{\"a}tze f{\"u}r große Verformungen und finite Rotationen enth{\"a}lt. F{\"u}r die Vermeidung von Transversalschublocking wird ein ANS-Ansatz in die Formulierung integriert. Das Kapitel 3 beschreibt die Formulierung dieses SHELL4N-Elementes. Dort werden die Elementmatrizen und deren Aufbau ausf{\"u}hrlich dargestellt. Einige numerische Berechnungsbeispiele mit diesem neuen Element werden zur Evaluierung im Kapitel 4 dieser Arbeit dargestellt.},
  subject      = {Schalenelement},
  language  = {de}
}