@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}
}
@inproceedings{HaefnerKesselKoenke,
  author    = {H{\"a}fner, Stefan and Kessel, Marco and K{\"o}nke, Carsten},
  title     = {MULTIPHASE B-SPLINE FINITE ELEMENTS OF VARIABLE ORDER IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2964},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29643},
  pages     = {37},
  abstract  = {Advanced finite elements are proposed for the mechanical analysis of heterogeneous materials. The approximation quality of these finite elements can be controlled by a variable order of B-spline shape functions. An element-based formulation is developed such that the finite element problem can iteratively be solved without storing a global stiffness matrix. This memory saving allows for an essential increase of problem size. The heterogeneous material is modelled by projection onto a uniform, orthogonal grid of elements. Conventional, strictly grid-based finite element models show severe oscillating defects in the stress solutions at material interfaces. This problem is cured by the extension to multiphase finite elements. This concept enables to define a heterogeneous material distribution within the finite element. This is possible by a variable number of integration points to each of which individual material properties can be assigned. Based on an interpolation of material properties at nodes and further smooth interpolation within the finite elements, a continuous material function is established. With both, continuous B-spline shape function and continuous material function, also the stress solution will be continuous in the domain. The inaccuracy implied by the continuous material field is by far less defective than the prior oscillating behaviour of stresses. One- and two-dimensional numerical examples are presented.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}