TY - THES A1 - Kessel, Marco T1 - Implementierung rechteckiger Scheibenelemente mit B-Spline Ansätzen n-ter Ordnung N2 - Diese Arbeit stellt die Implementierung von Scheibenelementen mit B-Spline Ansätzen n-ter Ordnung speziell für 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 Rändern 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. KW - B-Splines KW - FEM KW - Finite Elemente KW - Scheibenelemente KW - Implementierung Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-6822 N1 - Der Volltext-Zugang wurde im Zusammenhang mit der Klärung urheberrechtlicher Fragen mit sofortiger Wirkung gesperrt. ER - TY - THES A1 - Nguyen-Thanh, Nhon T1 - Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis N2 - 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. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2013,4 KW - Isogeometric analysis KW - NURBS KW - FEM KW - RHT-splines KW - Isogeometric analysis KW - NURBS KW - FEM KW - RHT-splines Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20131125-20781 SN - 1610-7381 ER -