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Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis

  • 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 anThis 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.show moreshow less

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Metadaten
Document Type:Doctoral Thesis
Author:Dr.-Ing. Nhon Nguyen-Thanh
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2078Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20131125-20781Cite-Link
ISSN:1610-7381
Series (Serial Number):ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar (2013,4)
Referee:Prof.Dr.-Ing. Stéphane Pierre Alain Bordas, Prof. Dr. rer. nat. habil. Klaus GürlebeckGND
Advisor:Prof.Dr.-Ing. Timon RabczukORCiDGND
Language:English
Date of Publication (online):2013/11/25
Date of first Publication:2013/11/25
Date of final exam:2013/09/30
Release Date:2013/11/25
Publishing Institution:Bauhaus-Universität Weimar
Granting Institution:Bauhaus-Universität Weimar, Fakultät Bauingenieurwesen
Institutes:Fakultät Bauingenieurwesen / Professur Baustatik und Bauteilfestigkeit
Pagenumber:196
Tag:FEM; Isogeometric analysis; NURBS; RHT-splines
GND Keyword:Isogeometric analysis; NURBS; FEM; RHT-splines
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften
BKL-Classification:31 Mathematik
50 Technik allgemein
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)