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 -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Kiendl, J.
A1 - Nguyen-Xuan, Hung
A1 - Wüchner, R.
A1 - Bletzinger, Kai-Uwe
A1 - Bazilevs, Yuri
A1 - Rabczuk, Timon
T1 - Rotation free isogeometric thin shell analysis using PHT-splines
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Rotation free isogeometric thin shell analysis using PHT-splines
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 3410
EP - 3424
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Muthu, Jacob
A1 - Zhuang, Xiaoying
A1 - Rabczuk, Timon
T1 - An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics
JF - Computational Mechanics
N2 - An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
SP - 369
EP - 385
ER -
TY - JOUR
A1 - Chen, Lei
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Xuan, Hung
A1 - Rabczuk, Timon
A1 - Bordas, Stéphane Pierre Alain
A1 - Limbert, Georges
T1 - Explicit finite deformation analysis of isogeometric membranes
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Explicit finite deformation analysis of isogeometric membranes
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
SP - 104
EP - 130
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
T1 - An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates
JF - Finite Elements in Analysis & Design
N2 - An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 519
EP - 535
ER -
TY - JOUR
A1 - Nguyen-Xuan, Hung
A1 - Rabczuk, Timon
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Thoi, T.
A1 - Bordas, Stéphane Pierre Alain
T1 - A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates
JF - Computational Mechanics
N2 - A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
SP - 679
EP - 701
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
T1 - An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes
JF - Journal of Computational and Applied Mathematics
N2 - An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2009
SP - 2112
EP - 2135
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
A1 - Rabczuk, Timon
T1 - Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 1892
EP - 1908
ER -
TY - JOUR
A1 - Thai, Chien H.
A1 - Nguyen-Xuan, Hung
A1 - Bordas, Stéphane Pierre Alain
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
T1 - Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory
JF - Mechanics of Advanced Materials and Structures
N2 - Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 451
EP - 469
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Thai-Hoang, C.
A1 - Nguyen-Xuan, Hung
A1 - Rabczuk, Timon
T1 - A smoothed finite element method for the static and free vibration analysis of shells
JF - Journal of Civil Engineering and Architecture
N2 - A smoothed finite element method for the static and free vibration analysis of shells
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
SP - 13
EP - 25
ER -
TY - CHAP
A1 - Nguyen-Thanh, Nhon
A1 - Rabczuk, Timon
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - A SMOOTHED FINITE ELEMENT METHOD FOR THE STATIC AND FREE VIBRATION ANALYSIS OF SHELLS
N2 - A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28777
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -
TY - JOUR
A1 - Thai, Chien H.
A1 - Nguyen-Xuan, Hung
A1 - Nguyen-Thanh, Nhon
A1 - Le, T.H.
A1 - Nguyen-Thoi, T.
A1 - Rabczuk, Timon
T1 - Static, free vibration and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach
JF - International Journal for Numerical Methods in Engineering
N2 - This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2012
U6 - http://dx.doi.org/10.1002/nme.4282
SP - 571
EP - 603
ER -
TY - JOUR
A1 - Nguyen-Xuan, Hung
A1 - Rabczuk, Timon
A1 - Nguyen-Thoi, T.
A1 - Tran, T.
A1 - Nguyen-Thanh, Nhon
T1 - Computation of limit and shakedown loads using a node-based smoothed finite element method
JF - International Journal for Numerical Methods in Engineering
N2 - This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2012
U6 - http://dx.doi.org/10.1002/nme.3317
SP - 287
EP - 310
ER -
TY - JOUR
A1 - Nguyen-Thanh, Nhon
A1 - Valizadeh, Navid
A1 - Nguyen, Manh Hung
A1 - Nguyen-Xuan, Hung
A1 - Zhuang, Xiaoying
A1 - Areias, Pedro
A1 - Zi, Goangseup
A1 - Bazilevs, Yuri
A1 - De Lorenzis, Laura
A1 - Rabczuk, Timon
T1 - An extended isogeometric thin shell analysis based on Kirchhoff-Love theory
JF - Computer Methods in Applied Mechanics and Engineering
N2 - An extended isogeometric thin shell analysis based on Kirchho_-Love theory
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2015
SP - 265
EP - 291
ER -