@article{NguyenThanhRabczukNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Rabczuk, Timon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain}, title = {An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes}, series = {Journal of Computational and Applied Mathematics}, journal = {Journal of Computational and Applied Mathematics}, pages = {2112 -- 2135}, abstract = {An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenXuanRabczukNguyenThanhetal., author = {Nguyen-Xuan, Hung and Rabczuk, Timon and Nguyen-Thanh, Nhon and Nguyen-Thoi, T. and Bordas, St{\´e}phane Pierre Alain}, title = {A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates}, series = {Computational Mechanics}, journal = {Computational Mechanics}, pages = {679 -- 701}, abstract = {A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhThaiHoangNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Thai-Hoang, C. and Nguyen-Xuan, Hung and Rabczuk, Timon}, title = {A smoothed finite element method for the static and free vibration analysis of shells}, series = {Journal of Civil Engineering and Architecture}, journal = {Journal of Civil Engineering and Architecture}, pages = {13 -- 25}, abstract = {A smoothed finite element method for the static and free vibration analysis of shells}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhKiendlNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Kiendl, J. and Nguyen-Xuan, Hung and W{\"u}chner, R. and Bletzinger, Kai-Uwe and Bazilevs, Yuri and Rabczuk, Timon}, title = {Rotation free isogeometric thin shell analysis using PHT-splines}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {3410 -- 3424}, abstract = {Rotation free isogeometric thin shell analysis using PHT-splines}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhRabczukNguyenXuanetal., author = {Nguyen-Thanh, Nhon and Rabczuk, Timon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain}, title = {An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates}, series = {Finite Elements in Analysis \& Design}, journal = {Finite Elements in Analysis \& Design}, pages = {519 -- 535}, abstract = {An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThanhNguyenXuanBordasetal., author = {Nguyen-Thanh, Nhon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {1892 -- 1908}, abstract = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenVinhBakarMsekhetal., author = {Nguyen-Vinh, H. and Bakar, I. and Msekh, Mohammed Abdulrazzak and Song, Jeong-Hoon and Muthu, Jacob and Zi, Goangseup and Le, P. and Bordas, St{\´e}phane Pierre Alain and Simpson, R. and Natarajan, S. and Lahmer, Tom and Rabczuk, Timon}, title = {Extended Finite Element Method for Dynamic Fracture of Piezo-Electric Materials}, series = {Engineering Fracture Mechanics}, journal = {Engineering Fracture Mechanics}, doi = {10.1016/j.engfracmech.2012.04.025}, pages = {19 -- 31}, abstract = {We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukDiasdaCostaetal., author = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D. and Piresh, E.B.}, title = {Implicit solutions with consistent additive and multiplicative components}, series = {Finite Elements in Analysis and Design}, journal = {Finite Elements in Analysis and Design}, doi = {10.1016/j.finel.2012.03.007}, pages = {15 -- 31}, abstract = {This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangWangRabczuk, author = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon}, title = {Acoustic and breathing phonon modes in bilayer graphene with Moire-acute patterns}, series = {Applied Physics Letters}, journal = {Applied Physics Letters}, doi = {10.1063/1.4735246}, abstract = {The lattice dynamics properties are investigated for twisting bilayer graphene. There are big jumps for the inter-layer potential at twisting angle θ=0° and 60°, implying the stability of Bernal-stacking and the instability of AA-stacking structures, while a long platform in [8,55]° indicates the ease of twisting bilayer graphene in this wide angle range. Significant frequency shifts are observed for the z breathing mode around θ=0° and 60°, while the frequency is a constant in a wide range [8,55]°. Using the z breathing mode, a mechanical nanoresonator is proposed to operate on a robust resonant frequency in terahertz range.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangZhaoZhouetal., author = {Jiang, Jin-Wu and Zhao, Jun-Hua and Zhou, K. and Rabczuk, Timon}, title = {Superior thermal conductivity and extremely high mechanical strength in polyethylene chains from ab initio calculation}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, doi = {10.1063/1.4729489}, abstract = {The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the ab initio calculation and applying the quantum mechanical non-equilibrium Green's function approach. Specially, there are two main findings from our calculation: (1) the thermal conductivity can reach a high value of 310 Wm-1 K-1 in a 100 nm polyethylene chain at room temperature and the thermal conductivity increases with the length of the chain; (2) the Young's modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain 32.85\%±0.05\% (ultimate) strain before undergoing structural phase transition into gaseous ethylene.}, subject = {Angewandte Mathematik}, language = {en} }