@article{JiangWangRabczuk, author = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon}, title = {Why twisting angles are diverse in graphene Moir'e patterns?}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, abstract = {Why twisting angles are diverse in graphene Moir'e patterns?}, subject = {Angewandte Mathematik}, language = {en} } @article{IlyaniAkmarLahmerBordasetal., author = {Ilyani Akmar, A.B. and Lahmer, Tom and Bordas, St{\´e}phane Pierre Alain and Beex, L.A.A. and Rabczuk, Timon}, title = {Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties}, series = {Composite Structures}, journal = {Composite Structures}, doi = {10.1016/j.compstruct.2014.04.014}, pages = {1 -- 17}, abstract = {Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacRafieeZhuangetal., author = {Vu-Bac, N. and Rafiee, Roham and Zhuang, Xiaoying and Lahmer, Tom and Rabczuk, Timon}, title = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters}, series = {Composites Part B: Engineering}, journal = {Composites Part B: Engineering}, pages = {446 -- 464}, abstract = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiRafieeZhuangetal., author = {Ghasemi, Hamid and Rafiee, Roham and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {295 -- 305}, abstract = {Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling}, subject = {Angewandte Mathematik}, language = {en} } @article{NanthakumarLahmerZhuangetal., author = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Park, Harold S. and Rabczuk, Timon}, title = {Topology optimization of piezoelectric nanostructures}, series = {Journal of the Mechanics and Physics of Solids}, journal = {Journal of the Mechanics and Physics of Solids}, pages = {316 -- 335}, abstract = {Topology optimization of piezoelectric nanostructures}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoLuRabczuk, author = {Zhao, Jiyun and Lu, Lixin and Rabczuk, Timon}, title = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {567 -- 572}, abstract = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers}, subject = {Angewandte Mathematik}, language = {en} } @article{BenZhaoZhangetal., author = {Ben, S. and Zhao, Jun-Hua and Zhang, Yancheng and Rabczuk, Timon}, title = {The interface strength and debonding for composite structures: review and recent developments}, series = {Composite Structures}, journal = {Composite Structures}, abstract = {The interface strength and debonding for composite structures: review and recent developments}, subject = {Angewandte Mathematik}, language = {en} } @article{AreiasRabczukBarbosa, author = {Areias, Pedro and Rabczuk, Timon and Barbosa, J.I.}, title = {The extended unsymmetric frontal solution for multiple-point constraints}, series = {Engineering Computations}, journal = {Engineering Computations}, abstract = {The extended unsymmetric frontal solution for multiple-point constraints}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoKouJiangetal., author = {Zhao, Jun-Hua and Kou, Liangzhi and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures}, series = {Nanotechnology}, journal = {Nanotechnology}, doi = {10.1088/0957-4484/25/29/295701}, abstract = {Tension-induced phase transition of single-layer molybdenum disulphide (MoS2) at low temperatures}, subject = {Angewandte Mathematik}, language = {en} } @article{GhorashiValizadehMohammadietal., author = {Ghorashi, Seyed Shahram and Valizadeh, Navid and Mohammadi, S. and Rabczuk, Timon}, title = {T-spline based XIGA for Fracture Analysis of Orthotropic Media}, series = {Computers \& Structures}, journal = {Computers \& Structures}, pages = {138 -- 146}, abstract = {T-spline based XIGA for Fracture Analysis of Orthotropic Media}, 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} } @article{VuBacLahmerZhangetal., author = {Vu-Bac, N. and Lahmer, Tom and Zhang, Yancheng and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)}, series = {Composites Part B Engineering}, journal = {Composites Part B Engineering}, pages = {80 -- 95}, abstract = {Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacLahmerKeiteletal., author = {Vu-Bac, N. and Lahmer, Tom and Keitel, Holger and Zhao, Jun-Hua and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations}, series = {Mechanics of Materials}, journal = {Mechanics of Materials}, pages = {70 -- 84}, abstract = {Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations}, subject = {Angewandte Mathematik}, language = {en} } @article{KerfridenSchmidtRabczuketal., author = {Kerfriden, Pierre and Schmidt, K.M. and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain}, title = {Statistical extraction of process zones and representative subspaces in fracture of random composites}, series = {International Journal for Multiscale Computational Engineering}, journal = {International Journal for Multiscale Computational Engineering}, abstract = {Statistical extraction of process zones and representative subspaces in fracture of random composites}, subject = {Angewandte Mathematik}, language = {en} } @article{ThaiNguyenXuanNguyenThanhetal., author = {Thai, Chien H. and Nguyen-Xuan, Hung and Nguyen-Thanh, Nhon and Le, T.H. and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {Static, free vibration and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, doi = {10.1002/nme.4282}, pages = {571 -- 603}, abstract = {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.}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangZhaoRabczuk, author = {Jiang, Jin-Wu and Zhao, Jun-Hua and Rabczuk, Timon}, title = {Size-Sensitive Young's Modulus of Kinked Silicon Nanowires}, series = {Nanotechnology}, journal = {Nanotechnology}, doi = {10.1088/0957-4484/24/18/185702}, abstract = {We perform both classical molecular dynamics simulations and beam model calculations to investigate the Young's modulus of kinked silicon nanowires (KSiNWs). The Young's modulus is found to be highly sensitive to the arm length of the kink and is essentially inversely proportional to the arm length. The mechanism underlying the size dependence is found to be the interplay between the kink angle potential and the arm length potential, where we obtain an analytic relationship between the Young's modulus and the arm length of the KSiNW. Our results provide insight into the application of this novel building block in nanomechanical devices.}, subject = {Angewandte Mathematik}, language = {en} } @article{NatarajanChakrabortyThangaveletal., author = {Natarajan, S. and Chakraborty, S. and Thangavel, M. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {Size dependent free flexural vibration behavior of functionally graded nanoplates}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {74 -- 80}, abstract = {Size dependent free flexural vibration behavior of functionally graded nanoplates}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiBrighentiZhuangetal., author = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Sequential reliability based optimization of fiber content and dispersion in fiber reinforced composite by using NURBS finite elements}, series = {Structural and Multidisciplinary Optimization}, journal = {Structural and Multidisciplinary Optimization}, abstract = {Sequential reliability based optimization of fiber content and dispersion in fiber reinforced composite by using NURBS finite elements}, 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{BeexKerfridenRabczuketal., author = {Beex, L.A.A. and Kerfriden, Pierre and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain}, title = {Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, abstract = {Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangWeiZhaoetal., author = {Zhang, Yancheng and Wei, Ning and Zhao, Jun-Hua and Gong, Yadong and Rabczuk, Timon}, title = {Quasi-analytical solution for the stable system of the multi-layer folded graphene wrinkles}, series = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, abstract = {Quasi-analytical solution for the stable system of the multi-layer folded graphene wrinkles}, subject = {Angewandte Mathematik}, language = {en} } @article{HamdiaLahmerNguyenThoietal., author = {Hamdia, Khader and Lahmer, Tom and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {Predicting The Fracture Toughness of PNCs: A Stochastic Approach Based on ANN and ANFIS}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {304 -- 313}, abstract = {Predicting The Fracture Toughness of PNCs: A Stochastic Approach Based on ANN and ANFIS}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangWangRabczuk, author = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon}, title = {Phonon modes in single-walled molybdenum disulphide nanotubes: lattice dynamics calculation and molecular dynamics simulation}, series = {Nanotechnology}, journal = {Nanotechnology}, abstract = {Phonon modes in single-walled molybdenum disulphide nanotubes: lattice dynamics calculation and molecular dynamics simulation}, subject = {Angewandte Mathematik}, language = {en} } @article{AmiriMillanShenetal., author = {Amiri, Fatemeh and Mill{\´a}n, D. and Shen, Y. and Rabczuk, Timon and Arroyo, M.}, title = {Phase-field modeling of fracture in linear thin shells}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, pages = {102 -- 109}, abstract = {Phase-field modeling of fracture in linear thin shells}, subject = {Angewandte Mathematik}, language = {en} } @article{JamshidianRabczuk, author = {Jamshidian, M. and Rabczuk, Timon}, title = {Phase field modelling of stressed grain growth: Analytical study and the effect of microstructural length scale}, series = {Journal of Computational Physics}, journal = {Journal of Computational Physics}, pages = {23 -- 35}, abstract = {Phase field modelling of stressed grain growth: Analytical study and the effect of microstructural length scale}, subject = {Angewandte Mathematik}, language = {en} } @article{ChauDinhZiLeeetal., author = {Chau-Dinh, T. and Zi, Goangseup and Lee, P.S. and Song, Jeong-Hoon and Rabczuk, Timon}, title = {Phantom-node method for shell models with arbitrary cracks}, series = {Computers \& Structures}, journal = {Computers \& Structures}, doi = {10.1016/j.compstruc.2011.10.021}, abstract = {A phantom-node method is developed for three-node shell elements to describe cracks. This method can treat arbitrary cracks independently of the mesh. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Several numerical examples are presented to illustrate the proposed method.}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiBrighentiZhuangetal., author = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach}, series = {Structural and Multidisciplinary Optimization}, journal = {Structural and Multidisciplinary Optimization}, pages = {99 -- 112}, abstract = {Optimum _ber content and distribution in _ber-reinforced solids using a reliability and NURBS based sequential optimization approach}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiBrighentiZhuangetal., author = {Ghasemi, Hamid and Brighenti, Roberto and Zhuang, Xiaoying and Muthu, Jacob and Rabczuk, Timon}, title = {Optimization of fiber distribution in fiber reinforced composite by using NURBS functions}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {463 -- 473}, abstract = {Optimization of fiber distribution in fiber reinforced composite by using NURBS functions}, subject = {Angewandte Mathematik}, language = {en} } @article{BakarKramerBordasetal., author = {Bakar, I. and Kramer, O. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {Optimization of Elastic Properties and Weaving Patterns of Woven Composites}, series = {Composite Structures}, journal = {Composite Structures}, pages = {575 -- 591}, abstract = {Optimization of Elastic Properties and Weaving Patterns of Woven Composites}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiSamaniegoSamaniegoetal., author = {Talebi, Hossein and Samaniego, C. and Samaniego, Esteban and Rabczuk, Timon}, title = {On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, doi = {10.1002/nme.3275}, pages = {1009 -- 1027}, abstract = {Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node.}, subject = {Angewandte Mathematik}, language = {en} } @article{SilaniTalebiArnoldetal., author = {Silani, Mohammad and Talebi, Hossein and Arnold, Daniel and Ziaei-Rad, S. and Rabczuk, Timon}, title = {On the coupling of a commercial finite element package with lammps for multiscale modeling of materials}, series = {Steel Research International}, journal = {Steel Research International}, abstract = {On the coupling of a commercial finite element package with lammps for multiscale modeling of materials}, subject = {Angewandte Mathematik}, language = {en} } @article{ValizadehNatarajanGonzalezEstradaetal., author = {Valizadeh, Navid and Natarajan, S. and Gonzalez-Estrada, O.A. and Rabczuk, Timon and Tinh Quoc, Bui and Bordas, St{\´e}phane Pierre Alain}, title = {NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter}, series = {Composite Structures}, journal = {Composite Structures}, pages = {309 -- 326}, abstract = {NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter}, subject = {Angewandte Mathematik}, language = {en} } @article{ArashRabczukJiang, author = {Arash, Behrouz and Rabczuk, Timon and Jiang, Jin-Wu}, title = {Nanoresonators and their applications: a state of the art review}, series = {Applied Physics Reviews}, journal = {Applied Physics Reviews}, abstract = {Nanoresonators and their applications: a state of the art review}, subject = {Angewandte Mathematik}, language = {en} } @article{MortazaviRabczuk, author = {Mortazavi, Bohayra and Rabczuk, Timon}, title = {Multiscale modeling of heat conduction in graphene laminates}, series = {Carbon}, journal = {Carbon}, pages = {1 -- 7}, abstract = {Multiscale modeling of heat conduction in graphene laminates}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangNanthakumarLahmeretal., author = {Zhang, Chao and Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon}, title = {Multiple cracks identification for piezoelectric structures}, series = {International Journal of Fracture}, journal = {International Journal of Fracture}, pages = {1 -- 19}, abstract = {Multiple cracks identification for piezoelectric structures}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangParkRabczuk, author = {Jiang, Jin-Wu and Park, Harold S. and Rabczuk, Timon}, title = {MoS2 nanoresonators: intrinsically better than graphene?}, series = {Nanoscale}, journal = {Nanoscale}, pages = {3618 -- 3625}, abstract = {MoS2 nanoresonators: intrinsically better than graphene?}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiSilaniBordasetal., author = {Talebi, Hossein and Silani, Mohammad and Bordas, St{\´e}phane Pierre Alain and Kerfriden, Pierre and Rabczuk, Timon}, title = {Molecular Dynamics/XFEM Coupling by a Three-Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture}, series = {International Journal for Multiscale Computational Engineering}, journal = {International Journal for Multiscale Computational Engineering}, abstract = {Molecular Dynamics/XFEM Coupling by a Three-Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangRabczuk, author = {Jiang, Jin-Wu and Rabczuk, Timon}, title = {Modulation of Thermal Conductivity in kinked Silicon Nanowires: Phonon interchanging and pinching effects or Reduction of thermal conductivity in kinked silicon nanowire superlattices}, series = {Nano Letters}, journal = {Nano Letters}, abstract = {Modulation of Thermal Conductivity in kinked Silicon Nanowires: Phonon interchanging and pinching effects or Reduction of thermal conductivity in kinked silicon nanowire superlattices}, subject = {Angewandte Mathematik}, language = {en} } @article{KumarSinghMishraetal., author = {Kumar, S. and Singh, I. and Mishra, B.K. and Rabczuk, Timon}, title = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {1425 -- 1466}, abstract = {Modeling and Simulation of Kinked Cracks by Virtual Node XFEM}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhaoWeiFanetal., author = {Zhao, Jun-Hua and Wei, Ning and Fan, Z. and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Mechanical properties of three types of carbon allotropes}, series = {Nanotechnology}, journal = {Nanotechnology}, abstract = {Mechanical properties of three types of carbon allotropes}, subject = {Angewandte Mathematik}, language = {en} } @article{MortazaviCunibertiRabczuk, author = {Mortazavi, Bohayra and Cuniberti, G. and Rabczuk, Timon}, title = {Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {285 -- 289}, abstract = {Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study}, subject = {Angewandte Mathematik}, language = {en} } @article{JiangRabczuk, author = {Jiang, Jin-Wu and Rabczuk, Timon}, title = {Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring}, series = {Applied Physics Letters}, journal = {Applied Physics Letters}, abstract = {Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring}, subject = {Angewandte Mathematik}, language = {en} } @article{ZhangZhuangMuthuetal., author = {Zhang, Yancheng and Zhuang, Xiaoying and Muthu, Jacob and Mabrouki, Tarek and Fontaine, Micha{\"e}l and Gong, Yadong and Rabczuk, Timon}, title = {Load transfer of graphene/carbon nanotube/polyethylene hybrid nanocomposite by molecular dynamics simulation}, series = {Composites Part B Engineering}, journal = {Composites Part B Engineering}, pages = {27 -- 33}, abstract = {Load transfer of graphene/carbon nanotube/polyethylene hybrid nanocomposite by molecular dynamics simulation}, 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{NguyenKerfridenBordasetal., author = {Nguyen, V.P. and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon}, title = {Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm}, series = {Computer-Aided Design}, journal = {Computer-Aided Design}, abstract = {Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm}, subject = {Angewandte Mathematik}, language = {en} } @article{ThaiNguyenXuanBordasetal., author = {Thai, Chien H. and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain and Nguyen-Thanh, Nhon and Rabczuk, Timon}, title = {Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory}, series = {Mechanics of Advanced Materials and Structures}, journal = {Mechanics of Advanced Materials and Structures}, pages = {451 -- 469}, abstract = {Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory}, subject = {Angewandte Mathematik}, language = {en} } @article{ThaiFerreiraBordasetal., author = {Thai, Chien H. and Ferreira, A.J.M. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon and Nguyen-Xuan, Hung}, title = {Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory}, series = {European Journal of Mechanics}, journal = {European Journal of Mechanics}, pages = {89 -- 108}, abstract = {Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory}, subject = {Angewandte Mathematik}, language = {en} } @article{GhasemiKerfridenBordasetal., author = {Ghasemi, Hamid and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain and Muthu, Jacob and Zi, Goangseup and Rabczuk, Timon}, title = {Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients}, series = {Composite Structures}, journal = {Composite Structures}, pages = {221 -- 230}, abstract = {Interfacial shear stress optimization in sandwich beams with polymeric core using nonuniform distribution of reinforcing ingredients}, 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{XuMourrainGalligoetal., author = {Xu, G. and Mourrain, B. and Galligo, A. and Rabczuk, Timon}, title = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods}, series = {Computational Mechanics}, journal = {Computational Mechanics}, abstract = {High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods}, subject = {Angewandte Mathematik}, language = {en} }