@article{NguyenThoiPhungVanRabczuketal., author = {Nguyen-Thoi, T. and Phung-Van, P. and Rabczuk, Timon and Nguyen-Xuan, Hung and Le-Van, C.}, title = {An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThoiPhungVanRabczuketal., author = {Nguyen-Thoi, T. and Phung-Van, P. and Rabczuk, Timon and Nguyen-Xuan, Hung and Le-Van, C.}, title = {Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenThoiRabczukLamPhatetal., author = {Nguyen-Thoi, T. and Rabczuk, Timon and Lam-Phat, T. and Ho-Huu, V. and Phung-Van, P.}, title = {Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3)}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, abstract = {Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3)}, 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{NguyenXuanLiuBordasetal., author = {Nguyen-Xuan, Hung and Liu, G.R. and Bordas, St{\´e}phane Pierre Alain and Natarajan, S. and Rabczuk, Timon}, title = {An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {252 -- 273}, abstract = {An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order}, subject = {Angewandte Mathematik}, language = {en} } @article{NguyenXuanNguyenBordasetal., author = {Nguyen-Xuan, Hung and Nguyen, Hiep Vinh and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon and Duflot, Marc}, title = {A cell-based smoothed finite element method for three dimensional solid structures}, series = {KSCE Journal of Civil Engineering}, journal = {KSCE Journal of Civil Engineering}, doi = {10.1007/s12205-012-1515-7}, pages = {1230 -- 1242}, abstract = {This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation.}, 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{NguyenXuanRabczukNguyenThoietal., author = {Nguyen-Xuan, Hung and Rabczuk, Timon and Nguyen-Thoi, T. and Tran, T. and Nguyen-Thanh, Nhon}, title = {Computation of limit and shakedown loads using a node-based smoothed finite element method}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, doi = {10.1002/nme.3317}, pages = {287 -- 310}, abstract = {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.}, subject = {Angewandte Mathematik}, language = {en} } @article{PhanDaoNguyenXuanThaiHoangetal., author = {Phan-Dao, H. and Nguyen-Xuan, Hung and Thai-Hoang, C. and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {An edge-based smoothed finite element method for analysis of laminated composite plates}, series = {International Journal of Computational Methods}, journal = {International Journal of Computational Methods}, abstract = {An edge-based smoothed finite element method for analysis of laminated composite plates}, subject = {Angewandte Mathematik}, language = {en} } @article{RabizadehSaboorBagherzadehRabczuk, author = {Rabizadeh, Ehsan and Saboor Bagherzadeh, Amir and Rabczuk, Timon}, title = {Application of goal-oriented error estimation and adaptive mesh refinement on thermo-mechanical multifield problems}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {27 -- 44}, abstract = {Application of goal-oriented error estimation and adaptive mesh re_nement on thermo-mechanical multi_eld problems}, 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{SilaniTalebiZiaeiRadetal., author = {Silani, Mohammad and Talebi, Hossein and Ziaei-Rad, S. and Hamouda, A.M.S. and Zi, Goangseup and Rabczuk, Timon}, title = {A three dimensional Extended Arlequin Method for Dynamic Fracture}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {425 -- 431}, abstract = {A three dimensional Extended Arlequin Method for Dynamic Fracture}, subject = {Angewandte Mathematik}, language = {en} } @article{SilaniZiaeiRadTalebietal., author = {Silani, Mohammad and Ziaei-Rad, S. and Talebi, Hossein and Rabczuk, Timon}, title = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites}, series = {Theoretical and Applied Fracture Mechanics}, journal = {Theoretical and Applied Fracture Mechanics}, abstract = {A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites}, subject = {Angewandte Mathematik}, language = {en} } @article{SimpsonBordasTrevelyanetal., author = {Simpson, R. and Bordas, St{\´e}phane Pierre Alain and Trevelyan, J. and Kerfriden, Pierre and Rabczuk, Timon}, title = {An Isogeometric Boundary Element Method for elastostatic analysis}, series = {Computer Methods in Applied Mechanics and Engineering}, journal = {Computer Methods in Applied Mechanics and Engineering}, doi = {10.1016/j.cma.2011.08.008}, abstract = {The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.}, 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{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{TalebiSilaniBordasetal., author = {Talebi, Hossein and Silani, Mohammad and Bordas, St{\´e}phane Pierre Alain and Kerfriden, Pierre and Rabczuk, Timon}, title = {A computational library for multiscale modeling of material failure}, series = {Computational Mechanics}, journal = {Computational Mechanics}, abstract = {A computational library for multiscale modeling of material failure}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiSilaniRabczuk, author = {Talebi, Hossein and Silani, Mohammad and Rabczuk, Timon}, title = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation}, series = {Advances in Engineering Software}, journal = {Advances in Engineering Software}, pages = {82 -- 92}, abstract = {Concurrent Multiscale Modelling of Three Dimensional Crack and Dislocation Propagation}, subject = {Angewandte Mathematik}, language = {en} } @article{TalebiZiSilanietal., author = {Talebi, Hossein and Zi, Goangseup and Silani, Mohammad and Samaniego, Esteban and Rabczuk, Timon}, title = {A simple circular cell method for multilevel finite element analysis}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, doi = {10.1155/2012/526846}, abstract = {A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.}, 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} }