TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Detection of flaws in piezoelectric structures using extended FEM JF - International Journal for Numerical Methods in Engineering N2 - Detection of flaws in piezoelectric structures using extended FEM KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2013 SP - 373 EP - 389 ER - TY - JOUR A1 - Vu-Bac, N. A1 - Rafiee, Roham A1 - Zhuang, Xiaoying A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters JF - Composites Part B: Engineering N2 - Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2015 SP - 446 EP - 464 ER - TY - JOUR A1 - Zhang, Chao A1 - Wang, Cuixia A1 - Lahmer, Tom A1 - He, Pengfei A1 - Rabczuk, Timon T1 - A dynamic XFEM formulation for crack identification JF - International Journal of Mechanics and Materials in Design N2 - A dynamic XFEM formulation for crack identification KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 427 EP - 448 ER - TY - JOUR A1 - Vu-Bac, N. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Nguyen-Thoi, T. A1 - Rabczuk, Timon T1 - A software framework for probabilistic sensitivity analysis for computationally expensive models JF - Advances in Engineering Software N2 - A software framework for probabilistic sensitivity analysis for computationally expensive models KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 19 EP - 31 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Park, Harold S. A1 - Rabczuk, Timon T1 - Topology optimization of piezoelectric nanostructures JF - Journal of the Mechanics and Physics of Solids N2 - Topology optimization of piezoelectric nanostructures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 316 EP - 335 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Zi, Goangseup A1 - Rabczuk, Timon T1 - Detection of material interfaces using a regularized level set method in piezoelectric structures JF - Inverse Problems in Science and Engineering N2 - Detection of material interfaces using a regularized level set method in piezoelectric structures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 153 EP - 176 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Detection of multiple flaws in piezoelectric structures using XFEM and level sets JF - International Journal for Numerical Methods in Engineering N2 - Detection of multiple flaws in piezoelectric structures using XFEM and level sets KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 960 ER - TY - JOUR A1 - Ghorashi, Seyed Shahram A1 - Lahmer, Tom A1 - Bagherzadeh, Amir Saboor A1 - Zi, Goangseup A1 - Rabczuk, Timon T1 - A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials JF - Engineering Geology N2 - A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 ER - TY - JOUR A1 - Zhang, Chao A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Multiple cracks identification for piezoelectric structures JF - International Journal of Fracture N2 - Multiple cracks identification for piezoelectric structures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2017 SP - 1 EP - 19 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-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 - 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 - 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-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 - 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 - Simpson, R. A1 - Bordas, Stéphane Pierre Alain A1 - Trevelyan, J. A1 - Kerfriden, Pierre A1 - Rabczuk, Timon T1 - An Isogeometric Boundary Element Method for elastostatic analysis JF - Computer Methods in Applied Mechanics and Engineering N2 - 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. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1016/j.cma.2011.08.008 ER - TY - JOUR A1 - Chau-Dinh, T. A1 - Zi, Goangseup A1 - Lee, P.S. A1 - Song, Jeong-Hoon A1 - Rabczuk, Timon T1 - Phantom-node method for shell models with arbitrary cracks JF - Computers & Structures N2 - 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. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1016/j.compstruc.2011.10.021 ER - TY - JOUR A1 - Talebi, Hossein A1 - Samaniego, C. A1 - Samaniego, Esteban A1 - Rabczuk, Timon T1 - On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods JF - International Journal for Numerical Methods in Engineering N2 - 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. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1002/nme.3275 SP - 1009 EP - 1027 ER - TY - JOUR A1 - Chen, Lei A1 - Rabczuk, Timon A1 - Liu, G.R. A1 - Zeng, K.Y. A1 - Kerfriden, Pierre A1 - Bordas, Stéphane Pierre Alain T1 - Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth JF - Computer Methods in Applied Mechanics and Engineering N2 - This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting “edge-based” smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, “super-convergence” and “ultra-accurate” solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1016/j.cma.2011.08.013 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 -