TY - JOUR A1 - Areias, Pedro A1 - Rabczuk, Timon A1 - Dias-da-Costa, D. T1 - Assumed-metric spherically-interpolated quadrilateral shell element JF - Finite Elements in Analysis and Design N2 - Assumed-metric spherically-interpolated quadrilateral shell element KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2013 SP - 53 EP - 67 ER - TY - JOUR A1 - Areias, Pedro A1 - Rabczuk, Timon A1 - Dias-da-Costa, D. T1 - Asymmetric Shell Elements Based on a Corrected Updated-Lagrangian Approach JF - CMES: Computer Modeling in Engineering and Sciences N2 - Asymmetric Shell Elements Based on a Corrected Updated-Lagrangian Approach KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2013 ER - TY - JOUR A1 - Areias, Pedro A1 - Rabczuk, Timon A1 - Dias-da-Costa, D. A1 - Piresh, E.B. T1 - Implicit solutions with consistent additive and multiplicative components JF - Finite Elements in Analysis and Design N2 - 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. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1016/j.finel.2012.03.007 SP - 15 EP - 31 ER - TY - JOUR A1 - Areias, Pedro A1 - Rabczuk, Timon A1 - Queiros de Melo, F. J. M. A1 - Cesar de Sa, J.M. T1 - Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems JF - Computational Mechanics N2 - Coulomb frictional contact by explicit projection in the cone for _nite displacement quasi-static problems KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 SP - 57 EP - 72 ER - TY - JOUR A1 - Bakar, I. A1 - Kramer, O. A1 - Bordas, Stéphane Pierre Alain A1 - Rabczuk, Timon T1 - Optimization of Elastic Properties and Weaving Patterns of Woven Composites JF - Composite Structures N2 - Optimization of Elastic Properties and Weaving Patterns of Woven Composites KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2013 SP - 575 EP - 591 ER - TY - JOUR A1 - Beex, L.A.A. A1 - Kerfriden, Pierre A1 - Rabczuk, Timon A1 - Bordas, Stéphane Pierre Alain T1 - Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation JF - Computer Methods in Applied Mechanics and Engineering N2 - Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2014 ER - TY - JOUR A1 - Ben, S. A1 - Zhao, Jun-Hua A1 - Zhang, Yancheng A1 - Rabczuk, Timon T1 - The interface strength and debonding for composite structures: review and recent developments JF - Composite Structures N2 - The interface strength and debonding for composite structures: review and recent developments KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 ER - TY - JOUR A1 - Budarapu, Pattabhi Ramaiah A1 - Gracie, Robert A1 - Bordas, Stéphane Pierre Alain A1 - Rabczuk, Timon T1 - An adaptive multiscale method for quasi-static crack growth JF - Computational Mechanics N2 - This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom–atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2014 U6 - http://dx.doi.org/10.1007/s00466-013-0952-6 SP - 1129 EP - 1148 ER - TY - JOUR A1 - Budarapu, Pattabhi Ramaiah A1 - Gracie, Robert A1 - Yang, Shih-Wei A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - Efficient Coarse Graining in Multiscale Modeling of Fracture JF - Theoretical and Applied Fracture Mechanics N2 - Efficient Coarse Graining in Multiscale Modeling of Fracture KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2014 SP - 126 EP - 143 ER - TY - JOUR A1 - Budarapu, Pattabhi Ramaiah A1 - Narayana, T.S.S. A1 - Rammohan, B. A1 - Rabczuk, Timon T1 - Directionality of sound radiation from rectangular panels JF - Applied Acoustics N2 - Directionality of sound radiation from rectangular panels KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 SP - 128 EP - 140 ER -