TY - JOUR A1 - Areias, Pedro A1 - Rabczuk, Timon A1 - Cesar de Sa, J.M. A1 - Garcao, J.E. T1 - Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains JF - Finite Elements in Analysis and Design N2 - Finite strain quadrilateral shell using least-squares _t of relative Lagrangian in-plane strains KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 SP - 26 EP - 40 ER - TY - JOUR A1 - Areias, Pedro A1 - Rabczuk, Timon A1 - Cesar de Sa, J.M. A1 - Jorge, R.N. T1 - A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares JF - Computational Mechanics N2 - A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 ER - 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 - Brehm, Maik A1 - Zabel, Volkmar A1 - Bucher, Christian T1 - An automatic mode pairing strategy using an enhanced modal assurance citerion based on modal strain energies JF - Journal of Sound and Vibration N2 - In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2010 U6 - http://dx.doi.org/10.1016/j.jsv.2010.07.006 SP - 5375 EP - 5392 ER -