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  - 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  - Pinto da Costa, A.
A1  - Rabczuk, Timon
A1  - Queiros de Melo, F. J. M.
A1  - Dias-da-Costa, D.
T1  - An alternative formulation for quasi-static frictional and cohesive contact problems
JF  - Computational Mechanics
N2  - An alternative formulation for quasi-static frictional and cohesive contact problems
KW  - Angewandte Mathematik
KW  - Strukturmechanik
Y1  - 2014
SP  - 807
EP  - 824
ER  - 
TY  - JOUR
A1  - Jia, Yue
A1  - Anitescu, Cosmin
A1  - Ghorashi, Seyed Shahram
A1  - Rabczuk, Timon
A1  - Dias-da-Costa, D.
T1  - Extended Isogeometric Analysis for Material Interface Problems
JF  - Journal of Applied Mathematics
N2  - Extended Isogeometric Analysis for Material Interface Problems
KW  - Angewandte Mathematik
KW  - Strukturmechanik
Y1  - 2014
ER  -