Master-slave elimination scheme for arbitrary nonlinear multi-point constraints
Theory, numerics, implementation and application
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Nonlinear multi-point constraints are required in the modeling and simulation of various engineering problems. One method for considering constraints is the masterslave elimination, which satisfies the constraints exactly and, in contrast to the Lagrange multiplier method and the penalty method, has the advantage of reducing the dimension of the problem. However, the existing master-slave elimination is limited to linear constraints. In this thesis, an innovative method is presented which extends the master-slave elimination to arbitrary nonlinear multi-point constraints. Special attention is ...
Nonlinear multi-point constraints are required in the modeling and simulation of various engineering problems. One method for considering constraints is the masterslave elimination, which satisfies the constraints exactly and, in contrast to the Lagrange multiplier method and the penalty method, has the advantage of reducing the dimension of the problem. However, the existing master-slave elimination is limited to linear constraints. In this thesis, an innovative method is presented which extends the master-slave elimination to arbitrary nonlinear multi-point constraints. Special attention is also paid to the problem of redundant constraints. A method for the identification and elimination of redundancy is presented and it is shown that this method can also be used for the automatic identification of slave degrees of freedom in master-slave elimination. After the theoretical derivation, the numerical aspects and the implementation in FE software are explained and discussed. The computational complexity of the new method is analyzed in comparison to existing methods. It can be shown that the master-slave elimination exhibits a reduced computational complexity compared to existing methods. The new master-slave elimination for nonlinear constraints as well as the algorithms for the identification, elimination and treatment of redundancy are examined using several numerical examples and compared with existing methods. For this, novel examples were developed for which analytical or reference solutions were derived. Therefore, they are suitable as benchmark tests. The findings demonstrate that the new method is as accurate, robust and flexible as the Lagrange multipliers, and more efficient due to the reduction of the total number of degrees of freedom, which is particularly advantageous when a large number of constraints have to be considered.
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