%0 Conference Paper %1 hartmann2006primaldual %A Hartmann, Stefan %A Brunssen, S. %A Ramm, Ekkehard %A Wohlmuth, Barbara %B Proc. of 3rd Europ. Conf. on Comp. Mech., Lisbon 2006, 'Solids, Structures and Coupled Problems in Engineering', (eds. C.A. Mota-Soares et al.), Springer %D 2006 %K ibb from:maltevonscheven inproceedings %T A primal-dual active set strategy for unilateral non-linear dynamic contact problems of thin-walled structures %X The efficient modeling of 3D contact problems is still a challenge in non-linear implicit structural analysis. Most of the existing contact algorithms use penalty methods to satisfy the contact constraints, which necessitates a user defined penalty parameter. As it is well known, the choice of this additional parameter is somehow arbitrary, problem dependent and influences the accuracy of the analysis. We use a primal-dual active set strategy, based on dual Lagrange multipliers to handle the nonlinearity of the contact conditions. This allows us to enforce the contact constraints in a weak, integral sense without any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers can be locally eliminated. We perform a static condensation to get a reduced system for the displacements. The Lagrange multipliers, representing the contact pressure, can be easily recovered from the displacements in a variationally consistent way. For our application to thin-walled structures we adapt a three-dimensional non-linear shell formulation, including the thickness stretch of the shell to contact problems. A reparametrization of the geometric description of the shell body gives us a surface oriented shell element, which allows to apply the contact conditions directly to nodes lying on the contact surface. The discretization in time is done with the implicit Generalized Energy-Momentum Method. To conserve the total energy within our contact framework, we follow an approach from Laursen and Love who introduce a discrete contact velocity to update the velocity field in a post processing step. Various examples show the good performance of the primal-dual active set strategy applied to the implicit dynamic analysis of thin-walled structures.

@inproceedings{hartmann2006primaldual, abstract = {The efficient modeling of 3D contact problems is still a challenge in non-linear implicit structural analysis. Most of the existing contact algorithms use penalty methods to satisfy the contact constraints, which necessitates a user defined penalty parameter. As it is well known, the choice of this additional parameter is somehow arbitrary, problem dependent and influences the accuracy of the analysis. We use a primal-dual active set strategy, based on dual Lagrange multipliers to handle the nonlinearity of the contact conditions. This allows us to enforce the contact constraints in a weak, integral sense without any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers can be locally eliminated. We perform a static condensation to get a reduced system for the displacements. The Lagrange multipliers, representing the contact pressure, can be easily recovered from the displacements in a variationally consistent way. For our application to thin-walled structures we adapt a three-dimensional non-linear shell formulation, including the thickness stretch of the shell to contact problems. A reparametrization of the geometric description of the shell body gives us a surface oriented shell element, which allows to apply the contact conditions directly to nodes lying on the contact surface. The discretization in time is done with the implicit Generalized Energy-Momentum Method. To conserve the total energy within our contact framework, we follow an approach from Laursen and Love who introduce a discrete contact velocity to update the velocity field in a post processing step. Various examples show the good performance of the primal-dual active set strategy applied to the implicit dynamic analysis of thin-walled structures.}, added-at = {2021-03-09T13:40:57.000+0100}, author = {Hartmann, Stefan and Brunssen, S. and Ramm, Ekkehard and Wohlmuth, Barbara}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2dde77e455a0c1ee0d2ff5c493cd1095e/ibb-publication}, booktitle = {Proc. of 3rd Europ. Conf. on Comp. Mech., Lisbon 2006, 'Solids, Structures and Coupled Problems in Engineering', (eds. C.A. Mota-Soares et al.), Springer}, interhash = {c445bbbf6817ab647a79963107221d3a}, intrahash = {dde77e455a0c1ee0d2ff5c493cd1095e}, keywords = {ibb from:maltevonscheven inproceedings}, timestamp = {2021-03-09T12:40:57.000+0100}, title = {A primal-dual active set strategy for unilateral non-linear dynamic contact problems of thin-walled structures}, year = 2006 }