A primal-dual active set strategy for unilateral non-linear dynamic contact problems of thin-walled structures
S. Hartmann, S. Brunssen, E. Ramm, und B. Wohlmuth. 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, (2006)
Zusammenfassung
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.
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
%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
}