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Non‐linear dynamic contact of thin‐walled structures

In many areas of mechanical engineering contact problems of thin–walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment–rotation characteristics of a bolted beam–column joint, contact occurs. Effective simulation of these and other contact problems, especially in three–dimensional non–linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin–walled character and dynamic effects into account. We use a segment–to–segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized‐α Method and the Generalized Energy–Momentum Method. Using the “Velocity–Update” Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)