Implicit and explicit time integration schemes in conjunction with the finite element method are presented for the transient response of highly non‐linear problems such as impact situations exhibiting important material dissipation. Surprisingly the implicit schemes lead to excellent convergence properties that make them a cost‐efficient alternative to explicit scheme generally advocated as the best choice for these problems. As numerical illustrations, we present here the academic impact between two flexible bodies, a long tube and a long plate, as well as a more industrial‐oriented application: the impact between a fan blade and a double casing.
The aim of the present study was to carry out a numerical comparison of different frictional contact algorithms. Therefore three different contact algorithms (Lemke, penalty and Augmented Lagrangian) have been implemented into two finite element codes. The correct implementation and behavior of these contact algorithms has been investigated by modeling four different tribological devices. It is shown that all these different methodologies lead to extremely similar results. Besides these four applications have been carefully described and detailed in such a way that the presented tests can be reproduced. The authors wish that they could serve as a benchmark set in order to allow comparison with other finite element software including frictional contact capabilities.
Classical and non-classical implicit time integration schemes are presented for the transient response of highly nonlinear problems of large deformation analysis exhibiting important material behaviour. These schemes have shown to lead to excellent convergence properties that make them cost efficient alternative to explicit schemes generally advocated as the best choice for these problems. To qualify the theory, examples are presented, whereby performance of the crushed shock-absorber devices, as well as their resolution based on the dynamic buckling of thin steel cylinder phenomenon are given. In these examples, it is shown that implicit schemes are more efficient (less CPU-cost for a given precision of the contact situation and capable of reaching higher precision) than the explicit scheme, despite that both use the Penalty method for the treatment of contact problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.