Franke, DavidDavidFrankeRank, ErnstErnstRankDüster, AlexanderAlexanderDüster2022-08-252022-08-252011International Journal of Computational Methods 8 (3): 493-512 (2011)http://hdl.handle.net/11420/13479In this paper we present an rp-adaptive discretization strategy to perform unilateral two-dimensional (2D) mechanical contact simulations by combining the r- and p-versions of the finite element method (FEM). The p-version leaves the finite element mesh unchanged and increases the shape function's polynomial degree in order to obtain convergence toward the exact solution of the underlying mathematical model. The r-method relocates nodes of an existing FE-mesh to improve the discretization of a given problem without introducing additional degrees of freedom, therefore, keeping the problem size fixed. The rp-version, which is a combination of the two aforementioned methods, is used in our study to move a node of the FE-mesh to the end of the contact zone to account for the loss of regularity that arises due to the change from contact to noncontact along the edge. It will be shown that highly accurate results can be obtained by using high-order (p) finite elements in combination with the penalty method and a relocation (r) of element nodes. © 2011 World Scientific Publishing Company.en0219-876220113493512World Scientific PublishingContact mechanicshigh-order FEMp-versionpenalty methodr-versionrp-methodInformatikTechnikIngenieurwissenschaftenJournal Article10.1142/S0219876211002630Other