A unilateral contact model with buckling in von Kármán platesA unilateral contact model with buckling in von Kármán plates Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-112007enThe unilateral contact problem for the von Kármán plate including postbuckling is numerically studied in this paper. The mathematical model consists of a system of nonlinear inequalities and equations for the transversal displacements and the stress function on the middle plane of the plate, respectively. The boundary conditions correspond to simply supported or partially clamped plates. The lateral displacements are constrained by the presence of a rigid support. A variational principle with penalty is used to treat the mechanical model. Then the variational penalized problem is solved by a spectral method. For the obtained discrete model we develop an iterative scheme based on Newton's iterations, combined with numerical continuation coupled with an appropriate procedure for the choice of the penalty and regularization parameters. Numerical results demonstrate the effectiveness of the proposed method.http://creativecommons.org/licenses/by/4.0/Nonlinear Analysis: Real World Applications481261-1271 Aliki D. Muradova Stavroulakis Georgios Σταυρουλακης Γεωργιος Elsevier Greek mathematics mathematics greek greek mathematics