Previous |  Up |  Next


obstacle problem; variational formulation; semi-coercive problem; finite elements; semismooth Newton method; method of successive approximations
The paper deals with existence and uniqueness results and with the numerical solution of the nonsmooth variational problem describing a deflection of a thin annular plate with Neumann boundary conditions. Various types of the subsoil and the obstacle which influence the plate deformation are considered. Numerical experiments compare two different algorithms.
[1] Aubin, J.-P.: Applied functional analysis. Wiley-Interscience New York (2000). MR 1782330 | Zbl 0946.46001
[2] Chen, X., Nashed, Z., Qi, L.: Smoothing methods and semismooth methods for nondifferentiable operator equations. SIAM J. Numer. Anal. 38 (2000), 1200-1216. DOI 10.1137/S0036142999356719 | MR 1786137 | Zbl 0979.65046
[3] Drábek, P., Milota, J.: Lectures on Nonlinear Analysis. Vydavatelský Servis Plzeň (2004). Zbl 1078.47001
[4] Kufner, A.: Weighted Sobolev Spaces. Teubner Leipzig (1980). MR 0664599 | Zbl 0455.46034
[5] Lagnese, J. E., Lions, J.-L.: Modelling Analysis and Control of Thin Plates. Mason Paris (1988). MR 0953313 | Zbl 0662.73039
[6] Salač, P.: Optimal design of an elastic circular plate on a unilateral elastic foundation. II: Approximate poblems. ZAMM, Z. Angew. Math. Mech. 82 (2002), 33-42. DOI 10.1002/1521-4001(200201)82:1<33::AID-ZAMM33>3.0.CO;2-0 | MR 1878481
[7] Salač, P.: Shape optimization of elastic axisymmetric plate on an elastic foundation. Appl. Math. 40 (1995), 319-338. MR 1331921 | Zbl 0839.73036
[8] Sysala, S.: Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem. Appl. Math. 53 (2008), 347-379. DOI 10.1007/s10492-008-0030-0 | MR 2433726 | Zbl 1199.49051
Partner of
EuDML logo