Finite Element Approximations of The Obstacle Problem
for a Clamped Plate.
H. Sissaoui, N.Nasri, M.Rahal
Institut de Mathematiques, Universite de Annaba
B.P 12 Annaba 23000 Algeria
AMS Subject Classification: 65N30
Keywords: Elastic plates, duality, Variational inequalities, conforming
and noncorming finite elements.
Abstract: The obstacle problem for a clamped thin plate [2] is a fourth
order variational inequality [2]. We derive dual variational formulations
for this problem by using a decomposition theorem due to Moreau [1].
The primal formulation which represents the potential energy of the plate
displaced by a rigid fictionless body is the clasical displacement method.
This is discretized by both triangular and rectangular nonconforming
elements. The dual formulation which represents the complementary principle
is an equilibrium method. In its turn, this formulation is discretized by
conforming triangular and rectangular elements in order to obtain
approximations of the bending moment.
The discrete variational formulations are solved by optimization techniques.
Convergence, error estimates and computational results together with
numerical approximations of the region of contact are given.
References
[1] W.D. Collins: Dual Extremum Principles and Hilbert Space decomposition
In Duality and Complementarity in Mechanics.
Praca ZBIORWA (Ed). WROCLAU, 1979.
[2] R.Glowinski, J.L.Lions, R. Tremoliere:
Numerical Analysis of Variational Inequalities.
North Holland, 1981.