Existence result and discontinuous finite element discretization for a plane stresses Hencky problem. (English) Zbl 0693.73022

Ben Dhia, H.; Hadhri, T.

Math. Methods Appl. Sci. 11, No. 2, 169-184 (1989).

The authors propose and analyze a discontinuous finite element method for a plane stress Hencky problem. Relaxing the boundary condition on that part of the boundary, where the plate is clamped, they develop existence results justifying the relaxation not only from the mathematical point of view but also from a physical one. For a finite element discretization they prove an existence result and show the convergence to the original solution in a weak sense.
Numerical tests are not presented in this work but the authors give references where examples may be found.

Reviewer: N.Herrmann

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49N15	Duality theory (optimization)
49Q20	Variational problems in a geometric measure-theoretic setting
65D99	Numerical approximation and computational geometry (primarily algorithms)

Keywords:

Hencky body; weak convergence; subsequence of discrete solutions; displacement problem; convex optimization problem; space of integrable displacement fields; deformations; bounded measures; relaxation

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