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Approximation of the Axisymmetric Elasticity Equations with Weak Symmetry
In this article we consider the linear elasticity problem in an axisymmetric
three dimensional domain, with data which are axisymmetric and have zero
angular component. The weak formulation of the the three dimensional problem
reduces to a two dimensional problem on the meridian domain, involving weighted
integrals. The problem is formulated in a mixed method framework with both the
stress and displacement treated as unknowns. The symmetry condition for the
stress tensor is weakly imposed. Well posedness of the continuous weak
formulation and its discretization are shown. Two approximation spaces are
discussed and corresponding numerical computations presented