  In this article we suggest two discretization methods based on isogeometric
analysis (IGA) for planar linear elasticity. On the one hand, we apply the
well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a
well-posed mixed formulation. Such modified mixed problems have been already
studied by different authors. But we concentrate on the exploitation of IGA
results to handle also curved boundary geometries. On the other hand, we
consider the more complicated situation of strong symmetry, i.e. we discretize
the mixed weak form determined by the so-called Hellinger-Reissner variational
principle. We show the existence of suitable approximate fields leading to an
inf-sup stable saddle-point problem. For both discretization approaches we
prove convergence statements and in case of weak symmetry we illustrate the
approximation behavior by means of several numerical experiments.
