Error estimates for a lumped stress method for plane elastic problems

The variational properties and the convergence order of a Lumped Stress Method (LSM) for 2D anisotropic elasticity are presented. Such a method can be thought of as a rational procedure to approximate a plane continuous body by a truss-like structure. The traction problem of plane elasticity is considered, making use of the Airy stress function. Under suitable assumptions, the convergence of the LSM is proved on using arguments of the mathematical theory of mixed finite element methods. The given result is useful in order to prove the accuracy of the discrete-continuum approximation in technical applications