An efficient methodology for stress-based finite element approximations in two-dimensional elasticity

We present an efficient approach to compute the matrices used in finite element formulations where self-equilibrated (zero divergence) approximations of the stress field are used. The fundamental aspect of this approach is that it is applicable to polynomial approximations of high degree (it was tested up to degree 10), providing closed-form expressions for the elementary matrices involved. The components of the stress field are defined as a function of the coordinates in the master element, facilitating the postprocessing of the finite element results and allowing for the consideration of geometric parameters in reduced order models.