Efficient Truly-Mixed Finite Elements for the Optimal Design of Structures

The so–called truly–mixed version of the Hellinger–Reissner variational principle implements a regular stress field as main variable of the elasticity problem. A small number of robust discrete schemes are available in the literature that fulfil the stability condition, mainly through ad hoc composite finite elements or weak enforcements of the symmetry of the stress tensor. This is generally tied to increased computational cost with respect to conventional displacement–based finite elements. Recently, new families of mixed finite elements have been proposed in the literature to address the analysis of linear elastic bodies adopting regular grids and a limited number of degrees of freedom per element. The lowest order two–dimensional finite element of this new family is adopted to formulate a topology optimization problem where stresses play the role of main variables. The compliance is computed through the evaluation of the complementary energy and the enforcement of stress constraints is straightforward. Preliminary numerical simulations investigate the features of the proposed framework, providing comparisons with a conventional displacement–based scheme. Keywords: