On the solution of the checkerboard problem in mixed-FEM topology optimization

The paper deals with an alternative formulation for the classical topology optimization problem of getting structures with minimum compliance with constraint on volume, relying on the adoption of a mixed finite-element discretization scheme instead of a common displacement-based one. Using mixed methods not only displacements are main variables but also stresses enter the formulation. Two dual variational principles of Hellinger–Reissner are presented in their continuous and discrete form and included in the topology optimization problem that is solved through the method of moving asymptotes (MMA). Numerical simulations are performed for both the formulations and in particular for the truly-mixed setting coupled to a mixed-FEM discretization that uses the composite element of Johnson and Mercier referring to the discretization of the stress field. This formulation is shown to achieve pure 0–1 designs with the relevant feature of being checkerboard-free without the adoption of any filtering technique. Ongoing extensions are outlined including the optimization of incompressible materials and the imposition of stress constraints that both find in the truly-mixed setting their natural environment.