Topology optimization of incompressible materials based on the mixed SBFEM

• A mixed scaled boundary finite element formulation with near incompressibility.
• Novel material interpolation in SBFEM for describing geometrical topology.
• New algorithm of combining SBFEM with the moving iso-surface threshold (MIST) method.
• The algorithm can generate optimum topologies in designing incompressible solids.

This paper presents the topology optimization based on a semi-analytical mixed scaled boundary finite element method (SBFEM) for problems involving incompressible materials using a moving iso-surface threshold method (MIST). The mixed SBFEM does not have volumetric issues in the presence of incompressibility and it can pass the inf–sup stability conditions without requiring any mesh-dependent and stabilization parameters. Thus the topology optimization of incompressible materials is also possible based on the mixed SBFEM. The solutions of stress and strain in the mixed SBFEM are derived semi-analytically. A response function in MIST is chosen as the mutual strain energy density which is formulated by the stress and the strain obtained in the mixed SBFEM. Numerical examples including the optimal design problems of compressible and incompressible materials as well as the rubber mounts containing incompressible solid and fluid are presented. The present results are also verified with the available reference results.