Topology optimization for the development of eco-efficient masonry units

The shape of the cross-section of hollow blocks that maximizes the thermal insulation of masonry buildings is sought, by minimizing the thermal transmittance of any wall. The heat flux across the wall surfaces is supposed to be uniform along the wall height, so that the problem can be formulated as 2D. Topology optimization is employed to define the layout of the block section, prescribing constraints on the block stiffness under in-plane and out-of-plane loads. Blocks of square or rectangular cross-section, either with flat or indented sides, are considered in the applications. The influence of the design constraints and the geometry of the boundary on the optimal layout of the blocks is numerically investigated. The decrease in thermal transmittance of the optimized units compared to commercially available blocks can be extremely significant (down to -30%, depending on the prescribed constraints). Accordingly, the proposed formulation seems to be a promising candidate for the design of thermally efficient masonry blocks.