Topology optimization for thermal insulation: an application to building engineering

This article deals with a numerical implementation for topology optimization that is based on the heat conduction equation and addresses problems such as the optimal design of thermal insulation in building engineering. The formulation handles heat diffusivity under the steady-state assumption for a domain with assigned convective-like boundary conditions. The optimization framework is implemented within a general-purpose finite-elements code that is set to solve the thermal problem iteratively, thus allowing for a straightforward handling of two-dimensional and three-dimensional problems. A few numerical results are firstly presented to compare classical formulations for maximum heat conduction and the addressed scheme for optimal thermal insulation. The proposed methodology is therefore exploited to cope with issues peculiar to the optimal design of building envelopes, such as the mitigation of the effects of thermal bridges and the design for minimum thermal transmittance of the components of a modular curtain wall.