Surface developability constraint for density-based topology optimization

Abstract

Methods are provided for designing a structure with developable surfaces using a surface developability constraint. The surface developability constraint is developed based on the discovery of a sufficient condition for surface piecewise developability, namely surface normal directions lie on a small, finite number of planes. Automated methods and algorithms may include providing a design domain and a characteristic function of a material in the design domain to be optimized. The methods include defining a nodal density of the material, and determining surface normal directions of a plurality of planes. A density gradient that describes the surface normal directions is then determined. The methods include performing a topology optimization process on the design domain using a surface developability constraint that is based, at least in part, on the characteristic function. A geometric domain is then created for the structure using results from the topology optimization.