Topology and shape optimization with explicit geometric constraints using a spline-based representation and a fixed grid

Topology optimization is a computational method for finding the distribution of material such that an objective function is minimized subject to a set of constraints. In the context of structures, topology optimization aims to find the layout by changing the shape of the boundary and the number and shape of holes. Such optimized designs ultimately lead to energy savings, efficient usage of materials, and to faster and sustainable manufacturing. In this paper, we present an optimization approach that is based on explicit B-spline representation of the design, conforming with CAD standards. This parametrization enables to incorporate explicit constraints on minimum and maximum areas of holes and on curvatures of boundaries. Therefore practical design considerations such as avoiding stress concentrations in sharp corners and flexibility with respect to locations and sizes of holes can be embedded into the optimization problem. Furthermore, control of curvature can simplify machining processes leading to more efficient and sustainable manufacturing.