Spline-based structural optimization with explicit geometric constraints using a fixed grid

A structural optimization problem aims to achieve the best performance of a design while satisfying all the constraints. Specifically, the class of methods known as structural topology optimization aim to find the layout of the design 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 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 over curvatures can simplify machining processes and lead to more efficient manufacturing. The presented method is applied to several minimum compliance problems. The results demonstrate the capabilities of this approach to incorporate explicit geometric constraints in a straightforward manner.