Structural optimization with explicit geometric constraints using a B-spline representation

Abstract

In this paper we present a structural optimization approach that is based on explicit B-spline representation of the design, conforming with CAD standards. The methodology and implementation are general and can accommodate arbitrary B-spline degrees. The spline-based parametrization enables to incorporate explicit constraints on minimum and maximum areas of holes and on curvatures of boundaries. Therefore, practical design considerations such as 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, as well as influence the peak stresses in the structure. The presented method is applied to several stiffness optimization problems. The results demonstrate the capabilities of this approach to incorporate explicit geometric constraints in a straightforward manner. The utilization of curvature constraints as an efficient alternative to stress constraints is demonstrated as well.

Keywords:

• Topology optimization
• shape optimization
• CAD
• B-splines
• explicit geometric constraints
• curvature constraints

Additional information

Funding

The financial support from the Israel Science Foundation, Grant No. 750/15, is gratefully acknowledged.