Smooth boundary topology optimization using B-spline and hole generation

Abstract

A topology optimization methodology, named “smooth boundary topology optimization,” is proposed using a simple idea of combining parameterized boundary shape optimization and selection criterion for hole making. For implementation, material boundary is represented by B-spline curves and their control points are considered as design variables. The design is improved by either creating a hole or moving control points. To determine which is more beneficial, a selection criterion is defined. Once determined to create a hole, it is represented by a new B-spline and recognized as a new boundary. Because the proposed method deals with the control points of B-spline as design variables, their total number is much smaller than cell-based methods and it ensures smooth boundaries. It is shown that our method is a natural way of obtaining smooth boundary topology design effectively combining computer graphics technique and design sensitivity analysis.