Discretization-independent node-based shape optimization with the Vertex Morphing method using design variable scaling

Abstract The Vertex Morphing method is a node-based shape parameterization that uses an explicit filtering approach to regularize the optimization problem and generate smooth shapes. It has been successfully applied to shape optimization problems of industrial size in recent years. This work investigates in detail how irregular discretizations, design surface boundaries, and complex geometries can influence the progress of a gradient-based optimization using the standard Vertex Morphing formulation. A sensitivity weighting approach based on the available shape morphing functions is presented, which eliminates all of the aforementioned influences. Subsequently, a design variable scaling strategy is developed that transforms the optimization problem into an alternative design space and allows the use of arbitrary, even highly irregular surface discretizations in combination with black-box optimization algorithms for shape optimization with the Vertex Morphing method. Illustrative academic examples and an application case of an additively manufactured part are presented to support the work.