Combined parameterization of material distribution and surface mesh for stiffener layout optimization of complex surfaces

TL;DR

This paper introduces a combined parameterization approach for optimizing stiffener layouts on complex surfaces, integrating material distribution parameterization with mesh mapping to improve design efficiency.

Contribution

It develops a novel combined parameterization method using B-spline and mesh mapping for stiffener layout optimization on complex surfaces, addressing the challenge of mesh-based surface representation.

Findings

Effective handling of complex 3D surface meshes without analytical equations

Demonstrated improvements in stiffener layout optimization accuracy

Validated method through numerical examples

Abstract

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener layout by means of B-spline. The other is to build the mapping relationship from the known 3D surface mesh of the thin-walled structure to its parametric domain by means of mesh parameterization. The influence of mesh parameterization upon the stiffener layout is discussed to reveal the matching issue of the combined parameterization. 3D complex surfaces represented by the triangular mesh can be dealt with even though analytical parametric equations are not available. Some numerical examples are solved to demonstrate the direct advantage and effectiveness of the proposed method.