Adaptive Isogeometric Topology Optimization of Shell Structures based on PHT-splines

TL;DR

This paper introduces an adaptive isogeometric topology optimization method for shell structures using PHT-splines, which enhances computational efficiency by local mesh refinement driven by density, reducing degrees of freedom.

Contribution

The paper presents a novel PHT-spline based adaptive topology optimization framework that improves efficiency and accuracy for shell structures by local refinement and inheritance of density values.

Findings

Significant reduction in degrees of freedom compared to tensor-product spline methods

Effective local refinement driven by density improves interface resolution

Numerical experiments confirm the method's efficiency and effectiveness

Abstract

This paper proposes an Adaptive Isogeometric Topology Optimization framework for shell structures based on PHT-splines (PHT-AITO). In this framework, the design domain, displacement, and density are represented by PHT-splines. Leveraging the local refinement capability of PHT-splines, mesh elements defining the density function are adaptively refined to achieve a suitable resolution at the interface between solid and void regions. This addresses the issue of excessive degrees of freedom resulting from global refinement. The refinement of the mesh elements is driven by their density. During the optimization of the density on a refined mesh, the initial value of the density is inherited from the optimization results on the previous mesh to accelerate the iteration process and maintain the stability of the optimized structure. Numerical experiments on various shell structures have verified the effectiveness of PHT-AITO. Compared with isogeometric topology optimization based on tensor-product splines, PHT-AITO can significantly reduce the degrees of freedom in the optimization problem, thereby improving computational efficiency.