  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.
