An Isogeometric Topology Optimization Method for Free-Form Shell Structures Using T-splines

An isogeometric topology optimization method based on T-splines for complex thin shell structures is proposed in this paper. T-spline is ideal for creating complex structural models since its local refinement capability overcomes the limitation in NURBS. The design domain of complicated shell structures is produced from CAD by T-splines surface, and the analysis result is shown by the triangulation principle to simplify the post-processing. The structural density is the design variable for topology optimization, which is assigned to each control point on the optimization surface of the shell structures. The density distribution is represented by the T-splines using Bézier extraction, which is used for geometric description and structural response. The issue of the design of thin shell structures with arbitrary geometries can be resolved based on the framework. Finally, several classical and complicated examples are shown to demonstrate the viability of the proposed methods. Generally, the approach offers a unified framework for the analysis and optimization of complicated thin-walled structures, which eliminates a significant number of redundant design variables, streamlines the analysis and optimization processes, and lowers the computing expense of optimization.