An efficient 2D/3D NURBS-based topology optimization implementation using page-wise matrix operation in MATLAB

This paper presents a computationally efficient MATLAB implementation of two-dimensional/three-dimensional (2D/3D) topology optimization in non-uniform rational basis spline (NURBS) framework for educational purposes. The pseudo-densities and the related weights at control points define the NURBS-based density surface and are also simultaneously taken as the design variables, which extremely increases the computational expense due to the iterative numerical operations at Gauss integration points for isogeometric analysis (IGA) and sensitivity calculation. Thus, this paper designs the page-wise matrix operation and its implementation on graphics processing unit (GPU) to replace the element loop-based iteration to improve the computational efficiency. For the 2D problems, the main program of valid 34 lines of code (Appendix 1) is mainly divided by initialization of lines 3–11, IGA and sensitivity analysis of lines 13–30, and optimizer of lines 32–34. The sensitivity analysis function of valid 51 lines of code (Appendix 2) is programmed by the page-wise matrix operation. The optimization problems are solved by the Method of Moving Asymptotes (MMA) algorithm. The computational efficiency is largely improved in terms of the performance evaluation of the benchmark cases between the page-wise matrix-based procedure structure and the conventional element loop-based iteration algorithm. All programs that support the results of this study are completely provided and serve educational purposes for students and newcomers.