MATLAB codes of the parametrized level set method for structural topology optimization using B-spline’s simple or repeated knots

This educational paper aims to introduce RDBLS2D, a 99-line MATLAB code that integrates the advantages of the B-spline-based level set function and the reaction–diffusion update scheme to achieve efficient and effective structural topology optimization. It uses 66 and 33 lines for the main program and the B-spline level set representation method updated by the reaction–diffusion scheme, respectively. Also, repeated B-spline’s knots on the boundary of the design domain were used in the code, which can naturally guarantee the connection between neighboring cells in the design of functionally graded materials. Numerical examples of mean compliance minimization demonstrate that the algorithm is capable of producing refined structural profiles featuring exceptionally smooth boundaries in just 20 iteration steps.