IgaTop: an implementation of topology optimization for structures using IGA in MATLAB

Abstract

In this paper, the key intention is to present a compact and efficient MATLAB code for the implementation of the isogeometric topology optimization (ITO) method published by Jie Gao et al. (Int J Numer Methods Eng 119: 991–1017, 2019). A main function IgaTop2D with eight inputs in the 56-line MATLAB code is developed, mainly including nine components: (1) Geom_Mod subfunction that uses non-uniform rational B-splines (NURBS) to develop the geometrical model; (2) the preparation of the isogeometric analysis (IGA) that is implemented in Pre_IGA subfunction; (3) the definition of Dirichlet and Neumann boundary conditions in Boun_Cond subfunction; (4) the initialization of control densities and the densities at Gauss quadrature points implemented from lines 11 to 20 of the main function; (5) a Shep_Fun subfunction for the smoothing mechanism; (6) IGA to solve structural responses in three steps: compute IGA element stiffness matrices in Stiff_Ele2D subfunction, assemble all IGA element stiffness matrices in Stiff_Ass2D subfunction, and Solving; (7) calculation of the objective function and sensitivity analysis in lines 32–46 of IgaTop2D; (8) OC to advance design variables; and (9) the representations of the optimized solutions in Plot_Data and Plot_Topy subfunctions. Finally, several numerical examples are shown to demonstrate the effectiveness of the ITO MATLAB implementation IgaTop2D, which are attached in the Appendix, also offering an entry point for newcomers who have an interest in the field of the ITO.