Algorithms of isogeometric analysis for MIST-based structural topology optimization in MATLAB

In this paper, a new isogeometric topology optimization (ITO) method based on the moving iso-surface threshold (MIST) method is proposed, and the corresponding MATLAB code is provided. The same nonuniform rational B-splines (NURBS) basis functions are used to construct a geometrical model and evaluate the objective function for minimal compliance problems. In MIST-based ITO, the physical response function is calculated by using the same NURBS basis functions as the geometry model. First, the physical response function values of control points are calculated by using the NURBS basis function and the physical response function values of the Gauss points. Second, the physical response function values of the knots (the element nodes) are obtained by fitting the control points using NURBS basis functions. Finally, the physical response surface is formed by connecting its nodal values. The structure topology is iteratively updated by using an iso-surface with an appropriate threshold to cut the physical response surface. Compared to traditional MIST, MIST-based ITO can improve the computational accuracy and computational efficiency of high-order elements. Several numerical examples demonstrate the effectiveness of the proposed method, verifying the validity of isogeometric topology optimization MATLAB codes in implementing MIST_based_ITO, which is provided in Online Appendix 1.