Efficient MATLAB implementation of NURBS-based IGA and material design using isogeometric topology optimization

In this paper, we present compact and efficient MATLAB codes for NURBS-based IGA and material design using isogeometric topology optimization. We make full use of the advantages of MATLAB in the vector and matrix computation and calculate the span indexes of and NURBS basis functions at multi-parameters simultaneously, so that the efficiency in generating IGA element and global stiffness matrices can be increased significantly. Based on the presented IGA MATLAB codes, we apply the IGA-based SIMP topology optimization into material design with extreme properties, such as shear modulus maximization and negative Poisson's ratio, where the effective macroscopic elasticity tensor is calculated by the energy-based homogenization approach. Numerical examples demonstrate the efficiency of the presented codes in generating stiffness matrices and the effectiveness in material optimization design. All the codes are included as appendixes.