Shape Optimization for Hyperelastic Materials Model Based on Isogeometric Analysis

Isogeometric analysis (IGA) is a numerical method that has gained significant attention in engineering design due to its fast convergence rate, and high-order continuity of the numerical solutions. This work proposes an IGA-based shape optimization method for hyperelastic material models, which has several advantages over traditional shape optimization methods based on finite element nodes, such as high efficiency and good continuity. Firstly, the discrete matrix assembly process for hyperelastic materials is derived within the IGA framework, and the solution procedure for this nonlinear system is presented. Secondly, two optimization problems with objective functions and constraints are formulated, and analytical expressions for sensitivity calculation are provided. Furthermore, the sensitivity transfer method between analysis and design models is developed to improve the accuracy of simulations during the optimization. Finally, the effectiveness and reliability of the proposed method are demonstrated through a series of 2D and 3D shape optimization examples.