Shape Optimization of Hyperelastic Materials Model for Isogeometric Analysis

Isogeometric analysis, as a numerical method with fast convergence and high-order numerical solutions, has attracted significant attention in the field of engineering design. Based on its excellent properties, a shape optimization method for hyperelastic material models is proposed, focusing on the computation of hyperelastic materials within the isogeometric analysis framework, as well as the corresponding shape optimization method. Firstly, the discrete matrix assembly procedure and the solution process for nonlinear systems are derived within the isogeometric analysis framework. Secondly, mathematical models are defined for hyperelastic materials with the objectives of minimizing compliance and displacement. Furthermore, analytical sensitivities are derived by the dual method to effectively improve optimization accuracy. Finally, an efficient optimization framework is constructed by combining IGA with the method of moving asymptotes. Shape optimization experiments on three benchmark cases of the cantilever beam, plate with a hole, and wrench demonstrate the effectiveness and reliability of the proposed method. In the experiments, the displacement and compliance at specified points can be reduced by 90% and 7% with geometric constraints respectively, which are the same as the expected shapes.