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基于等几何分析的超弹性材料模型形状优化

Shape Optimization for Hyperelastic Materials Model Based on Isogeometric Analysis

  • 摘要: 等几何分析作为一种收敛速度快, 数值解高阶连续性好的数值方法, 当今广受工程设计领域关注. 基于其优良的性质, 本工作提出了一种针对超弹性材料模型的等几何形状优化方法. 相较于基于有限元节点的形状优化方法, 具有高效、连续性好的优势. 首先, 在等几何分析框架下推导了对超弹性材料的离散矩阵装配流程, 并给出该非线性系统的求解流程; 其次, 构建了两种目标函数和约束函数下的优化问题, 并给出灵敏度计算的解析形式; 此外, 构建了分析模型和设计模型灵敏度传递方式, 进一步提高优化过程中仿真的精度; 最终, 通过一系列二维和三维算例的形状优化验证了本方法的有效性和可靠性.

     

    Abstract: 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.

     

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