In this study, a DisContinuous IsoGeometric Reanalysis (DCIGR) method is proposed to analyze and optimize the model of Non-Uniform Rational B-Splines (NURBS) patches with non-matching interfaces. In the DCIGR, the Nitsche method is adapted to couple NURBS patches with gaps and the smooth algorithm is developed to correct singular stresses resulting from gaps. However, the additional stiffness matrices (interfacial stiffness matrices) must be calculated when using the Nitsche method, which will inevitably increase the computational cost. Therefore, Combined Approximation (CA) is introduced to reduce the computational cost of the optimization. Theoretically, the larger and more complex a problem is, the more efficient the DCIGR will be. Moreover, since the modifications of the model can be accurately represented by the IGA, the proposed method can be easily integrated with the closed-loop optimization. Compared with existing methods for non-matching interfaces, the DCIGR fully takes the advantage of the IGA and achieves the fast optimization based on the CA. Numerical examples are given to verify the accuracy and efficiency of the proposed method.

中文翻译：

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不连续等几何重分析方法及其在闭环优化问题中的应用


在本研究中，提出了一种不连续等几何重分析（DCIGR）方法来分析和优化具有非匹配界面的非均匀有理B样条（NURBS）面片模型。在 DCIGR 中，Nitsche 方法适用于将 NURBS 面片与间隙耦合，并开发平滑算法来校正由间隙产生的奇异应力。然而，使用Nitsche方法时必须计算附加的刚度矩阵（界面刚度矩阵），这不可避免地增加了计算成本。因此，引入组合逼近（CA）来降低优化的计算成本。理论上，问题越大、越复杂，DCIGR 的效率就越高。此外，由于模型的修改可以通过 IGA 准确地表示，因此所提出的方法可以很容易地与闭环优化集成。与现有的非匹配接口方法相比，DCIGR充分发挥了IGA的优势，实现了基于CA的快速优化。给出数值例子来验证该方法的准确性和效率。