A discontinuous isogeometric reanalysis method and its application in closed-loop optimization problems

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.