Fast Discontinuous Isogeometric Reanalysis Method

Iso Geometric Analysis(IGA)was a new Finite Element Analysis(FEA)method that proposed by foreign scholars at the beginning of 21^st century.Compared with traditional FEA,IGA performs CAE analysis based on Non-Uniform Rational B-Spline(NURBS)basis function.It realizes the true seamless combination of Computer Aided Design(CAD)and Computer Aided Engineering(CAE)model and provides a theoretical basis for closed-loop optimization.However,due to the limitation of the tensor product form of NURBS basis function,it is easy to cause the discontinuity of model when used to construct complex geometric model.The discontinuity of model will lead to the failure of CAE analysis.To solve this problem and fully take the advantage of IGA on the seamless combination of CAD and CAE,the main work of this paper is as follows:(1)A reanalysis calculation method based on discontinuous isogeometric model is establishBased on Nitsche method,a weak continuity constraint is imposed on the discontinuous boundary to realize the IGA of the discontinuous model.A stress smooth algorithm is developed for singular stress caused by geometric discontinuity.Based on the cubic spline function,the singular stress at the boundary is corrected by the interpolation and the continuity of the stress at the boundary is guaranteed.In view of the multiple computation that may occur in the design process of isogeometric model,the reanalysis technique is introduced to accelerate the solution process.Moreover,the larger the size of the model,the more obvious the improvement of solving efficiency.(2)A fast closed-loop optimization framework for discontinuous isogeometric model is establishedThe reanalysis method for the discontinuous isogeometric model was applied to the optimization problem.For the first time,A fast closed-loop optimization framework for the discontinuous model is built by combining the method with Particle Swarm Optimization(PSO)algorithm.The framework realizes the efficient closed-loop optimization of discontinuous model.It takes the position information of control points as optimization parameters and fully take the advantage of IGA.The stress of structure is optimized directly by modify the coordinates of control points so that the optimal structure can be obtained.(3)A fast calculation program is developed based on the proposed closed-loop optimization frameworkBased on the closed-loop optimization framework,a set of fast calculation program is developed in the Matlab environment and the structure optimization of multi-patch complex discontinuous isogeometric model is realized by using this program.The results of numerical examples show that the displacement and stress errors of the model can be controlled within an acceptable range by the proposed fast reanalysis method for discontinuous isogeometric model and the wall solving time of the optimization problem can be saved by more than 70%.In summary,the fast discontinuous isogeometric reanalysis method proposed in this paper can effectively solve the problems of static analysis and fast structural optimization of discontinuous isogeometric models.This method has a certain reference value for the application of IGA in the practical engineering field.