Fast Isogeometric Analysis Method Based On Complex Products

In the process of industrial product research and development,geometric design and performance optimization of products are two inseparable parts,because the research and development of product often needs to meet some certain physical properties.In the traditional research and development process,the CAD model for geometric design and the CAE model for performance optimization are independent of each other,therefore the interactive operation is inevitable.Isogeometric analysis technique carries out the discrete analysis on the spline geometric model directly,which realizes the unification of the CAD/CAE models and avoids the interaction between man-machine interaction in the research and development process.However,in the process of product development,computational cost limits the application of simulation analysis algorithm to a certain extent.Therefore,reanalysis technology is introduced in this paper to accelerate the product development process from the simulation stage.Specific research work is carried out as follows:Based on the existing theoretical formulas of isogeometric analysis and reanalysis techniques,an isogeometric reanalysis solver is proposed.This method is technically not limited by the representation of the CAD model,avoids solving the complete modified equation,saves a lot of computational cost,and expands the application of simulation analysis.In addition,in order to accelerate the convergence of structural local optimization problems,a sensitivity reanalysis method is proposed.At the same time,the validity of the sensitivity reanalysis method is evaluated by speed-up ratio,and the accuracy and efficiency of the method are further verified by numerical examples.Subsequently,the proposed isogeometric reanalysis solver is integrated into the closed-loop optimization framework,and the optimization framework is tested by specific local optimization examples.The results show that the optimization framework can improve the efficiency of large-scale complex problems more obviously under the premise of ensuring the optimization accuracy.In view of the limitation of modifying grid and modifying scale in structural modification,a novel auxiliary projection based MultiGrid-Isogeometric Reanalysis(MG-IGR)method is proposed in this paper.Due to the proposed auxiliary mesh is used to construct the mapping relation of arbitrary modified structures in the optimization process,the proposed isogeometric reanalysis method can be applied to the problem of the optimization of global change without considering the requirement of consistency before and after grid modification.Subsequently,an efficient optimization framework by integrating auxiliary projection based MultiGridIsogeometric Reanalysis(MG-IGR)and metaheuristic searching techniques is developed in this study.In this optimization framework,the parameterized design based on NURBS model can be directly fed back to the evaluation stage,which not only ensures the simulation accuracy,but also accelerates the optimization process.Finally,the high-precision and high-efficiency performance of the optimization framework is verified by the high-dimensional and even global optimization of the actual structural examples.