Research On Parameterization Of Complex Planar Regions For Isogeometric Analysis

Isogeometric analysis(IGA)is a new numerical analysis method proposed by professor T.J.R.Hughes of the University of Texas at Austin in 2005,which unifies the geometric and simulation analysis models using spline representation.It improves the accuracy and efficiency of analysis.However,the geometric model generated by modern CAD software is usually a boundary spline representation,and the internal information of the model is unknown.The process of obtaining the overall representation of the model from a given boundary is called isogeometric analysis parameterization.The quality of parameterization affects the accuracy and speed of convergence of the isogeometric analysis.Although there are a number of well-established methods to produce high quality parameterization results for isogeometric analysis,there are still some unresolved issues:(1)Existing methods of parameterization do not take geometry similarity into account,hence parameterization of two similar domain cannot establish a one-to-one correspondence between them.(2)Existing methods of parameterization do not consider internal features where constraints are required in some applications.The study of parameterization with constraints can meet specific requirements in analysis,and has certain theoretical and practical value.This paper discusses these problems for complex planar models,and the main work of this paper is summarized as follows:1.A parameterization transfer for planar computational domain is proposed which is suitable for isogeometric analysis.First,this paper establishes a one-to-one correspondence between the original model and the target model boundary through boundary registration.Then,discrete harmonic mapping is performed to transform the parameterization results of source model to the target.Experiments show that for two similar models,high quality parameterization transfer results are obtained by the method proposed in this paper.The resulted parameterization is C1 continuous in the regular region and G1 continuous around singular points.And we demonstrate that the result of parameterization transfer in this paper is appropriate for isogeometric analysis.2.A parameterization method for complex planar models with constraints is proposed.Firstly,we classify the features according to their location;Then,patches around the constraints are moved smoothly based on an RBF interpolation;Finally,quality of the parametrization of the model is optimized to obtain better parametrization result while the constraint is satisfied.Experiments show that the method yields high quality parametric results.It makes a given feature lies at the boundary of the internal patch of the model and is suitable for isogeometric analysis.