Some Key Problems On Isogeometry Collocation Method In CAE

High-Precision numerical simulation is the key to intelligent manufacturing and advanced manufacturing.Isogeometric analysis(IGA for short)approach originally proposed by Hughes et al.can use the same geometric representation based on NURBS for all design and analysis tasks.This method has attracted wide attention in the fields of computational mechanics,geometric calculation and computer aided engineering.Isogeometric collocation method(IGA-C)is a new geometric calculation method.Compared with the Galerkin method,it has the advantages of less computation and so on.In this paper,Isogeometric collocation method(IGA-C),Galerkin method(IGA-G)and Isogeometric collocation method using superconvergent points(IGA-SC)are compared.The numerical solutions of the three methods under different parameter fields are compared.Then,the traditional isogeometric collocation method is extended and a generalized isogeometric collocation method is proposed.The main work of this paper is as follows:1.In this paper,the sensitivity of Galerkin method,traditional Isogeometric collocation method and superconvergence Isogeometric collocation method are analyzed.First,for the three methods,different parameterization has an effect on the numerical approximate solution.Therefore,when the boundary control points are given,the boundary control points are kept unchanged,only internal control points need to be changed,and different parameterization schemes are obtained.The numerical variation rates of the three methods under different parameterization are analyzed.Finally,according to the convergence of the three methods and the variation of the global error,it is proved that the traditional Isogeometric collocation method has the characteristics of good stability and high sensitivity to different parameterization.2.In this paper,we propose a generalized Isogeometric collocation framework by geometry-independent field approximation method.In the proposed framework,the spline spaces can be chosen and adapted independently for geometry and the field variables.The proposed method not only can preserve geometric exactness and tight CAD integration as traditional Isogeometric collocation approach,but also can achieve a much more accurate numerical results because of the flexible choice of spline space of solution field.Several numerical examples are presented to show the effectiveness of the proposed generalized Isogeometric collocation method.