The Analysis Of Complex Structures Based On Isogeometric Theory And Multiple Patches Method

The method of isogeometric analysis aims at the effective unity of CAD and CAE.The essential part in this method is that the non-uniform rational B-spline basis functions which are used in the construction modeling are also been used as the shape functions in the mechanical analysis.It can solve the error caused by the inconsistent models using in geometric modeling and analysis modeling effectively.Due to the intrinsic characteristics of the non-uniform rational B-spline function,it is difficult for isogeometric analysis to deal with the complex structures with holes and the like.In this paper,the multiple problem based on isogeometric analysis is deeply studied.Firstly,the basic spline theory is introduced in detail and a explicit introduction of non-uniform rational B-spline theory used in the isogeometric analysis.The pre-processing part of the isogeometric analysis is established by the spline theory which is the establishment of the geometric model and the corresponding modeling steps are given.By introducing the basic principle of isogeometric element,the main differences between traditional finite element method and isogeometric analysis method are given.The overall balance equation of the linear elasticity mechanics problem based on the isogeometric analysis method is deduced through the related theory.Finally,the numerical methods for solving the relevant stiffness matrices are introduced with the combined steps.The principle of conforming multiple patches isogeometric analysis is analysed in detail.The derivation process is given for the solution of the stiffness matrix of different domains in the multiple patches problem and the combination of multiple patches stiffness matrix.Conforming multiple patches programs and conforming multiple patches theory for structural linear elasticity analysis have achieved good results.The theory of heat transfer problems is discretized by isogeometric analysis,and conforming multiple patches isogeometric analysis methods are used to analyze heat conduction problems.The paper reduction the principle of nonconforming multiple patches isogeometric analysis and the detailed derivation process is given for the solution of the stiffness matrix in different domains of nonconforming multiple patches problem and the combination of multi-domains stiffness matrix.Nonconforming multiple patches programs are written andnoncoordinated multiple patches theory is used for isogeometric analysis of structural linear elasticity and heat conduction problems.