Research On Isogeometric Analysis Methods Such As Trimmed Model Based On PHT Splines

In Isogeometric Analysis(IGA),the basis functions in Computer Aided Design(CAD)are used to discretely solve Partial Differential Equations(PDE).Non-Uniform Rational B-Splines(NURBS)is commonly used in CAD systems.However,their full tensor product form does not exist in trimming,and it is not suitable for IGA directly.In order to solve this problem,this paper attempts to introduce spline called polynomial splines over hierarchical T-meshes(PHT)into IGA.Based on the principle of PHT local refinement,this paper gives isogeometric analysis methods such as PHT spline based trimmed models from three aspects: modeling,analysis and solution.The main work are as follows:1.The corresponding isogeometric analysis model is constructed by PHT spline for the trimmed solid geometry model.Firstly,the basic three parameter PHT spline is constructed based on the geometric information of the original CAD solid model.Then,according to the classification rules of refinement elements relative to the trimmed surface,the original CAD model is decomposed into multi-level approximate trimmed model with three parameter information.2.An isogeometric analysis method for trimmed model based on PHT is proposed.Based on the idea of fitting reconstruction,the approximation method and data update strategy of the trimmed model are given,and then obtains the analysis space of the trimmed model.In terms of stiffness calculation,a special element assembly algorithm suitable for PHT trimming analysis is specially proposed.At the same time,the stiffness correction algorithm improves the calculation efficiency of the elements near the trimmed surface.In addition,the natural boundary conditions are loaded in an equivalent way to realize the weak loading of trimmed analysis.Finally,this paper attempts to give an adaptive PHT spline analysis method based on splicing to deal with the trimmed model of simple topology,which is used as a supplement to the trimmed analysis method.3.Research on iterative solution method of discrete equations obtained from isogeometric analysis such as trimmed model.Taking the method of this paper as the object of discrete assembly to obtain the total stiffness matrix,try to use the Algebraic Multigrid(AMG)method to calculate the trimmed stiffness matrix,and compare it with the convergence and stability of other common iterative algorithms.In addition,this paper compares and summarizes the efficiency of AMG algorithm from different decomposition levels and spline orders of the trimmed model.This paper attempts to propose a complete process of geometric analysis methods such as the PHT of the trimmed model.The method realizes the IGA and adaptation process of the trimmed model,and partially solves the needs of local refinement of the trimmed region.Based on the algorithm of this paper,IGA can be used in more complex engineering analysis.