Research On New Types Of Isogeometric Analysis Method For Complex Geometries

Finite element analysis?FEA?plays an important role in the geometric design of large-scale machinery,engineering construction and other fields,With the rapid development of surface modeling technology,the limitations of finite element hinder its development and application.Isogeometric analysis was proposed to overcome the limitations of the traditional finite element analysis,not only the accuracy of the analytical model can be improved,but also the efficiency of analysis and numerical accuracy are greatly improved.In this paper,some new types of isogeometric Analy-sis method for complex geometries were proposed under the context of isogeometric analysis.The main contents includes three aspects:?1?Based on the theory of B-spline,a novel patch-merging method to construct high-precision single-patch representation from a multi-patch representation is explored explored.The proposed method can achieve high-continuity at surface stitching region,and the merging error of proposed method is smaller than the direct merging approach by fitting sampling points with given boundaries while the local feature of the surface can be well-preserved with high precision.By the proposed patch-merging method,we can get more accurate isogeometric analysis results with the new single-patch compared with the original multi-patch structure.Several examples are presented to illustrate the effectiveness of the proposed method.?2?Trimmed technology is an effective way to generate complex geometric models.In this paper,we present a new method to improve one of the trimmed isogeometric analysis.The improved isogeometric analysis?IGA?approach proposed in this paper can reduce the numerical error of physical solution by 50%for simple trimmed geometries,and the condition number of stiffness matrix is also decreased.Furthermore,the number of integration elements and integration points involved in the solving process can be significantly reduced compared to previous approaches,drastically improving the computational efficiency for IGA problems on the trimmed geometry.?3?A new unified approach to construct the generalized non-uniform B-splines over the space spanned by{??t?,??t?,??t?,??t?,1,t,?43?,t^n-4}is proposed,and the corr-esponding corresponding isogeometric analysis framework for PDE solving is also studied.Geometric analysis is proposed based on NURBS basis functions.However,NURBS is a rational function,it is difficult to calculate the partial differential and integral of NURBS.In addition,they play an important role in mechanical engineering,such as the involute of circle,the helix,helicoid,the catenary,catenoid and the cycloid,and they can not be accurately expressed with NURBS.In this paper,we propose several generalized splines that are not polynomial spaces and can be used for geometric modeling and IGA.Compared with the NURBS-IGA method,the proposed framework has the advantages of high accuracy,easy calculation of derivatives and integrals.In addition,for the proposed spline model,isogeometric analyzes such as round involutes,helices,catenaries,and cycloid can be performed on the computational domain.