Spline Volume Interpolation And Conversion Method For Iso-geometric Analysis

Finite element analysis is the most widely used numerical algorithm in engineering analysis today.In the process of finite element analysis,it has well versatility,so it becomes a hot topic in academia.Along with the rapid development of computer science and technology,the finite element analysis method has become an important part of CAE and CAD system.In 2005,Hughes et a,proposed a new type of finite element method:Isogeometric Analysis.Its purpose is to achieve seamless integration of engineering and design,to achieve the unity of design and analysis.Today,the field of geometric modeling focuses on the study of surface problems,while the research on the body is relatively small.In this paper,in order to solve the geometric analysis of the curved body modeling and conversion methods of existing problems,mainly from the following aspects of the study:(1)In this papaer,I propose two methods to model B-spline volume for isogeometric analysis.In the geometric analysis,the basic geometric shapes of the solid are three-variable tensor product volume and three-variable tetrahedron.Therefore,I study the interpolation method of three-variable tensor product volume and the three-variable tetrahedron interpolation method.In the interpolation method of three-variable tensor curves volume,using six hexahedrons as input data for the hexahedral construction method and using four tetrahedrons as input data for the three-variable tetrahedral construction method,and combined with the correction terms is patched so that both the volume constructed with these two interpolation methods and each input satisfy the interpolation along the boundary.The volume constructed by this method not only has its shape changed according to the boundary data but also its internal grid of control points is related to the shape of the input volume and the material properties.(2)In this paper,I propose two transformation methods of B(?)zier tetrahedron and B(?)zier hexahedron for three-dimensional geometric analysis are proposed in this paper,which provide an effective solution to the problem of mutual transformation between different geometric representations.In the first method,a B(?)zier tetrahedron can be transformed into a degenerate B(?)zier hexahedron of the same order.In the second way,a regular B(?)zier tetrahedron can be transformed into four regular B(?)zier hexahedra.For each of these two methods,I give the control point sets that show the calculation formulas for calculating the B(?)zier volume of the transformed tensor product.In addition,for the second method,I show that the contiguity is satisfied G~k continuous after the transformation from a group of C~k continuous B(?)zier tetrahedra into a set of B(?)zier hexahedra.