Research On The Theory And Algorithm Of Geometric Analysis Of Contact Problem

Isogeometrica analysis (IGA) method is a kind of numeric computation method proposed by Professor Hughes in 2005. Its purpose is to achieve unity between CAD and CAE. During processes of both geometric modeling and mechanic analysis, the unified geometric representation is used in IGA, i.e. non-uniform rational B-splines (NURBS) curves and curved surfaces are applied to construct exact geometric model, and meanwhile to be analysis model. IGA can avoid loss of exact geometric information in conventional finite element method (FEM) due to using approximate grids. Under the background of the National Natural Science Foundation Project "Isogeometric Analysis of Sliding Contact between Projectile and Rifle", investigation is concerned with contact analysis by IGA in this thesis.Basic theory of NURBS and IGA is introduced in chapter 2. The algorithm of Isogeometrica analysis is derived based on Galerkin method, which was quite similar to the framework of traditional FEA. Some important concepts such as basis function and its properties are described. The method of building NURBS curve, curved surface and solid are introduced, and some examples are given.An isogeometric framework for the numerical analysis of contact problems is introduced in chapter 3. The code of isogeometric contact analysis is written by Mathematica. The Hertz contact problem is used as a numerical example to validate the isogeometric contact code for 2D problems, and the result is quite similar to the theoretical solution. The influence of the penalty parameter value on calculation precision are discussed, and an augmented method for isogeometric contact problem is evaluated which can alleviate the influence of penalty parameter.The modeling method bsaed on multi-patch NURBS is discussed in this thesis. The isogeometric analysis method is used to analysis the contact problem of involute gear transmission, and the result is compared with traditional finite element analysis results. The contact betwen gun barrel and projectile is analyzed. The correctness of isogeometrica contact analysis is compared with the theoretical solution and the finite element analysis results.In light of 2D dynamic contact problem with friction, dynamic contact detection is carried out on NURBS curves. Numeric computation of dynamic contact between two blocks is conducted, and which can validate the proposed dynamic contact algorithm. Engraving problem with friction is examined, and the resluts from IGA are compared with those from FEA including linear element, and quadratic element, respectively, which illustrates that numeric computation of IGA can reach high precision with less elements than FEM.The preliminary research findings of isogeometric contact analysis in this thesis can provide certain reference to further research of contact problem.