Free Boundary Finite Element Method Based On Isogeometric Analysis

The incapable integration of CAD technology and CAE technology,is an important factor to hinder the development of finite element analysis.Hughes et al put forward a new type of numerical calculation method,which is isogeometric analysis(IGA).This method breaks the barrier of mathematical description of non unity between the CAD geometric model and the CAE analytic model,and provides a new way for the seamless integration of CAD technology and CAE technology.This thesis systematically presents the use of B-spline theory and non-uniform rational B-spline theory.The basis function of NURBS can not only accurately express the geometrical model,but the model can be directly used as the subsequent model of analysis or optimization.The refinement of isogeometric analysis model is based on the constructed initial geometric model by NURBS basis function,the refinement can be implemented by knot insertion and order elevation,and the initial geometric shape and parameter can't be changed after the refinement.In this thesis,the refinement methods commonly used in B-spline curves and surfaces,and the special k refinement method in isogeometric analysis are presented.After discussing of B-spline theory and non-uniform rational B-spline theory in this thesis,the similarities and differences between the isogeometric analysis and the conventional finite element analysis are presented,and the basic flow chart of the isogeometric analysis is given as well.According to the application of finite element method in solving the plane problem of elastic mechanics,systematically presents the isogeometric analysis of the plane problem of elastic mechanics based on the NURBS basis function,including the expressions of the element displacement field,stress and strain field and element stiffness matrix based on the NURBS basis function.And an example is given to illustrate the effectiveness and accuracy of isogeometric analysis method in solving plane problems of elastic mechanics.In this thesis,according to the study of the filling and deformation mechanism of the polymer matrix in the nano-imprint process,the theoretical model of nano-imprint flow process is established.After a series of simplifications of the nano-imprint flow process,the continuity equation and momentum equation are presented in the circular runner for the filling phase of nano-pore,and the pressure control equation in nano circular runner is derived.The numerical solution of the pressure field in a one-dimensional circular runner is presented based on the isogeometric analysis method,and compared with the numerical solution obtained by the conventional finite element method.The feasibility of isogeometric analysis method in solving the simulation analysis process of nano-imprint is discussed.