Isogeometric Analysis Base On UE Splines

In the recent years,isogeometric analysis is frequently seen in mechanical and physical simulation.The basis function of CAD which describes the geometric is applied to numerical solution.The most commonly used basis function in geometric analysis is NURBS,mainly because it can represent the majority of general-purpose figures and builds geometric models accurately.In this paper,we propose an isometric analysis based on UE splines.UE splines have all the good properties of NURBS.They not only can accurately represent the geometric model generated by NURBS,but also can represent the triangular polynomial mixed curve and hyperbolic polynomial mixed curves which can not been represented accurately by NURBS.In addition,UE splines is non-rational form and is easier to do the calculation on the evaluation and derivation than NURBS.This paper mainly takes the Poisson and linear elastic problems in two-dimensional and three-dimensional models for examples and introduces the isogeometric analysis frame and its detailed introduction.Firstly,the problem domain is modeled by using UE splines.Based on the concept of isoparametric element,UE spline is also used as the basis function of numerical method solution domain to solve Poisson and linear elasticity problems of single boundary conditions and mixed boundary conditions.The experiments compared with the NURBS have witnessed the superiority and effective of our proposed algorithm.Subsequently,the isogeometric analysis based on UE splines was applied to the fluid and electromagnetic field problems.Extensive experiments on other examples have given to further prove the feasibility of the isogeometric analysis based on UE splines in multi-field.