基于数值计算方法的非均匀有理B样条性质分析  

Analyses on the Properties of Non-uniform Rational B-spline by Numerical Calculation Method

作　　者：王霄腾 薛齐文[1] WANG Xiao-teng;XUE Qi-wen(School of Civil and Safety Engineering,Dalian Jiaotong University,Dalian 116021,China)

机构地区：[1]大连交通大学土木与安全工程学院,大连116021

出　　处：《科学技术与工程》2018年第17期1-6,共6页Science Technology and Engineering

基　　金：国家自然科学基金(10802015);辽宁省自然科学基金联合基金(2015020119)资助

摘　　要：针对等几何分析(IGA)中替代传统多项式差值函数进行结构分析的非均匀有理B样条(NURBS)基函数,采用数值计算的手段对其主要性质进行讨论。通过数值算例,分别对NURBS基函数的非负性、参数性、局部支撑性以及高阶连续性进行了验证和分析。数值算例结果不仅从数值计算角度验证了NURBS基函数的主要性质;还验证了所建数值分析模式的有效性和可行性;并对NURBS基函数及其导数的性质给出了较为详细的说明,可为相关研究人员对新型数值计算模型的提出提供一个新的方向。NURBS＇s key characteristics are investigated by numerical calculation methods based on the isogeometric analysis（ IGA） and NURBS is adopted for structural analysis instead of conventional polynomial difference function. By analyzing numerical cases,some properties of NURBS such as nonnegativity,parameterization,local support and high-order continuity are verified separately. From conclusions from selected cases,the main properties of NURBS are numerically verified and the numerical analysis model built by author is proved to be valid and feasible. Furthermore,the detailed characteristics of NURBS and its derivatives may provide future researchers with different approaches to propose new numerical calculation models.

关 键 词：非均匀有理B样条 基函数 数值计算 等几何分析 

分 类 号：O157.1[理学—数学]