Kirchhoff-Love壳的等几何分析

ISOGEOMETRIC ANALYSIS OF KIRCHHOFF-LOVE SHELLS

论文利用等几何分析研究了基于Kirchhoff-Love理论的薄壳的静态问题.等几何分析采用等参思想,将精确描述几何形状的NURBS基函数同时作为场变量的插值函数,保证了在分析和网格优化过程中模型的几何精确性,并可以轻易地构造任意高阶连续的单元.该方法具有很高的数值精度.计算结果表明,在等几何分析中,NURBS单元的阶次越高,网格数越多,计算结果越精确.

Isogeometric analysis(IGA)based on non-uniform rational B-splines(NURBS)is applied for static analysis of shells with Kirchhoff-Love theory.The basic idea of IGA is that NURBS basis functions,which accurately represent the geometry are directly used as the interpolation functions of the unknown field variables.Thus,the NURBS elements can represent the geometry exactly during the analysis and mesh refinement process.Moreover,it is very easy and straightforward to construct high order NURBS elements.Therefore,IGA significantly improves the computational accuracy.Numerical examples in this thesis show that as the order and number of NURBS elements increase,numerical results become more accurate.