基于等几何分析的比例边界有限元方法

提出了一种具有比例边界有限元的半解析特性和等几何分析的几何特性的新方法。该新方法是在比例边界有限元框架中用NURBS曲线或曲面精确描述域边界几何形状,同时域边界位移场采用描述几何形状的NURBS形函数等参构造。这种新方法具有比例边界有限元固有的径向解析特性和NURBS的高阶连续性的优点。数值算例显示,与传统的比例边界有限元相比,基于等几何分析的比例边界有限元方法提高了域边界单元和域内应力场的连续性,减少了计算自由度。应用此方法可以用较少的计算自由度获得更高连续阶和更高精度的位移、应力和应变场。

Scaled boundary finite element method based on isogeometric analysis

This paper presents a new approach,the scaled boundary finite element method based on isogeometric analysis which possesses the semi-analytical feature of scaled boundary finite element method and the exact geometry feature of isogeometric analysis.In this method NURBS basis functions are employed to construct boundary geometry shape and displacement field in the sense of isoparametric concept.This method possesses intrinsic analytical property along radial direction and the higher continuity property of NURBS basis around circumferential directions.Numerical example exhibits that this method rather than traditional scaled boundary finite element method improves continuity and accuracy of stress field across not only boundary elements but also domain elements,costs less DOFs,and obtains more accurate displacement and stress solution.