基于HB样条的平面大变形结构动力学等几何分析  

Isogeometric Analysis with Hierarchical B-Splines for Planar Structural Dynamics with Large Deformation

作　　者：荣吉利[1] 熊丽园 刘铖[1] 辛鹏飞[1,2] 刘志超 RONG Ji-li;XIONG Li-yuan;LIU Cheng;XIN Peng-fei;LIU Zhi-chao(School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;Institute of Spacecraft System Engineering, Beijing 100094,China;Science andTechnology on Space Physics Laboratory, Beijing 100076,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]北京空间飞行器总体设计部,北京100094 [3]空间物理重点实验室,北京100076

出　　处：《北京理工大学学报》2020年第6期592-601,共10页Transactions of Beijing Institute of Technology

基　　金：民用航天预研项目(D020205);国家自然科学基金资助项目(11672034)。

摘　　要：为实现大变形结构动力学问题中的网格自适应算法,研究了等几何分析中的层次B样条(HB样条)基函数构造以及多层贝塞尔提取方法问题,并将多层贝塞尔提取方法用于HB样条建模分析以实现形函数的统一.同时,采用超收敛修复方法(SPR)获得修复应力作为参考值,通过误差估计获取系统的能量范数误差,给出网格细化区域.最后,通过带圆孔平板静力学与平面大变形结构动力学算例,验证了基于HB样条等几何分析方法的有效性和准确性.In order to develop the adaptive mesh refinement algorithm for planar structural dynamics with large deformation,the construction of hierarchical B-spline basis functions for isogeometric analysis and the multi-level Bézier extraction approach restudied.In order to maintain the uniformity of element basis functions,the multi-level Bézier extraction approach was employed to present a standard element structure for the hierarchical B-spline during analysis process.Furthermore,the super-convergence patch recovery method was applied to obtain the reference stress in the adaptive analysis.Therefore,the refinement domain determined based on the energy norm error,which calculated via the reference stress and the numerical stress during the error estimation.Finally,the effectiveness and accuracy of the isogeometric analysis based on the hierarchical B-spline are validated by a static example of an elastic plate with circular hole and a planar structural dynamic example with large deformation.

关 键 词：等几何分析 HB样条 多层贝塞尔提取方法 局部细化 

分 类 号：O313.7[理学—一般力学与力学基础]