含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析  

ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR ELASTIC BUCKLING OF CRACKED CIRCULARLY CURVED BEAMS

作　　者：王永亮[1,2] WANG Yong-liang(School of Mechanical and Civil Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China;State Key Laboratory of Coal Resources and Safe Mining,China University of Mining and Technology(Beijing),Beijing 100083,China)

机构地区：[1]中国矿业大学(北京)力学与建筑工程学院,北京100083 [2]中国矿业大学(北京)煤炭资源与安全开采国家重点实验室,北京100083

出　　处：《工程力学》2021年第2期8-15,35,共9页Engineering Mechanics

基　　金：国家自然科学基金项目(41877275,51608301);中央高校基本科研业务费专项资金项目(2019QL02);天津市重点实验室开放课题基金项目(2017SCEEKL003);中国矿业大学(北京)越崎青年学者计划项目(2019QN14)。

摘　　要：该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实现裂纹大小(深度)、位置、数目的模拟。引入变截面Euler-Bernoulli梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁弹性屈曲问题,得到优化的网格和满足预设误差限的高精度屈曲荷载和屈曲模态解答。数值算例表明该算法中网格非均匀加密可适应裂纹损伤引起的屈曲模态变化,应用于各类曲梁夹角和裂纹损伤分布工况下的弹性屈曲研究,定量分析了裂纹损伤程度对圆弧曲梁的屈曲荷载和屈曲模态的影响,检验了该文算法的精确性和可靠性。The scheme for the cross-section damage defects in circularly curved beam is established to simulate the magnitude(depth),location and number of the cracks.The h-version adaptive finite element method for nonuniform Euler-Bernoulli beam is introduced to solve the elastic buckling of circularly curved beam with cracks.Using the proposed method,the final optimized meshes and high-precision buckling loads and modes meeting the preset error tolerance can be obtained.Numerical examples show that the non-uniform mesh refinement can adapt to the change of buckling mode induced by crack damage,which is applied to the elastic buckling analysis for some typical kinds of subtended angles and crack damage distribution conditions of circularly curved beams.Furthermore,the influence of crack damage on the buckling load and mode of circular curved beams is quantitatively analyzed,and the accuracy and reliability of the proposed algorithm are verified.

关 键 词：裂纹损伤 圆弧曲梁 弹性屈曲 超收敛拼片恢复 网格自适应划分 有限元法 

分 类 号：O242.21[理学—计算数学]