Euler梁弯曲分析的无网格高阶曲率光顺方案  

High order curvature smoothing scheme for meshfree Euler beam bending analysis

作　　者：王冰冰[1] 段庆林[1] 李锡夔[1] 张洪武[1] 杨迪雄[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《计算机辅助工程》2017年第4期1-6,共6页Computer Aided Engineering

基　　金：科学挑战计划(JCKY2016212A502);国家自然科学基金(11232003;11372066);中央高校基本科研业务费专项资金(DUT15LK07);水资源与水电工程科学国家重点实验室开放基金(2015SGG03);地质灾害防治与地质环境保护国家重点实验室开放基金(SKLGP2016K007)

摘　　要：针对Euler梁弯曲问题的无网格法数值求解,提出与挠度近似相一致的高阶曲率光顺方案。采用耦合权函数方法准确施加固定挠度边界条件,并在曲率光顺过程中引入转角边界条件。数值计算结果表明:该方案能精确反映纯弯曲模式和线性弯曲模式;与标准的高斯积分及现有的常曲率光顺方案相比,该高阶曲率光顺方法可显著改善该类问题的数值求解精度。A high order curvature smoothing scheme which is consistent with the approximation of the deflection is proposed in the meshfree analysis of Euler beam bending problems. The boundary condition of constant deflection is imposed by coupling with weight function,and the rotation boundary condition is imposed in the process of curvature smoothing. The numerical calculation results show that,the scheme can accurately reflect the pure bending mode and the linear bending mode; in comparison with the standard Gauss integration method and the existing constant curvature smoothing method,the proposed high order curvature smoothing method remarkably improves the solution accuracy of such problems.

关 键 词：Euler梁 曲率光顺 数值积分 无单元伽辽金法 梁单元 耦合形函数 高阶近似 

分 类 号：O302[理学—力学]