北京大学学报（自然科学版） ›› 2016, Vol. 52 ›› Issue (4): 687-691.DOI: 10.13209/j.0479-8023.2016.086

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Kirchhoff弹性杆不连续量的奇异函数表达

薛纭1, 翁德玮2   

  1. 1. 上海应用技术大学机械工程学院, 上海 201418
    2. 上海大学, 上海市应用数学和力学研究所, 上海 200072
  • 收稿日期:2015-10-10 修回日期:2016-03-16 出版日期:2016-07-20 发布日期:2016-07-20
  • 通讯作者: 薛纭, E-mail: xy(at)sit.edu.cn
  • 基金资助:
    国家自然科学基金(11372195, 10972143)资助

Discontinuous Quantities of Kirchhoff Elastic Rod Expressed by Singularity Function

XUE Yun1, WENG Dewei2   

  1. 1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072
  • Received:2015-10-10 Revised:2016-03-16 Online:2016-07-20 Published:2016-07-20
  • Contact: XUE Yun, E-mail: xy(at)sit.edu.cn

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摘要：

弹性细杆静力学和动力学的Kirchhoff方程要求在外力、质量几何以及本构方程的间断或不光滑点处分段表达, 这不利于数值计算。根据计算梁弯曲变形的奇异函数法, 将奇异函数引入Kirchhoff方程, 将弹性杆分段定义的量拓展为沿全杆的连续函数。借助Mathematica软件, 对存在侧向集中载荷的弹性杆进行数值模拟, 结果表明, 引入奇异函数可以避免分段导致的繁琐计算, 提高计算效率。

关键词: Kirchhoff弹性杆, 不连续量, 奇异函数, 局部载荷, 平衡位形

Abstract:

Kirchhoff equation of thin elastic rod statics and dynamics must be written in piecewise at section with discontinuous or nonsmooth quantities such as external forces, mass geometry and physical parameters, which leads to inconvenience to the numerical calculation. According to singular function method in calculation of beam bending deformation, these discontinuous or nonsmooth quantities of the rod are expressed by singular function and become continues quantities alone centerline of the rod. Numerical simulations of equilibrium configuration of the rod acted by lateral concentrated load are made by means of Mathematics software. Results explain that introducing singular function to express discontinuous or nonsmooth quantities can avoid complicated calculation and improve the computational efficiency.

Key words: Kirchhoff elastic rod, discontinuous quantities, singularity function, local loads, equilibrium configuration

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