力学与实践 ›› 2020, Vol. 42 ›› Issue (6): 794-796.DOI: 10.6052/1000-0879-20-049

• 教育研究 • 上一篇    下一篇

推导弹性力学极坐标中平衡微分方程和几何方程的解析法

陈彦1), 陈丰2), 邵红才3)   

  1. 扬州市职业大学土木工程学院,江苏扬州 225000
  • 收稿日期:2020-02-11 修回日期:2020-03-31 出版日期:2020-12-20 发布日期:2020-12-20
  • 通讯作者: 1)陈彦,讲师,主要从事工程力学与弹性力学等方面的教学与研究工作。E-mail: 363111098@qq.com;
    2) 陈丰,讲师,主要从事结构设计原理等方面的教学与研究工作。E-mail: chen2496@qq.com;
    3)邵红才,讲师,主要从事结构力学与岩土工程等方面的教学与研究工作。E-mail: 30368191@qq.com

ANALYTICAL METHOD FOR DERIVING EQUILIBRIUM DIFFERENTIAL EQUATIONS AND GEOMETRIC EQUATIONS OF ELASTICITY IN POLAR COORDINATES

CHEN Yan1), CHEN Feng2), SHAO Hongcai3)   

  1. School of Civil Engineering, Yangzhou Polytechnic College, Yangzhou 225000, Jiangsu, China
  • Received:2020-02-11 Revised:2020-03-31 Online:2020-12-20 Published:2020-12-20

摘要: 根据直角坐标和极坐标中偏微分算子的转换式、应力和应变分量的坐标变换式以及基矢量变换矩阵,提出了推导极坐标中平衡微分方程和几何方程的解析法,不需要作图,可以从直角坐标中的平衡微分方程和几何方程直接导出极坐标中的方程形式,丰富了弹性力学课程教学内容。

关键词: 偏微分算子转换式, 应力分量坐标变换式, 应变分量坐标变换式, 基矢量变换矩阵

Abstract: According to the transformation of the partial differential operator in rectangular and polar coordinates, the coordinate transformations of the stress and strain components, and the basis vector transformation matrix, an analytical method for deriving equilibrium differential equations and geometric equations in polar coordinates is proposed. No drawing is needed, the equations in polar coordinates can be directly derived from the equilibrium differential equations and geometric equations in rectangular coordinates, and the teaching content of elasticity course is enriched.

Key words: partial differential operator transformation, stress component coordinate transformation, strain component coordinate

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