| 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 |
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| 引用本文： | 陈彦, 陈丰, 邵红才. 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[J]. 力学与实践, 2020, 42(6): 794-796. doi: 10.6052/1000-0879-20-049 |
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| 作者姓名： | 陈彦 陈丰 邵红才 |
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| 作者单位： | 扬州市职业大学土木工程学院,江苏扬州 225000 |
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| 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。
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| 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 |
| 收稿时间： | 2020-02-11 |
| 修稿时间： | 2020-03-31 |
ANALYTICAL METHOD FOR DERIVING EQUILIBRIUM DIFFERENTIAL EQUATIONS AND GEOMETRIC EQUATIONS OF ELASTICITY IN POLAR COORDINATES |
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| CHEN Yan, CHEN Feng, SHAO Hongcai. ANALYTICAL METHOD FOR DERIVING EQUILIBRIUM DIFFERENTIAL EQUATIONS AND GEOMETRIC EQUATIONS OF ELASTICITY IN POLAR COORDINATES[J]. Mechanics in Engineering, 2020, 42(6): 794-796. doi: 10.6052/1000-0879-20-049 |
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| Authors: | CHEN Yan CHEN Feng SHAO Hongcai |
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| Affiliation: | School of Civil Engineering, Yangzhou Polytechnic College, Yangzhou 225000, Jiangsu, China |
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| 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. |
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| Keywords: | partial differential operator transformation stress component coordinate transformation strain component coordinate |
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