基于曲梁弹性理论的弯曲覆岩变形及应力分析

卜万奎; 徐慧; 赵玉成

doi:10.21656/1000-0887.400081

基于曲梁弹性理论的弯曲覆岩变形及应力分析

doi: 10.21656/1000-0887.400081

¹菏泽学院城市建设学院, 山东菏泽 274015;²中国矿业大学力学与土木工程学院, 江苏徐州 221116

基金项目: 国家自然科学基金(面上项目)（51574228）；山东省高等学校科研发展计划一般项目（J17KB044）

详细信息

作者简介:
卜万奎（1980—），男，教授，博士（通讯作者. E-mail: bwk239@126.com).

中图分类号: O343
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- 被引次数: 0
出版历程
- 收稿日期: 2019-03-01
- 修回日期: 2019-04-02
- 刊出日期: 2020-03-01

Analysis on Deformation and Stress of Bending Stratum Based on the Elastic Theory for Curved Beams

¹College of Urban Construction, Heze University, Heze, Shandong 274015, P.R.China;²School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P.R.China

Funds: The National Natural Science Foundation of China(General Program)（51574228）

摘要

摘要: 引入适用于极坐标下曲梁的位移函数，通过理论分析得出用位移函数表示的曲梁控制方程和位移分量、应力分量.在此基础上，采用差分原理给出曲梁控制方程、位移分量和应力分量的差分代数方程.最后，采用数值计算方法，分析了煤层开采后弯曲覆岩的位移和应力分布特征，结果表明：1）煤层开采后弯曲覆岩产生下沉变形；弯曲岩层环向位移既有拉伸也有压缩.2）离开切眼不远处径向应力将达到峰值，径向应力由内边界向外逐渐增大；工作面后方不远处环向应力将达到峰值，环向应力较容易引起压缩破断；离开切眼不远处剪应力将达到峰值，对于小角度截面上的剪应力由内边界向外逐渐增大.研究结果为煤矿工程提供了科学依据与参考.
- 曲梁 /
- 弹性力学 /
- 有限差分 /
- 覆岩变形 /
- 应力分析
Abstract: A displacement function suitable for plane curved beams in polar coordinates was introduced, and the partial differential governing equation for plane curved beams was obtained through theoretical analysis. Then, the displacement components and stress components were formulated with the displacement function. On this basis, the finite difference schemes of the partial differential governing equation, the displacement components and the stress components for the curved beam in polar coordinates were presented. Finally, these theoretical formulas were applied to analyze the displacement and stress distributions of the bending stratum. The results indicate that: 1) The bending stratum sinks down after excavation of the coal seam, and there are both tension and compression in the circumferential direction. 2) The radial stress reaches a peak value not far from the openoff cut and increases gradually from the inner surface to the outer surface along the radial direction; the circumferential stress reaches the peak value not far behind the working face and may cause circumferential compressive fracture in the bending stratum; the shear stress reaches the peak value not far from the openoff cut and increases from the inner surface to the outer surface along the radial direction for smallangle sections. The work provides a scientific basis and reference for coal mining engineering.
- curved beam /
- theory of elasticity /
- finite difference /
- deformation of overburden rock /
- stress analysis

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