差分方程理论的研究On the Theory of Difference Equation
卜万奎,徐慧
摘要(Abstract):
在总结计算数学、弹性力学中有限差分理论,结合向前差分、向后差分和中心差分等,选用二阶精度以上的差分公式,得出弹性体偏微分控制方程、位移分量和应力分量中各个偏导数的差分表达式.
关键词(KeyWords): 差分方程;弹性体;偏导数
基金项目(Foundation): 山东省高等学校科技计划一般项目(J17KB044);; 菏泽学院教学改革一般项目(2016064);菏泽学院培育项目(XYPY02)
作者(Author): 卜万奎,徐慧
DOI: 10.16393/j.cnki.37-1436/z.2018.05.009
参考文献(References):
- [1]Timoshenko S P,Goodier J N.Theory of Elasticity[M].New York:McGraw-Hill Book Company,1979.
- [2]徐芝纶.弹性力学[M].第3版.北京:高等教育出版社,2002.
- [3]Ahmed S R,Hossain M Z,Uddin M W.A general mathematical formulation for finite-difference solution of mixed-boundary-value problems of anisotropic materials[J].Computers&Structures,2005,83(1):35-51.
- [4]Li Z L,Dou L M,Cai W,et al.Investigation and analysis of the rock burst mechanism induced within fault-pillars[J].Int J Rock Mech Min Sci,2014,70:192-200.
- [5]Chen X H,Li W Q,Yan X Y.Analysis on rock burst danger when fully-mechanized caving coal face passed fault with deep mining[J].Safety Sci,2012,50:645-648.
- [6]Jiang Y D,Wang T,Zhao Y X,et al.Experimental study on the mechanisms of fault reactivation and coal bumps induced by mining[J].J Coal Sci Eng,2013,19:507-513.
- [7]Ji H G,Ma H S,Wang J A,et al.Mining disturbance effect and mining arrangements analysis of near-fault mining in high tectonic stress region[J].Safety Sci,2012,50:649-654.