分数阶黏弹性有限元及其在围岩变形中的应用  

Research of Fractional Order Viscoelasticity Meshless Method and the Application of the Surrounding Rock in Computing Deformation

作　　者：陈家瑞[1] 顾文虎[1] 张鹏 常建强 CHEN Jia-rui;GU Wen-hu;ZHANG Peng;CHANG Jian-qiang(Faculty of Architecture and Civil Engineering,Huaiyin Institute of Technology,Huai'an Jiangsu 223001,China;Changzhou City Investment Construction Project Tendering CO.,LTD,Changzhou Jiangsu 213000,China)

机构地区：[1]淮阴工学院建筑工程学院,江苏淮安223001 [2]常州市城投建设工程招标有限公司,江苏常州213000

出　　处：《淮阴工学院学报》2019年第5期1-4,共4页Journal of Huaiyin Institute of Technology

基　　金：国家自然科学基金资助项目(51904113);江苏省住建厅指导项目(2017ZD246,2015ZD49);淮安市自然科学研究计划项目(HAB201708,Z413B18327)

摘　　要：在经典力学所得到的黏弹性动力学方程的基础上,引入分数阶微积分基本理论,获得了分数阶黏弹性动力学方程。与有限单元法基本理论相结合,最终获得分数阶黏弹性有限单元法的方程表达式。参考整数阶New-mark积分方法,获得了分数阶New-mark的积分方案与数值实现方法。计算了开孔为巷道形状的无限大平面弹性区域的算例,对比了黏弹性有限单元法的整数阶与分数阶形式的计算数据。验证结果表明分数阶粘弹性有限单元法具有分数阶流变模型平稳的优势,同时又有比有限元法更好的收敛精度。Based on the viscoelastic dynamic equations obtained by classical mechanics,the basic theory of fractional calculus is introduced and the fractional viscoelastic dynamic equations are obtained.Combined with the basic theory of the finite element method,the equation expression of the fractional-order viscoelastic finite element method is finally obtained.With reference to the integer-order New-mark integration method,the integral scheme and numerical implementation method of the fractional New-mark are obtained.An example of an infinitely large plane elastic region in which the opening is a tunnel shape is calculated.The calculation data of the integer and fractional forms of the viscoelastic finite element method are compared.It is verified that the fractional-order viscoelastic finite element method has the advantage of fractional flow rheological model stationary,and it also has better convergence precision than finite element method.

关 键 词：围岩变形 分数阶微积分 有限单元法 黏弹性模型 

分 类 号：TD311[矿业工程—矿井建设]