开挖模拟在数值流形方法中的实现  

Simulation of excavation in numerical manifold method

作　　者：焦健[1] 乔春生[1] 徐干成 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044 [2]空军工程设计研究局,北京100068

出　　处：《岩土力学》2010年第9期2951-2957,共7页Rock and Soil Mechanics

基　　金：国家自然科学基金资助项目(No.50478061)

摘　　要：针对数值流形方法特有的覆盖剖分方式,提出了一种模拟岩土工程中开挖过程的算法。该算法采取某种措施,在覆盖剖分过程中将开挖面视为特殊的不连续面,这种不连续面将其所在的数学网格剖分成不同的流形单元,但却不对所在的数学覆盖作剖分。这样,开挖面两侧虽分属不同的流形单元,但开挖面两侧同一数学网格内的流形单元却具有相同的物理覆盖。采用该算法,无需对开挖面处的单元进行特殊处理,可在整个分析域采用统一的网格形式;同时,打破了原有数值流形方法的限制,将开挖面的位置完全当作连续介质来处理,避免了因将其视为不连续面而产生的误差。验证了算法的可靠性后,将其应用于某假想隧道的开挖模拟,计算结果表明该算法具有一定的应用前景。An algorithm that can simulate the excavation problem in numerical manifold method（NMM） is proposed according to the special cover system of NMM.In this algorithm,the excavation face is considered as a special kind of discontinuity that divides the mesh it crosses into different elements but doesn’t divide the mathematical cover it crosses.Such manner ensures that the elements on both sides of the excavation face are independent while the elements in the same mesh still have the same physical covers.So the algorithm retains the advantage of NMM that a uniform mesh can be competent to any geometrical conditions,and break the limitation of NMM that the excavation face must be treated as real discontinuity,which will result in unavoidable error.After being verified,the algorithm was used in an excavation simulation of a tunnel;and the results prove that the algorithm has a wide range of application.

关 键 词：数值流形方法 覆盖剖分 开挖模拟 开挖释放荷载 

分 类 号：O176[理学—数学]