增强有限元法及其在岩土工程非连续变形分析中的应用
发布时间：2018-07-20 12:31
【摘要】：剪切带是岩土工程灾变的常见形式,精确再现剪切带产生和扩展过程对揭示岩土工程灾变机理、制定灾害防控措施具有十分重要的意义。剪切带问题实质上是一类粘聚裂纹动态扩展问题,其模拟涉及非连续变形分析,是目前的热点研究课题之一。论文针对非连续变形及其扩展模拟中存在的若干关键问题开展研究,提出了一种基于网格分离的位移插值技术及增强有限元法,及基于增强有限元法、适合任意剪切带扩展模拟的非连续变形描述及网格自适应方法,并应用于断层错动导致上覆土层破裂问题的分析。主要研究成果如下： (1)将常规有限元网格分离为几何上相互独立的用于构造位移插值的数学网格和离散分析域的物理网格,提出了以网格分离和位移映射法则为核心的有限元位移插值技术,形成了基于常规有限元法的增强有限元法理论框架。数学网格和物理网格的几何分离与位移映射法则的引入使得网格剖分、良好性态的位移插值函数的构造更易实现,极大地增强了有限元法的灵活性和适用性。常规有限元法是增强有限元法的特殊形式,增强有限元法是常规有限元法的增强形式。 (2)引入过渡单元,提出了由关联数学单元与过渡单元位移的重构规则Rr和关联过渡单元与物理单元位移的覆盖规则Rc构成的统一映射法则。导出了增强有限元法的基本列式、光滑应力计算方法和单元元素矩阵的积分技术,给出了基于常规有限元软件的增强有限元实现方法。 (3)基于统一映射法则,借鉴无网格法、半解析有限元法等的近似位移场构造思想,提出了与之相应的重构规则,从而使得增强有限元法兼具无网格法、半解析有限元法和光滑有限元法的优点。此外,论文还基于增强有限元法提出了一种适用于移动边界问题的固定网格求解方法。 (4)保持位移映射法则不变,通过富集数学节点和过渡节点分别为裂纹穿越后形成的两个物理单元构造相应的过渡单元和数学单元,提出了适于描述穿越单元内部的非连续变形和模拟任意多裂纹扩展的方法,突破了常规有限元法必须将裂纹设置为单元边界的局限性,克服了扩展有限元法和Hansbo＆Hansbo法在处理几何关系复杂的多裂纹扩展问题时近似位移场构造上的困难。 (5)提出了在单元级别上处理任意阶非规则节点的统一方法,建立了以裂尖单元尺度和裂尖影响范围为控制参数、基于单元细划的裂纹动态扩展模拟网格自适应策略。分析结果表明,网格自适应技术提高了粘聚裂纹尖端附近应力场的计算精度和裂纹扩展过程的分析精度；裂尖附近的网格密度对荷载-位移曲线影响较大,但是对裂纹扩展路径的影响不大。 (6)提出了利用摩擦型粘聚区域模型表征剪切带粘聚力-剪切位移间的软化特性和剪切带能量耗散机制、利用增强有限元法描述非连续变形的土体剪切带扩展过程模拟方法。通过数值直剪试验确定粘聚区域模型本构参数,数值再现了断层错动导致上覆土层破裂的离心机试验结果,对比研究了流动法则和剪切带软化特性对上覆土层破裂的影响规律,分析结果表明基于关联流动法则确定的剪切带倾角更接近试验结果。
[Abstract]:The shear zone is a common form of rock - soil engineering disaster . It is of great significance to reveal the mechanism of shear band generation and expansion to reveal the catastrophe mechanism of geotechnical engineering and to establish disaster prevention and control measures . The simulation involves discontinuous deformation analysis , it is one of the hot research topics .
( 1 ) The traditional finite element mesh is separated into a physical grid which is geometrically independent and used to construct displacement interpolation , and a finite element displacement interpolation technique based on the conventional finite element method is proposed . The geometric separation and displacement mapping rules of the mathematical grid and the physical grid are introduced so that the structure of the displacement interpolation function is easier to realize , and the flexibility and applicability of the finite element method are greatly enhanced . The conventional finite element method is a special form of the reinforcement finite element method , and the reinforcement finite element method is the reinforcement form of the conventional finite element method .
( 2 ) Introducing the transition unit , this paper proposes a unified mapping rule consisting of the reconstruction rule Rr of the displacement of the associated mathematical unit and the transition unit and the covering rule Rc of the displacement of the associated transition unit and the physical unit . The basic determinant , the smooth stress calculation method and the integral technique of the element matrix are derived . A method for enhancing the finite element method based on the conventional finite element software is presented .
( 3 ) Based on the unified mapping rule , this paper presents the corresponding reconstruction rules by using the approximate displacement field structure idea of non - grid method , semi - analytic finite element method and so on , so that the enhanced finite element method has the advantages of no grid method , semi - analytic finite element method and smooth finite element method .
( 4 ) Maintaining the rule of displacement mapping is not the same . Through enriching the mathematical node and the transition node , the corresponding transition unit and the mathematical unit are constructed for the two physical units formed after the crack crossing , and the method suitable for describing the non - continuous deformation and the simulation of any multi - crack propagation inside the crossing unit is proposed . The limitation of the conventional finite element method that the crack is set to the boundary of the unit is broken , and the difficulty of the extended finite element method and the Hansbo & Hansbo method in dealing with the complicated multi - crack propagation problem is overcome .
( 5 ) The unified method of dealing with arbitrary order non - rule nodes at the unit level is put forward , and the simulation grid adaptation strategy based on the crack tip cell scale and the crack tip influence range is established . The results show that the grid adaptive technique improves the calculation precision of the stress field near the tip of the crack tip and the analysis accuracy of the crack propagation process .
The grid density near the crack tip has great influence on the load - displacement curve , but the influence on the crack propagation path is not large .
( 6 ) The softening characteristic and the shear band energy dissipation mechanism of shear band cohesion - shear displacement are characterized by using friction - type cohesive zone model , and the simulation method of shear zone expansion process is described by means of the enhanced finite element method . The influence of the flow law and the softening characteristics of shear zone on the rupture of overlying soil layer is studied . The results show that the shear band inclination determined based on the correlation flow rule is closer to the experimental results .
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU433
本文编号：2133522
[Abstract]:The shear zone is a common form of rock - soil engineering disaster . It is of great significance to reveal the mechanism of shear band generation and expansion to reveal the catastrophe mechanism of geotechnical engineering and to establish disaster prevention and control measures . The simulation involves discontinuous deformation analysis , it is one of the hot research topics .
( 1 ) The traditional finite element mesh is separated into a physical grid which is geometrically independent and used to construct displacement interpolation , and a finite element displacement interpolation technique based on the conventional finite element method is proposed . The geometric separation and displacement mapping rules of the mathematical grid and the physical grid are introduced so that the structure of the displacement interpolation function is easier to realize , and the flexibility and applicability of the finite element method are greatly enhanced . The conventional finite element method is a special form of the reinforcement finite element method , and the reinforcement finite element method is the reinforcement form of the conventional finite element method .
( 2 ) Introducing the transition unit , this paper proposes a unified mapping rule consisting of the reconstruction rule Rr of the displacement of the associated mathematical unit and the transition unit and the covering rule Rc of the displacement of the associated transition unit and the physical unit . The basic determinant , the smooth stress calculation method and the integral technique of the element matrix are derived . A method for enhancing the finite element method based on the conventional finite element software is presented .
( 3 ) Based on the unified mapping rule , this paper presents the corresponding reconstruction rules by using the approximate displacement field structure idea of non - grid method , semi - analytic finite element method and so on , so that the enhanced finite element method has the advantages of no grid method , semi - analytic finite element method and smooth finite element method .
( 4 ) Maintaining the rule of displacement mapping is not the same . Through enriching the mathematical node and the transition node , the corresponding transition unit and the mathematical unit are constructed for the two physical units formed after the crack crossing , and the method suitable for describing the non - continuous deformation and the simulation of any multi - crack propagation inside the crossing unit is proposed . The limitation of the conventional finite element method that the crack is set to the boundary of the unit is broken , and the difficulty of the extended finite element method and the Hansbo & Hansbo method in dealing with the complicated multi - crack propagation problem is overcome .
( 5 ) The unified method of dealing with arbitrary order non - rule nodes at the unit level is put forward , and the simulation grid adaptation strategy based on the crack tip cell scale and the crack tip influence range is established . The results show that the grid adaptive technique improves the calculation precision of the stress field near the tip of the crack tip and the analysis accuracy of the crack propagation process .
The grid density near the crack tip has great influence on the load - displacement curve , but the influence on the crack propagation path is not large .
( 6 ) The softening characteristic and the shear band energy dissipation mechanism of shear band cohesion - shear displacement are characterized by using friction - type cohesive zone model , and the simulation method of shear zone expansion process is described by means of the enhanced finite element method . The influence of the flow law and the softening characteristics of shear zone on the rupture of overlying soil layer is studied . The results show that the shear band inclination determined based on the correlation flow rule is closer to the experimental results .
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU433
【参考文献】
相关期刊论文 前10条
1 赵雷;李小军;霍达;;数值模拟软夹层对基岩上覆土层破裂的影响[J];北京工业大学学报;2007年03期
2 郭恩栋,冯启民,薄景山,洪峰;覆盖土层场地地震断裂实验[J];地震工程与工程振动;2001年03期
3 郭恩栋,邵广彪,薄景山,石兆吉;覆盖土层场地地震断裂反应分析方法[J];地震工程与工程振动;2002年05期
4 徐锡伟;闻学泽;叶建青;马保起;陈杰;周荣军;何宏林;田勤俭;何玉林;王志才;孙昭民;冯希杰;于贵华;陈立春;陈桂华;于慎鄂;冉勇康;李细光;李陈侠;安艳芬;;汶川M_S8.0地震地表破裂带及其发震构造[J];地震地质;2008年03期
5 赵纪生;陶夏新;师黎静;王海云;;An approach to evaluate ground surface rupture caused by reverse fault movement[J];Earthquake Engineering and Engineering Vibration;2006年01期
6 杨杰;陈新民;沈建;;断层错动在砂土中传播规律的模型试验研究[J];防灾科技学院学报;2011年02期
7 张国新,金峰,王光纶;用基于流形元的子域奇异边界元法模拟重力坝的地震破坏[J];工程力学;2001年04期
8 方修君;金峰;;基于ABAQUS平台的扩展有限元法[J];工程力学;2007年07期
9 方修君;金峰;王进廷;;用扩展有限元方法模拟混凝土的复合型开裂过程[J];工程力学;2007年S1期
10 金峰;方修君;;扩展有限元法及与其它数值方法的联系[J];工程力学;2008年S1期
，本文编号：2133522
本文链接：https://www.wllwen.com/guanlilunwen/chengjian/2133522.html
