无网格局部Petrov-Galerkin法及其在边坡稳定性评价中的应用

发布时间：2018-04-01 21:02

本文选题：无网格法　切入点：MLPG　出处：《中国地质大学(北京)》2016年博士论文

【摘要】：无网格法作为一种近年来新兴的数值计算方法引起了人们的高度重视。该方法在求解问题时不需要划分网格,只需求解域中一系列节点信息。无网格局部PetrovGalerkin(MLPG)法作为一种真正的无网格方法,既不需要划分网格,也不需要全局背景积分网格。本文通过MLPG法的改进,将该方法应用到弹性、超弹性和弹塑性问题中,提出一种岩土弹塑性MLPG法并应用到土质边坡中,通过实际工程案例验证了该方法的有效性。主要成果如下:(1)首先对MLPG法进行改进,通过选取合理的权函数,简化了系统方程刚度矩阵在内部积分域上的积分,提高了计算效率。鉴于总体刚度矩阵和节点力向量中只有两行与每个节点相关的特征,在本质边界条件的施加中采用直接施加法,便于复杂边界条件的施加,并通过算例验证了本方法的有效性。(2)分析了移动最小二乘法、径向基点插值法和再生核粒子法三种近似函数的特征。针对二维平面问题,提出了形函数的构造流程,并讨论了影响形函数精度的主要因素。特别针对移动最小二乘法和径向基点插值法分析了造成插值误差的精确性和收敛性,为后续形函数的构造提供了参考。(3)建立了一种仅依赖初始构型的MLPG法计算方案,基于超弹性材料的本构关系,采用Newton-Raphson迭代法求解格式对算例进行分析,结果与解析解对比验证了该方法在大变形计算中具有较好的稳定性。(4)基于MLPG法和弹塑性力学理论,推导了增量形式的弹塑性MLPG方程,编制了二维平面计算程序,通过算例验证了弹塑性MLPG法的可行性。此外,讨论了影响计算精度的主要因素,并将该方法应用到岩土工程材料中。通过MLPG法在不同屈服准则下对比分析,表明该方法应用到非均质材料问题中是可行的。(5)针对土质边坡的平面应变问题,建立了基于强度折减法的MLPG模型,得到了土质边坡在重力作用下的稳定系数,计算结果与有限元结果较吻合。基于峡口新滑坡实际工程地质条件、岩土体参数,建立了二维边坡无网格模型并进行了稳定性评价,将计算结果与前人通过有限元结果对比,验证了该方法在实际问题中的有效性。
[Abstract]:Meshless method has attracted great attention as a new numerical method in recent years.In order to solve the problem, the method does not need to be meshed, but only needs to solve a series of node information in the domain.As a real meshless method, meshless local PetrovGalerkin MLPGs need neither meshing nor global background integral meshes.In this paper, the improved MLPG method is applied to elastic, hyperelastic and elastoplastic problems, and a geotechnical elastoplastic MLPG method is proposed and applied to the soil slope. The effectiveness of the method is verified by practical engineering cases.The main results are as follows: 1) firstly, the MLPG method is improved. By selecting a reasonable weight function, the integral of the stiffness matrix of the system equation in the internal integral domain is simplified, and the calculation efficiency is improved.In view of the fact that there are only two lines of the total stiffness matrix and the nodal force vector related to each node, the direct application method is used in the application of essential boundary conditions, which facilitates the application of complex boundary conditions.An example is given to verify the effectiveness of this method.) the characteristics of moving least square method, radial base point interpolation method and reproducing kernel particle method are analyzed.In view of the two-dimensional plane problem, the construction flow of shape function is put forward, and the main factors that affect the precision of shape function are discussed.Especially, the accuracy and convergence of interpolation error caused by moving least square method and radial base point interpolation method are analyzed, and a calculation scheme of MLPG method based on initial configuration is established for the construction of subsequent shape function.Based on the constitutive relation of hyperelastic materials, the Newton-Raphson iterative method is used to solve the numerical examples. The results show that the method has good stability in large deformation calculation based on MLPG method and elastoplastic mechanics theory.An incremental elastoplastic MLPG equation is derived and a two-dimensional plane calculation program is developed. The feasibility of the elastoplastic MLPG method is verified by an example.In addition, the main factors affecting the calculation accuracy are discussed, and the method is applied to geotechnical engineering materials.The stability coefficient of the soil slope under the action of gravity is obtained, and the calculated results are in good agreement with the finite element results.Based on the actual engineering geological conditions of Xiakou new landslide and the parameters of rock and soil mass, a two-dimensional meshless slope model is established and its stability is evaluated. The calculated results are compared with those obtained by the predecessors through finite element method.The effectiveness of this method in practical problems is verified.
【学位授予单位】：中国地质大学(北京)
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TU43

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