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无单元法布点优化的一种新方法

ISSN号：1000-6915
期刊名称：岩石力学与工程学报
时间：0
页码：1841-1847
语言：中文
分类：O319.56[理学—一般力学与力学基础;理学—力学]
作者机构：[1]河海大学岩土工程研究所,南京210098
相关基金：国家自然科学基金重点项目（No.50539110）;国家重点基础研究发展规划973项目（No.2002CB412707）.
相关项目：岩石高边坡失稳的大型滑坡预警和防治

关键词：无单元法, 健康度, 影响域, 遗传算法, 编码, 适应度函数, 选择策略, 遗传算子, EFM, degree of health, domain of influence, genetic algorithms, encoding fitness, selection strategy, genetic operator

中文摘要：

研究了无单元法中单个影响域内的布点形式对误差的影响,提出了半径权值的概念。在经过充分的数值计算后,给出在半径权值对无单元法插值结果的精度的影响值的大小。研究对优化无单元法的节点布置、减小模拟误差有很大的作用,并且使得影响域的大小不再依靠点数的多少来确定,避免了影响域过大的情况和为了单个影响域内有足够多的插值点而使得整体插值点数目过多的弊端。运用单个区域内的插值点健康度的理论,研究了整个区域布点对无单元法模拟函数——滑动最小二乘法模拟精度的影响,并运用遗传算法对整个布点区域上的插值点进行了优化,给出了区域上的优化值。通过一个实例,得到一个具有普遍意义的插值点优化值与插值点密度的关系,并给出无单元法布点的一般性原则。

英文摘要：

The stationing situation＇s effect on error in the single domain of influence in element-free method（EFM） is studied.The idea of radius＇s weight has been presented.After completely numerical computing,the magnitude of influence on the accuracy of the EFM＇s interpolation result can be presented.The study can optimize the stationing situation of EFM,minimize the simulation errors;and the effect that the domain of influence does not depend on the number of the nodes can avoid the disadvantages of the oversize domain of influence and extra numbers of the whole interpolation nodes which is resulted from maintaining the enough interpolation nodes in single domain of influence.Then the paper also apply this theory of the stage of health in single domain for the work that take the distributing point effect on the simulation precision of MLSM which is the function EFM.The genetic algorithm is used to optimize the interpolating points;and the optimizing values are given.With an example,the relation between the optimi zing value of interpolating points that have a general significance are obtained;and the density of interpolating points following with the universal principle of distribution point in element-free method.

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