【作者】 司建辉；

【导师】 李九红； 简政；

【作者基本信息】 西安理工大学 ， 结构工程， 2004， 硕士

【摘要】 无网格伽辽金法(EFGM)是目前国内外数值分析研究的热点之一。 本文系统介绍了无网格法的发展现状及无网格伽辽金法(EFGM)的基本理论，着重阐述了基于移动最小二乘法的无网格伽辽金法的基本方程，并对影响计算精度的几个因素做了分析探讨。算例表明，该法解决实际问题是有效的。目前，无网格伽辽金法主要研究都集中在线弹性材料上，在结构工程中，混凝土构件受力后的本构关系为非线性或弹塑性，本文首次在无网格伽辽金法中引入混凝土的OTTOSEN本构模型和莫尔库仑强度破坏准则，对混凝土悬臂梁等构件进行了非线性无网格分析，并与国际著名结构分析软件ADINA的计算结果进行了对比，表明采用无网格伽辽金法解决混凝土非线性问题是可行的。对于混凝土结构的裂缝问题，本文首次在无网格伽辽金法中采用弥散式裂缝处理方式，可以较好的模拟混凝土构件裂缝的发生发展，并可计算出混凝土构件的开裂荷载及极限荷载，说明本文采用无网格伽辽金法引入弥散式裂缝处理方式可以很好的解决混凝土的开裂问题。更多还原

【Abstract】 Element Free Garlekin Method(EFGM)is one of the hot studies in numerical analysis by far both at home and abroad.The paper systematically introduces present development of Element Free Method and the basic theory of EFGM, and mainly describes the equation by which the Moving least square (MLS) is approximately used to deduce EFGM, meanwhile, discusses the factors which may effect the calculation precision and, the calculation shows that this method is feasible in practice. For the structural engineering, the constitutive relations of concrete members under the strength will be nonlinear or elasticoplasticness, in this paper, OTTOSEN constitutive model is adopted, and Mohr-Coulomb strength principle is selected as destructive principle, the concrete cantilever beam is analyzed by using nonlinear EFGM, the calculation result by nonlinear EFGM is compared with the analysis software of ADINA, the comparing proves that EFGM used to dissolve the concrete nonlinear problem is feasible. To the concrete crack, the dispersion treatment is taken by the paper, it’ s quite convenient to use EFGM to simulate the occurring and development of concrete crack. Simultaneously, the cleavage load and limit load can be obtained. The calculation shows that adopting EFGM and dealing with the cracks of concrete with dispersion treatment will be a suitable way.更多还原