基于非局部理论的一维损伤模型的有限元算法  

Finite Element Algorithm of One-dimensional Damage Model Based on Nonlocal Theory

作　　者：付丽[1] 杜星文[1] 

机构地区：[1]哈尔滨工业大学复合材料研究所,黑龙江哈尔滨150001

出　　处：《航空学报》2009年第5期879-885,共7页Acta Aeronautica et Astronautica Sinica

摘　　要：为了解决损伤局部化问题的网格依赖性,采用非局部理论,从损伤本构关系中引入特征长度入手,建立非局部损伤本构模型。提出了一种新的单元,将位移、非局部应变和非局部应变梯度作为基本的未知量,引入了C1连续的形函数,并推导了非局部损伤本构模型的有限元格式。在ABAQUS中进行了二次开发,嵌入了本文提出的单元和本构模型,并用ABAQUS软件分析了一维损伤结构的受力情况。计算结果表明,数值模拟与理论推导结果的总体趋势吻合得较好,证明了本文方法的正确性与可行性。In order to circumvent the mesh dependence of damage localization, the nonlocal theory is adopted. A nonlocal damage model is established by introducing a characteristic length into the damage constitutive equation. A new element is proposed and the basic unknown quantities in the equations are displacement, nonlocal strain, and nonlocal strain gradient. A finite element （FE） format of the nonlocal damage model is derived by introducing the C1 continuum shape function. A numerical example for a one-dimensional damage structure is analyzed in ABAQUS through the user subroutine UEL. The result shows that the trend of the numerical solution coincides with the analytical solution and the method can be used to analyze damage localization.

关 键 词：非局部理论 局部化 网格依赖性 C1 连续单元 ABAQUS 有限元方法 

分 类 号：O343.4[理学—固体力学]