基于偶应力理论的无网格Galerkin方法及尺度效应数值模拟研究  

ELEMENT FREE GALERKIN METHOD ON COUPLE STRESSES THEORY AND NUMERICAL SIMULATION STUDY OF SCALE EFFECT

作　　者：张敦福[1] 朱维申[1] 李术才[1] 

机构地区：[1]山东大学岩土与结构工程研究中心,济南250061

出　　处：《机械强度》2008年第4期628-632,共5页Journal of Mechanical Strength

基　　金：国家自然科学基金资助(50574053、50579033、90510019)~~

摘　　要：Cosserat介质理论又称为偶应力理论,它较传统连续介质力学更精确,在研究具有微结构介质的力学行为时具有优势。文中将偶应力理论和无网格方法结合在一起,建立基于偶应力理论的无网格方法的基本算法,导出离散模型的计算列式。首先以圆孔孔边应力集中问题和薄梁的弯曲问题为例,确定这一方法的基本参数,解决算法实施的关键技术。进而研究平面裂隙破裂问题,结果表明,裂隙破裂的尺度效应明显,偶应力对裂隙始裂的破裂方向、破裂步长和破裂载荷有较大影响。Cosserat continuum medium theory is called couple stresses theory. This theory is more precise than classical continuum mechanics. When the mechanical behavior of the materials with microstructure is studied, the couple stresses theory is superior to classical continuum theory. Couple stresses theory and element free Galerkin method （EFGM） were put together. The basic EFGM arithmetic on couple stresses theory was established. The formulae of discrete model had been derived. First, the stress concentration of circle hole edge and thin beam bending were taken examples for this method. The basic parameters were established for the arithmetic. The key arithmetic implementation technique was founded. Furthermore, the plane crack rupture problem was studied. The results indicate that scale effect on crack rupture is evident. The couple stresses have great influence on crack rupture orientation, step and rupturing load.

关 键 词：偶应力理论 无网格方法 裂隙破裂 尺度效应 数值模拟 

分 类 号：O346[理学—固体力学] O242[理学—力学]