正态分布非均匀各向同性弹性材料的有效力学性质分析  

ANALYSIS OF EFFECTIVE MACRO-MECHANICAL PROPERTIES OF HETEROGENEOUS ELASTIC ISOTROPIC MATERIALS WITH NORMAL DISTRIBUTION

作　　者：冯伟干[1] 杨新华[1] 陈传尧[1] 

机构地区：[1]华中科技大学力学系,武汉430074

出　　处：《机械强度》2008年第1期132-136,共5页Journal of Mechanical Strength

摘　　要：结合有限单元法和数理统计技术,采用随机格形模型研究正态分布非均匀各向同性弹性材料微结构非均匀性对有效力学性质的影响。首先,建立随机格形模型,结合舍选法得到若干组材料参数序列,作为随机格形模型的输入数据,以模拟材料正态分布的微结构力学性质,对模型试样施加单向位移拉伸载荷,开展数值模拟实验,获得非均匀材料有效力学性质子样,最后运用数理统计技术处理数据,得到材料有效力学性质的统计特征。结果表明,组分弹性模量呈正态分布的非均匀材料,其有效力学性质参数也呈正态分布,而且有效泊松比还表现出很弱的方向性;有效弹性模量期望值则小于组分弹性模量的期望值。The random lattice model combined with finite element method （FEM） and statistical theory was employed to research the influence of micro heterogeneity characteristics on the effective properties of the heterogeneous elastic isotropic materials with normal distribution. Random lattice model was buih first and the rejection method was adopted to simulate the stochastic normal distribution of microstructures. Numerical tests of the uniaxial tension were then implemented in ANSYS to calculate the effective elastic modulus and effective Poisson＇ s ratio of heterogeneous materials. Finally, the distributed statistical regularity of macro-mechanical properties and the influence of heterogeneity characteristics on the effective elastic modulus and effective Poisson＇ s ratio were analyzed through the statistical technology. The results indicate that when elastic modulus of heterogeneous material satisfies normal distribution, its macro-mechanical properties are normally distributed and the effective Poisson＇s ratio has very weak directivity.The expected value of the effective elastic modulus is smaller than the mean value of the componential modulus.

关 键 词：非均匀材料 有效力学性质 正态分布 随机格形模型 有限单元法 统计技术 

分 类 号：O343.7[理学—固体力学] TB115[理学—力学]