复合材料有效弹性模量的上、下限的求解

Calculation of the Upper Limit or Lower Limit of Efficacious Modulus of Elasticity of Compound Materials

计算复合材料有效弹性模量上、下限的方法中 ,Voigt和Reuss的上、下限近似解及Hashin和Shtrikman的上、下限计算公式较为精确 ,但Voigt-Reuss近似解通常忽略了各向异性非均匀体的研究 ,是一个不全面的结果 .而Hashin和Shtrikman未能准确运用变分法研究应变能的极值条件 .针对各向异性非均匀体 ,采用变分法及能量极值原理进行分析 ,得出了一个比Voight -Reuss和Hashin -Shtrikman上、下限近似解更为精确和合理的上。

At present, the approximate solution of Voigt and Reuss's upper limit or lower limit and the calculating formula of Hashin and Shtrikman's upper limit or lower limit are accurate. They are always utilized and adopted by materials science researcher.But the study of non-well-distributed substance of differency in nature in every direction has been ignored in the approximate solution of Voigt and Reuss, and as a result, it is not a overall conclusion. And Hashin and Shtrikman have not precisely wield calculus of variations to discuss the extreme value conditions of strain enery.In this paper, we apply calculus of variations and energy extreme value principle to analysis, primarily aiming at non-well-distributed substance of differency in nature.And we have acquired an improved calulating formula which is more accurate and more reasonable than Voigt-Reuss and Hashin-Shritman calculating formula.