论非均匀材料的热弹性静力学。I.一般积分方程
On the thermo-elastostatics of heterogeneous materials. I. General integral equation
摘要：
我们考虑一个线性热弹性复合介质，它由一个均匀的矩阵包含一个统计上不均匀的随机夹杂物集，当夹杂物的浓度是一个函数的坐标（所谓的功能梯度材料）。复合介质受到应力场、温度场和体积力（例如离心载荷）的基本上不均匀的载荷。对于夹杂物的随机场，得到了连接所考虑点和周围点的应力场和应变场的一般积分方程。该方法基于从已知的初始积分方程的两侧减去它们的统计平均值的定中心过程，而无需任何辅助假设，例如，在已知的定中心方法中隐含地利用了有效场假设。在这样做时，包含作用于单独一个的夹杂物的区域的大小是有限的，即局部性原理发生。
英文摘要：
We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates (so-called Functionally Graded Materials). The composite medium is subjected to essentially inhomogeneous loading by the fields of the stresses, temperature and body forces (e.g. for a centrifugal load). The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions. The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. In so doing the size of a region including the inclusions acting on a separate one is finite, i.e. the locality principle takes place.
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