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首页> 外文期刊>Journal of thermal stresses >THERMAL STRESS ANALYSIS FOR AN INCLUSION WITH NONUNIFORM TEMPERATURE DISTRIBUTION IN AN INFINITE KIRCHHOFF PLATE
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THERMAL STRESS ANALYSIS FOR AN INCLUSION WITH NONUNIFORM TEMPERATURE DISTRIBUTION IN AN INFINITE KIRCHHOFF PLATE

机译：无限基尔霍夫平板中包含非均匀温度分布的热应力分析

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摘要

An elliptic inclusion with prescribed polynomial eigenstrains in an infinite Kirchhoff plate is analyzed. The integral type general solutions for the in-plane and out-of-plane displacements on the mid-plane of the plate were derived. The integrals were simplified by using Green's function for the Kirchhoff plate. The integrals could be explicitly expressed by calculating two potential functions defined in this work. After some manipulation of Ferrers and Dyson's formula related to the integration of the harmonic potential for the three-dimensional ellipsoid, we evaluated the potential functions, which can be algebraically expressed by the I-integrals. The results were applied to the analysts of the thermal stress for an inclusion with non uniform temperature distribution that might be approximated by a polynomial. For mathematical convenience, we consider an inclusion with a linear temperature distribution. The expressions for the displacements were decomposed in order to separately investigate the effects of the constant and the first-order term of the temperature distribution. The elastic fields caused by an elliptic inhomogeneity with polynomial eigenstrains, which is called the inhomogeneous inclusion, were also determined by the equivalent eigenstrain method.
机译：分析了无限Kirchhoff板中具有规定多项式本征应变的椭圆包含。推导了板中平面上平面内和平面外位移的积分型一般解。通过对基尔霍夫板使用格林函数简化了积分。可以通过计算此工作中定义的两个潜在函数来明确表示积分。在对与三维椭球体的谐波电势积分相关的Ferrers和Dyson公式进行一些处理之后，我们评估了电势函数，该函数可以通过I积分代数表示。将结果应用于具有不均匀温度分布的夹杂物的热应力分析，该分布可能由多项式近似。为了数学上的方便，我们考虑温度线性分布的包含物。为了分别研究温度分布的常数项和一阶项的影响，对位移的表达式进行了分解。椭圆的不均匀性与多项式本征应变所引起的弹性场，即非均质包含，也通过等效本征应变法确定。

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