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二维非均质材料应力场的数值化计算方法

, PP. 1037-1045

Keywords: 非均质材料,等效夹杂方法,共轭梯度法,杂质,应力场

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Abstract:

等效夹杂方法是求解含杂质材料弹性应力场的一种有效方法,但是其解析求解只适用于椭球/椭圆类杂质问题。本文提出一种基于等效夹杂方法的数值化计算方法,介绍了其基本理论,并引入共轭梯度法求解该方法的一致性条件线性方程组。该方法通过计算区域的数值离散,能够实现对二维任意形状杂质弹性场的求解。将该方法得到的结果与解析解进行比较,验证了该方法的有效性。讨论了数值化等效夹杂方法在效率以及收敛性上的表现。通过对比证明,利用共轭梯度法实现该方法,能在保持精度的同时,相较于高斯消元法具有较大的效率优势。最后通过半椭圆杂质和氧化锆/氧化铝共挤复合材料算例验证了该方法处理任意形状杂质的能力。

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