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Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the method introduced here. 相似文献
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求解线性方程组的一种新方法 总被引:8,自引:1,他引:7
将线性方程组的一般系数矩阵转化为对称正定矩阵,从而把原线性方程组的求解问题转化为一个等价变分问题的极少值点寻优问题,借助对分寻优法进行求解。算例结果表明,本文方法不仅对于良态线性方程组的求解问题是有效的,而且对于病态线性方程组的求解问题同样是有效的。 相似文献
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直角平面内圆孔对稳态SH波的散射 总被引:2,自引:0,他引:2
利用复变函数方法和多极坐标移动技术,研究了直角平面内圆孔在直边分布有反平面稳态载荷时的sH波散射问题.首先构造出直角平面内不含有圆孔时满足边界应力条件的Green函数解;其次提出直角平面内存在圆孔时满足边界应力自由条件的散射波解,并利用叠加原理写出问题的位移总波场.借助于多极坐标移动技术和圆孔边界处应力自由条件,列出求解散射波解中未知系数的无穷代数方程组,在满足计算精度的前提下,通过有限项截断进行求解.作为算例,具体讨论了圆孔边界处的环向动应力随不同波数、圆孔位置及载荷分布位置和分布范围大小的变化情况,算例结果说明了算法的有效实用性. 相似文献
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