对偶积分方程(dual integral equation)是一类重要的奇异积分方程,最重要的三类奇异积分方程是:1. 柯西核的奇异积分方程(包括希尔伯特核的奇异积分方程),这是研究得最早和最完整的一类方程(其特点是未知函数出现在发散的积分号下,该积分只在柯西主值下有意义),以及和它的特征方程有密切联系的黎曼问题;2. 以维纳-霍普夫方程为代表的带差核的积分方程;3. 对偶积分方程。
首先利用付里叶变换,使问题的求解转换成对一对变量为裂纹面上位移差的对偶积分方程的求解。
By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jump of displacements across the crack surfaces.
考虑到混合边界值条件下,对偶积分方程的刚性扭转振动建立了横观各向同性饱和地基上圆板的休息。
Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established.
基于对偶边界积分方程(DBIE)构造代数方程组,采用广义极小残值迭代法(GMRES)求解。
The algebraic equation from the dual boundary integral equations(DBIE) was solved using the generalized minimum residual method(GMRES).
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