轴对称问题的积分方程的迭代解法
An Iteration Method for Integral Equations Arising from Axisymmetric Loading Problems
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摘要: 将集度分别为x(ξ)和y(ξ)的集中力和挤压中心沿物体外弹性空间z轴分布,并迭加应力为常数项的解,就能使轴对称应力问题归结为两个联立的一维Fredholm第一种积分方程,本文研究此类方程的迭代解法.给出与E.Rakotch收缩映射定理等价的引理和迭代收敛证明.Abstract: Let the concentrated forces and the centers of pressure with unknown density functions x(ξ) and y(ξ) respectively be distributed along the axis z outside the solid, then one can reduce an axismmetric loading problem of solids of revolution to two simultaneous Fredholm integral equations. An iteration method for solving such equations is duscussed. A lemma equivalent to E. Rakotch's contractive mapping theorem and a theorem concerning the convergent proof of the iteration method are presented.
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