关于胡海昌解的完备性
On the Completeness of Hu Hai-chang’s Solution
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摘要: 本文证明了对于z向凸的区域及另一条件下,各向同性的胡海昌解是完备的;反之,对z向不凸的区域,各向同性的胡海昌解是不完备的.Abstract: In this paper, the completeness of Hu Hai-chang's solution is proved in the case of convex regions in z-direction under a supplementary condition. On the other hand, for those non-convex regions in z-direction, Hu Hai-chang's solution is proved to be incomplete.
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[1] Mindlin,R.,Note on the Galerkin and Papkovitch stress functions.Bull.Amer.Math.Soc.42(1936),373-376. [2] 胡海昌,横观各向同性体的弹性力学的空间问题,物理学报,9卷3期(1953) 130-147. [3] Muki,Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plane,Progress in Solid Mechanics,I(ed.by Sneddon and Hill)(1960). [4] Eubanks,R.A.,and Sternberg,E.,On the completeness of the Papkovitch stress function.J.Rational Mech.Anal.,5(1956),735-748. [5] Kellogg,O.D.,Foundations of Potential Theory,Berling,Springer,(1929),260. [6] Слободянский М.Г.,Об общих и поиных Фориах Уравнения Упругости ЛММ,Т.ХХⅢ,Выл З (11959),468-482. -
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