一类算子的正定性
On the Positive Definiteness of a Class of Operators
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摘要: 本文给出了弹性力学和弹性结构力学中出现的一类十分广泛的算子的正定性的证明。通常遇到的二维三维弹性力学问题,薄板问题等的方程组的正定性问题可以看为它的特殊情形。Abstract: In this paper,a proof of the positive definiteness for a class of operators is given.The operators considered are general enough to include those in two-and three-dimensional elasticity,thin plates and shells as their special cases.
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[1] Fichera,G.,Existence Theorem in Elasticity,Encyclopedia of Physics,Vol,VIa/2(1972). [2] Bernadou,M.and P.G.Ciarlet,Sur Lellipticite du Modele Lineaire de Cogues de W.T.Koiter,Lecture Notes in Economics and Mathematics Systems 134,Computing Methods in Applied Sciences and Engineering,89-136,2nd Inetr.Symp.,Dec.(1975),15-19. [3] 武际可,薄壳方程组椭圆型条件的证明,1979年全国弹塑性力学学术交流会论文,固体力学学报,4(1931),436-444, [4] 王大均、胡海昌,弹性结构理.,中两类算子的正定性和紧致性的统一证明,力学学报,2(1980). [5] 武际可,对胡海昌-鴑津久一朗原理的推广,北京大学字报(自然科宇),3(1985). [6] 武际可、王敏中,《弹性力学引论》北京大学出版社(1931). [7] Ciarlet,P.G.,《有限元素法的数值分析》,蒋尔雄等译,上海科技出版社(1978). [8] 姜礼尚、先之垣,《有限元方法及其理论基础》,人民教育出版社(1980),143-144. -
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