Toupin-Бердичевский定理不能作为圣维南原理的数学表达
Toupin-Berdichevskii Theorem Can’t Be Considered as a Mathematical Expression of Saint-Venant’s Principle
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摘要: 本文对Toupin-Бердичевский定理的条件和结论进行了考查,从而说明并以实例演示该定理不能作为弹性力学圣维南原理的数学表达.Abstract: In this paper the condition and the conclusion of Toupin-Berdichevskii Theorem is examined, where by it is explained and demonstrated with an example that the theorem can't be considered as a mathematical expression of Saint-Venant's Principle in Elasticity.
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[1] Boussinesq,M.J.,Application of Potentials,Gauthier-Villars,Paris(1885). [2] Love,A.E.H.,A Treatise on the Mathematical Theory of Elasticity,4th ed.,The University Press,Cambridge(1927). [3] Toupin,R.A.,Saint-Venant's principle,Arch.Rational Mech.and Analysis,18,2(1965),83-96. [4] Бердичевский В.Л.,К доказателщству принпида Сен-Веана для тел произволъной формы,ПММ,.,38(1974),851-864. [5] 王敏中,圣维南原理发展简介,力学与实践,2,4(1980),72-73 [6] Timoshenko,S.P.and J.N.Goodier,Theory of Elasticity.3rd ed.,McGraw-Hill Book Company,New York,41-42． -
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