对称张量的分解和它的应用
Decomposition of Symmetric Tensor and Its Application
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摘要: 本文把任一对称张量分解成两个张量的和,其中之一是“应力型”张量,另一个是“应变型”张量.对称张量空间被分解成两个直交子空间的直和.并用几何语言证明了弹性力学的几个基本原理.Abstract: In this paper any symmetric tensor is decomposed into the sum of two tensors.One of them is a "type of stress",and another is a "type of strain" tensor. The inner product space of symmetric tensor is decomposed into the sum of two orthogonal subspaces. The geometric meaning of several principles in the theory of elasticity is given.
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[1] Synge,I.L.,The Hgpercircle in Mathematical Phgsics,Cambridge University Press(1975). [2] Oden,J.T.and J.N.Reddy,Irariational Methods,Theoretical Mechanics,Springer-Verlag(1976). [3] 胡海昌,广义变分原理在近似解中的合理应用.力学学报,1(1982). [4] Fichera,G.,Existence Theorem in Elasticity,edited by C,Truesdell,Berlin-Heideberg-New Vol,Ⅵ a/2,1-17.Handbuck der Physik,Berlin-Heideberg-New York,Spring(1972). [5] Nadesu,G.,Introduction to Edasticity,Holt,Rinehart and Winston,INC(1964). -
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