S-R分解定理的唯一性、存在性和客观性
On Uniqueness, Existence and Objectivity of S-R Decomposition Theorem
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摘要: 对于连续体的一切物理可能的变形场,其变形梯度张量F可被分解为一个对称张量S和一个正交张量R的直和,这便是S-R分解定理.本文通过矩阵方法和张量方法证明了S-R分解定理的唯一性、存在性和客观性.Abstract: For a physically possible deformation field of a continuum, the deformationgradient function F can be decomposed into direct sum of a symmetric tensor S andan orthogonal tensor R. which is called S-R decomposition theorem. In this paper,the S-R decomposition unique existence theorem is proved. by employing matrix andtensor method. Also, a brief proof of its objectivity is given.
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Key words:
- S-R decomposition theorem /
- uniqueness /
- existence /
- objectivity
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[1] 陈主达,《有理力学》,中国矿业大学出版社(1986),96-100. [2] 陈勉,非线性连续体力学中的杆、壳大变形问题,中国矿业大学博士l论文(1991). [3] 陈熙.有限变形和分解定理的存在性与唯一性,中国矿业大学硕士论文(1986). [4] Marvin Marcus and Henryk Minc,A Survey of Matrix Theory and Matrix Inequalities,Allyn and Bacon Inc.,Boston(1964),67. -
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