S-R分解定理的张量表述及其率形式  

The Tensor Form and Rate Form of S-R Decomposing Theorem

作　　者：谷凡[1,2] 黄承逵[1] 李林普[1] 周晶[1] 

机构地区：[1]大连理工大学土木水利学院,辽宁大连116024 [2]沈阳建筑大学土木工程学院,辽宁沈阳110168

出　　处：《沈阳建筑大学学报（自然科学版）》2009年第1期6-11,共6页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(59979003);国家自然科学基金重点项目(50439010)

摘　　要：目的研究S-R分解定理导出的应变率及旋转率,进一步完善S-R理论.方法以实方阵的对称、正交和分裂定理为基础,推导大变形、大转动情况下连续介质变形梯度张量的S-R分解定理,结合张量理论研究参数sinθ的本质及其在非笛卡尔坐标系下的计算公式,利用连续介质力学分析S-R分解定理前提条件、几何意义及由S-R分解定理导出的应变率和旋转率.结果由S-R分解定理导出的应变率、旋转率与通常使用的应变率、旋转率线性部分相同.结论将参数sinθ以张量形式表达可使S-R分解定理应用于非笛卡尔坐标系,同时需严格满足其前提条件.S-R理论体现了工程线应变、工程剪应变对应变张量S和局部刚体转动张量R的共同依赖性.In order to improve S-R decomposing theorem and investigate strain rate and rotation rate educed from S-R decomposing theorem,based on direct division theorem for real square matrix to symmetric matrix and orthogonal matrix, the derivation and tensor form of S-R decomposing theorem for continuous medium in the case of large deformation and rotation are illuminated. The essence of parameter sin0 is analyzed for ensuring isotropic property of S-R decomposing tensor equation and its computational formula in non-Des- cartes coordinate system is indicated. Combined with continuous medium mechanics, the precondition and geometric meaning of S-R decomposing theorem are presented. Meanwhile, the strain rate and rotation rate e- duced from S-R decomposing theorem are researched, linear parts of strain rate educed from S-R decompo- sing theorem and Green deformation are coincident. S-R decomposing theorem indicates that line-strain and shear-strain depend on both deformation and local rigid rotation.

关 键 词：实方阵 和分裂 连续介质 变形梯度张量 S—R分解定理 应变率 旋转率 

分 类 号：O151.21[理学—数学] O331[理学—基础数学]