Please use this identifier to cite or link to this item: https://hdl.handle.net/11681/5880
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dc.contributor.authorTakagi, Shunsuke, 1919--
dc.date.accessioned2016-03-21T21:09:06Z-
dc.date.available2016-03-21T21:09:06Z-
dc.date.issued1968-11-
dc.identifier.urihttp://hdl.handle.net/11681/5880-
dc.descriptionResearch Report-
dc.descriptionAbstract: A new tensor analysis, called the Gibbs-Einstein tensor analysis, is developed based on the concept that directions are algebraic quantities subject to the rule of forming scalar products, tensor products, and linear combinations. The new tensor analysis is explained in this paper by way of reformulating continuum mechanics and the Hamilton-Cayley theorem in matrix theory. The latter reformulation yields an explanation of the deformation dyads introduced in the former reformulation. A scalar product of two deformation dyads yields the strain tensor, which is a thermodynamic state variable for thermodynamically reversible deformations. Mathematics dealing with directions in a flat space becomes much simpler and more understandable when the Gibbs-Einstein tensor expression is used.-
dc.publisherCold Regions Research and Engineering Laboratory (U.S.)-
dc.publisherEngineer Research and Development Center (U.S.)-
dc.relationhttp://acwc.sdp.sirsi.net/client/en_US/search/asset/1013305-
dc.relation.ispartofseriesResearch report (Cold Regions Research and Engineering Laboratory (U.S.)) ; 221.-
dc.rightsApproved for public release; distribution is unlimited.-
dc.sourceThis Digital Resource was created from scans of the Print Resource-
dc.subjectTensor analysis-
dc.subjectContinuum mechanics-
dc.subjectScalar products-
dc.subjectTensor products-
dc.subjectLinear combinations-
dc.subjectMatrix theory-
dc.subjectDeformation dyads-
dc.subjectGibbs-Einstein tensor expression-
dc.subjectGibbs tensor expression-
dc.subjectEinstein tensor expression-
dc.subjectHamilton-Cayley theorem-
dc.subjectThermodynamics-
dc.subjectDeformation-
dc.subjectStrain measurement-
dc.subjectMathematical analysis-
dc.subjectMathematical models-
dc.titleThe Gibbs-Einstein tensor analysis with application to continuum mechanics and canonical forms of general second-order tensors-
dc.typeReporten_US
Appears in Collections:Research Report

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