Representation of symmetric second-rank III tensor in the space of resultant eigenvectors
E. E. Kuznetsov , I. N. Matchenko , N. M. Matchenko
Izvestiya MGTU MAMI ›› 2015, Vol. 9 ›› Issue (2-4) : 91 -94.
Representation of symmetric second-rank III tensor in the space of resultant eigenvectors
The article examines the possibility of representation of a symmetric second rank III tensor in the three-dimensional vector space of resultant eigenvectors. It has been shown that the vector space of resultant eigenvalues consists of six independent segments. Vector symmetric tensor may be represented in any of the segments independently. The authors introduce a local vector basis for each of the sectors. It is shown that the previously proposed by A.A. Ilyushin and K.F. Chernykh vector basis of the stress tensor are the second and third segments of the vector space of principal stresses.
symmetric tensor / tensor vector / eigenvalues vector space
| [1] |
Ильюшин А.А. Пластичность. Основы общей математической теории. - М.: Изд-во АН СССР, 1963. 272 с. |
| [2] |
Кузнецов Е.Е., Матченко И.Н., Матченко Н.М. О векторных базисах А.А. Ильюшина и В.В. Новожилова // Труды международной научно-практической конференции: Фундаментальные и прикладные проблемы механики деформируемого твердого тела, математического моделирования и информационных технологий. Чебоксары, 2013. Часть 1.- С. 131 - 139. |
| [3] |
Черных К.Ф. Введение в анизотропную упругость. - М.: Наука, 1988. 192 с. |
Kuznetsov E.E., Matchenko I.N., Matchenko N.M.
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