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Eigenvalue Problems of a Tensor and a Tensor-Block Matrix (TBM) of Any Even Rank with Some Applicationsстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Дата последнего поиска статьи во внешних источниках: 12 сентября 2019 г.
- Автор: Nikabadze Mikhail U.
- Сборник: Advanced Structured Materials, Generalized Continua as Models for Classical and Advanced Materials, H. Altenbach and S. Forest (eds.)
- Том: 42
- Глава в коллективной монографии
- Год издания: 2016
- Место издания: Springer International Publishing Switzerland
- Первая страница: 279
- Последняя страница: 317
- DOI: 10.1007/978-3-319-31721-2_14
- Аннотация: In this work, the eigenvalue problems of the symmetric tensor-block matrix of any even rank and sizes mxm, m>0 (sizes 2x2) is formulated (studied). Some definitions and theorems are formulated concerning the tensor-block matrix. Formulas expressing the classical invariants of the tensor-block matrix of any even rank and sizes through the first invariants of the powers of this tensor-block matrix are given. We also obtain formulas which are inverse to the latter. A complete orthonormal system of eigentensor columns for the tensor-block matrix of any even rank and sizes 2x2 is constructed. We formulate the generalized eigenvalue problems of the tensor-block matrix. As a special case, we consider the tensor-block matrix of the elastic modulus tensors. The canonical representation of the tensor-block matrix is given. Using this representation, we get the canonical forms of the elastic strain energy and the constitutive relations. Besides, a classification of the micropolar linear elastic anisotropic bodies that do not have a center of symmetry is given.
- Добавил в систему: Никабадзе Михаил Ушангиевич