Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N
type: Item
instance of: scholarly article
title: Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N
zbMATH Open document ID: 0625.73015
DOI: 10.1016/0020-7683(88)90099-6
author: Chyanbin Hwu
author: Ting, T. C. T.
published in: International Journal of Solids and Structures
publication date: 1988-01-01T00:00:00Z
review text: The sextic formalism of Stroh for anisotropic elasticity [\textit{A. N. Stroh}, J. Math. Phys. 41, 77-103 (1962; Zbl 0112.168)] leads to the eigen-relation \(N\xi =p\xi\) in which N is a \(6\times 6\) real matrix. The orthogonality and closure relations as well as many other relations involving the eigenvalues p and the eigenvectors \(\xi\) are based on the assumption that N is simple or semisimple so that the six eigenvectors \(\xi_{\alpha}\) span a six-dimensional space. Problems arise when N is non-semisimple. In fact there are problems even when N is almost non- semisimple. We present a modified formalism which is valid regardless of whether N is simple, almost non-semisimple or non-semisimple. The modified formalism does not apply when N is semisimple.
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A90
zbMATH DE Number: 4016293
zbMATH Keywords: application to sum rules
zbMATH Keywords: sextic formalism of Stroh
zbMATH Keywords: 6\(\times 6\) real matrix
zbMATH Keywords: simple, almost non-semisimple
MaRDI profile type: Publication
full work available at URL: 0020-7683(88)90099-6
OpenAlex ID: W2069938340
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description: scientific article; zbMATH DE number 4016293