Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Some identities and the structure of $ {\bf N}_i$ in the Stroh formalism of anisotropic elasticity


Author: T. C. T. Ting
Journal: Quart. Appl. Math. 46 (1988), 109-120
MSC: Primary 73C30
DOI: https://doi.org/10.1090/qam/934686
MathSciNet review: 934686
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Abstract: The Stroh formalism of anisotropic elasticity leads to a $ 6 \times 6$ real matrix N that can be composed from three $ 3 \times 3$ real matrices $ {N_i} \left( {i = 1, 2, 3} \right)$. The eigenvalues and eigenvectors of N are all complex. New identities are derived that express certain combinations of the eigenvalues and eigenvectors in terms of the real matrices $ {N_i}$ and the three real matrices H, S, L introduced by Barnett and Lothe. It is shown that the elements of $ {N_1}$ and $ {N_3}$ have simple expressions in terms of the reduced elastic compliances. We prove that $ - {N_3}$ is positive semidefinite and, with this property, we present a direct proof that L is positive definite.


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DOI: https://doi.org/10.1090/qam/934686
Article copyright: © Copyright 1988 American Mathematical Society


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