Some identities and the structure of 𝑁ᵢ in the Stroh formalism of anisotropic elasticity

Ting, T. C. T.

doi:10.1090/qam/934686

Some identities and the structure of $\textbf {N}_i$ 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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