Abstract
This paper establishes that the Stroh orthogonality relations for an anisotropic body are a direct consequence of the fact that the system of equations of equilibrium is self-adjoint and positive definite. It is demonstrated that, assuming a complex representation of displacements and boundary tractions, the Betti theorem of reciprocity implies the ‘orthogonality’, and positive definiteness of strain energy implies the full rank of the normalization matrix, in the Stroh orthogonality relations. The presented proof is applicable to both the Lekhnitskii and Eshelby theories of an anisotropic body.
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Mantič, V., París, F. On Stroh orthogonality relations: An alternative proof applicable to Lekhnitskii and Eshelby theories of an anisotropic body. J Elasticity 43, 137–145 (1996). https://doi.org/10.1007/BF00042507
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DOI: https://doi.org/10.1007/BF00042507