Octet formalism for Kirchhoff anisotropic plates
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abstract
An octet formalism is established for stretching and bending deformations of an anisotropic elastic plate based on the Kirchhoff theory. The plate is inhomogeneous in the thickness direction and thus includes the laminated plate as a special case. By defining a 4-eigenvector associated with two in-plane displacements and two rotational angles of a normal of the mid-plane, and a 4-eigenvector associated with four stress functions, the three equilibrium equations of the plate reduce to a standard eight-dimensional eigenrelation. The fundamental elastic plate matrix defined in this work is found to place the two eigenvectors in reverse order to form the left and right 8-eigenvectors of the matrix. The same capability has been observed for the fundamental elasticity matrix in Stroh's sextic formalism for generalized plane strain elasticity. Thus our octet formalism symbolically preserves extensive elegant properties and identities pertaining to the capability, e.g. the orthogonality and closure relations, which have been established in the Stroh sextic formalism. Having shown that the eigenvalues cannot be real, we provide the eigenvalue representations for special cases of material and geometry. The non-semisimple case including an isotropic material is briefly discussed.
