THE EIGENVALUES FOR A SELF-EQUILIBRATED, SEMIINFINITE, ANISOTROPIC ELASTIC STRIP

The linear theory of elasticity is used to study an homogeneous anisot ropic semi-infinite strip, free of tractions on its long sides and sub ject to edge loads or displacements that produce stresses that decay i n the axial direction. If one seeks solutions for the (dimensionless) Airy stress function of the form phi = e(-gammaX)F(y), gamma constant, then one is led to a fourth-order eigenvalue problem for F(y) with co mplex eigenvalues gamma. This problem, considered previously by Choi a nd Horgan (1977), is the anisotropic analog of the eigenvalue problem for the Fadle-Papkovich eigen-functions arising in the isotropic case. The decay rate for Saint-Venant end effects is given by the eigenvalu e with smallest positive real part. For an isotropic strip, where the material is described by two elastic constants (Young's modulus and Po isson's ratio), the associated eigencondition is independent of these constants. For transversely isotropic (or specially orthotropic) mater ials, described by four elastic constants, the eigencondition depends only on one elastic parameter. Here, we treat the fully anisotropic st rip described by six elastic constants and show that the eigenconditio n depends on only two elastic parameters. Tables and graphs for a scal ed complex-valued eigenvalue are presented. These data allow one to de termine the Saint-Venant decay length for the fully anisotropic strip, as we illustrate by a numerical example for an end-loaded off-axis gr aphite-epoxy strip.