End effects in multilayered orthotropic strips with imperfect bonding

The axial decay of Saint-Venant end effects is investigated for plane strain deformations of semi-infinite generally laminated orthotropic strips, subject to self-equilibrated end loading. General imperfect bonding conditions are imposed at the interfaces. The analytical approach, using an Airy stress function which decays exponentially in the axial direction, gives rise to a transcendental equation for the (generally complex) eigenvalues. The decay rate for the stresses is given in terms of the eigenvalue of smallest positive real part. The decay rates are examined analytically and numerically in a number of special cases. These include a bimaterial orthotropic strip and the special subcases of a symmetric single lap joint made of the same material, symmetric orthotropic sandwich strips and the classical symmetric double lap joint. Asymptotic estimates for the decay rates, in the case of large slip, are obtained which predict extremely slow decay of end effects.