The effect of a variation in the elastic moduli on Saint-Venant's principle for a half-cylinder

A semi-infinite prismatic cylinder composed of a linear anisotropic classical elastic material is in equilibrium under zero body force and either zero displacement or zero traction on the lateral boundary. The elastic moduli become perturbed. Under suitable conditions on the base load decay estimates are derived for the difference between corresponding quantities in the unperturbed and perturbed bodies. The amplitude in each estimate involves a multiplicative factor that tends to zero as the perturbation tends to zero. The analysis, based upon a first-order differential inequality, introduces apparently new modifications of Korn's inequalities of the first and second kind.