Spatial-decay estimates for a generalized biharmonic equation in inhomogeneous elasticity

A rectangular region of smoothly varying, inhomogeneous, isotropic elastic material is considered; two types of material are dealt with: if opposite pairs of edges are parallel to the x,y axes, in one case the elastic moduli vary smoothly with x, while in the other they vary smoothly with y. The region is in a state of plane strain, three of its edges being traction-free, the fourth being subjected to a self-equilibrated, in-plane, load. Inequality estimates are obtained descriptive of the spatial decay of effects away from the loaded end. The results of the paper imply how the estimated decay rate varies with the constitutive profile, and may have applications to functionally graded materials.