On a generalization of the Naghdi-Hsu transformation and its application to problems of elasticity theory (Q1118441)

The following model is considered for the inhomogeneity of an elastic material: the shear modulus of the material is constant, but Poisson's- ratio (or the modulus of elasticity) depends in an arbitrary manner on three Cartesian coordinates. A linear transformation of vector fields is introduced, which is a generalization of the well-known Naghdi-Hsu transformation (NHT) [see \textit{M. Z. Wang}, J. Elasticity 15, 103-108 (1985; Zbl 0559.73025)] that enables the solution of the equilibrium equation of elasticity theory for bodies with variable Poisson's ratio to be represented in terms of a vector function (harmonic when there are no body forces), and proof of its completeness. In passing, a new variation of the NHT is formulted in which the integrals over the body volume are replaced by integrals over its surface. The fundamental solution of the equilibrium equation in displacements is presented in explicit form for an unbounded body with inhomogeneity of the type under consideration.