CONCENTRATED RING LOADINGS IN A FULL SPACE OR HALF-SPACE - SOLUTIONS FOR TRANSVERSE ISOTROPY AND ISOTROPY

In this analysis solutions for concentrated ring loading in a transver sely isotropic full space or half space are found. The elastic field i s derived by integrating the known fundamental point force solutions a long a circular ring. Three cases of ring loading are considered. Taki ng the z axis along the material axis (the z = 0 plane is the isotropi c plane), the first case studied is when the ring load is in the z dir ection, referred to as normal loading. The other two cases are shear r ing loads directed in the plane of isotropy. In the first instance, th e ring load is unidirectional and independently applied in either the x or y direction: The second case considers the axisymmetric radial an d axisymmetric torsional ring loads. The solution for ring loading app lied to the surface of a half space is first obtained. Subsequently th e solutions for ring loading in a full space and buried ring loads in a half space are found. In all cases the elastic displacement and stre ss fields are evaluated in terms of closed form expressions containing complete elliptic integrals of the first, second and third kinds. An interesting feature of the full space solution is that the potential f unction and its radial derivatives exhibit a cylindrical discontinuity for negative z values. However, it is shown that these discontinuous functions do provide continuous displacement and stress fields. A limi ting form of the solutions for transverse isotropy also provides the c orresponding results for isotropic materials. (C) 1997 Elsevier Scienc e.