The displacement field in an orthotropic disc under parabolic pressure. Application to the case of transverse isotropy

An analytic solution for the displacement field developed in a circular disc made of an orthotropic material is presented assuming that the disc is loaded by a distribution of radial stresses varying according to a parabolic law and acting along two finite arcs of the disc's periphery, antisymmetric with respect to its center. The solution is achieved with the aid of the complex potentials technique for rectilinear anisotropic materials as it was formulated by Lekhnitskii. The complex potentials and the general expressions for the displacement components are obtained at any point of the disc for the general case of orthotropy and then they are particularized for a transversely isotropic disc, due to its increased importance in practical engineering applications.