Anisotropic discs loaded by parabolically distributed pressure

AbstractThe complex potentials which describe the elastic equilibrium of a circular disc made of a transversely isotropic, homogeneous material are presented. It is assumed that the disc is loaded by a parabolic distribution of radial stresses which act along two finite circular arcs, antisymmetric with respect to the disc’s center. The problem is here solved within the frame of linear elasticity assuming plane strain conditions. The complex potentials technique is adopted as it was formulated by Lekhnitskii in his pioneering contributions. When the complex potentials are determined, one can obtain the respective stress field developed all over the disc for any value of the angle between the axis of symmetry of pressure distribution and the planes of material isotropy. Attention is focused at the disc’s center and at the loaded diameter. Conclusions regarding the applicability of the Brazilian-disc test in case of specimens made of transversely isotropic materials are drawn