Smooth indentation of a transversely isotropic cantilever beam

The response of a transversely isotropic beam of finite length to a frictionless cylindrical and flat indenter is studied. Solutions are obtained through a global-local technique, which accounts for the local behavior near the indenter, as well as the global beam behavior. The method of analysis superposes an infinite elastic layer solution derived through the use of integral transforms with a beam theory solution. Local indenter stresses, as well as displacements and rotations, are computed for each case and plotted for various ratios of contact width to beam length and for various positions of the indenters. To study the effects of anisotropy, each problem is solved using two materials: one nearly isotropic, the other highly anisotropic. Results are compared to those of an earlier isotropic study, and to Hertz theory and beam theory solutions.