On complex potentials for finite plane deformation of a transversely isotropic material

We consider the finite deformation of plane equilibrium problem for a transversely isotropic layer, using the complex variable approach. We give the general expression for the pertinent complex potentials and state the corresponding fundamental problems. We discuss in detail the boundary value problem for fundamental problem-one. As an application of the espoused method, an analytical solution of “Lame's problem” for an infinite layer is obtained. The nonlinear effect of this is highlighted in the obtained figure.