ABSTRACT
The natural surface bases in the reference and current configuration are denoted by rα and Rβ, respectively. By N we denote the unit normal vector to O. We have
The components of the metric tensors of the surfaces o and O are given as
The principal stretches denoted by λ1 and λ2 are given in the from
The equilibrium equations of a cylindrical membrane made of an incompressible elastic material and subjected to the deformation (2) has the form (Kolesnikov 2008)
where L11 is the component of the Cauchy stress resultant tensor, 111 is the Christoffel symbol, B11 is the component of the curvature tensor of O, ξ1(u) and ξ(u) are the components of the load vector q, and W is the strain-energy function:
The system (6) agrees with the equilibrium equations of a flexible string in the plane (Merkin 1980, Antman 2005).
