Finite Axisymmetric Deformations of Elastic Membranes

摘要

The authors consider the axisymmetric deformations due to edge tractions and internal pressure of an elastic membrane composed of a homogeneous, incompressible and isotropic material possessing a strain-energy function. For a given initial thickness the undeformed membrane is determined in terms of the deformed configuration. The solution given to this inverse problem is exact and valid for a general strain-energy function. For the particular case of a neo-Hookean material an explicit solution is given. The theory is illustrated by its application to the specific example of the deformation of a membrane, under edge tractions, into a truncated conic surface. (Author)