Efficient methods for analyzing thin membranes subjected to transverse pressure and undergoing large deformation

Efficient methods are presented for analyzing thin membranes subjected to transverse pressure and undergoing large deformation based on developments by Adkins-Rivlin [1] and Yang-Feng [2], respectively. The particular boundary value problem studied is highly nonlinear due to large deformations resulting in dramatic changes in geometrical shape and large strains requiring the use of nonlinear material equations. The objectives of this thesis are to present detailed developments of the equations governing the structural response of pressurized membranes undergoing large deformations and to develop efficient computational methods for solving the governing equations. Toward these goals, the seminal work in this field by Adkins-Rivlin [1] was first studied and then the later reformulation of the Adkins-Rivlin equations by Yang-Feng [2] evaluated. The Yang-Feng work has not received significant attention in the literature on this subject. Also, details of the reformulation by Yang-Feng are not readily apparent. These details are provided in this thesis.