Axisymmetric pressure boundary loading for finite deformation analysis using p-FEM

Follower loads, i.e. loads which depend on the boundary displacements by definition, frequently occur in finite deformation boundary-value problems. Restricting to axisymmetrical applications, we provide analytical and numerical solutions for a set of problems in compressible Neo-Hookean materials so to serve as benchmark problems for verifying the accuracy and efficiency of various FE methods for follower load applications. Thereafter, the weak formulation for the follower-load in 3-D domain is reduced to an axisymmetrical setting, and, subsequently, consistently linearized in the framework of p-FEMs, exploiting the blending function mapping techniques. The set of axisymmetric benchmark solutions is compared to numerical experiments, in which the results obtained by a p-FEM code are compared to these obtained by a state-of-the-art commercial h-FEM code and to the “exact” results. These demonstrate the efficiency and accuracy of p-FEMs when applied to problems in finite deformations with follower loads.