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

• Published in: Computer methods in applied mechanics and engineering Vol. 196; no. 7; pp. 1261 - 1277
• Main Authors: Yosibash, Zohar, Hartmann, Stefan, Heisserer, Ulrich, Düster, Alexander, Rank, Ernst, Szanto, Mordechai
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-01-2007; Elsevier
• Subjects: Axisymmetry; Computational techniques; Exact sciences and technology; Finite strains; Follower load; Fundamental areas of phenomenology (including applications); Hyper-elasticity; Mathematical methods in physics; p-FEM; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Finite strains; Hyper-elasticity; Follower load; p-FEM; Axisymmetry; High strain; Experimental study; Modeling; Axial symmetry; Neohookean material; Finite element method; Boundary value problem; Weak solution; Compressible material; Follower force
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2006.09.006

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.