Isogeometric Collocation: A Mixed Displacement-Pressure Method for Nearly Incompressible Elasticity
  • S. Morganti1, F. Fahrendorf2, L. De Lorenzis3, J. A. Evans4, T. J. R. Hughes5,* and A. Reali6
1Department of Electrical, Computer and Biomedical Engineering, Universita degli Studi di Pavia, Pavia, 27100, Italy
2Institute of Applied Mechanics, Technische Universitat Braunschweig, Braunschweig, 38106, Germany
3Department of Mechanical and Process Engineering, Zurich, 8092, Switzerland
4Department of Aerospace Engineering Sciences, University of Colorado Boulder, Colorado, 80309, USA
5Institute for Computational Engineering and Sciences, The University of Texas at Austin, Texas, 78712, USA
6Department of Civil Engineering and Architecture, Universita degli Studi di Pavia, Pavia, 27100, Italy
*Corresponding Author: T. J. R. Hughes. Email: hughes@oden.utexas.edu
(This article belongs to this Special Issue:Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister
)
Received 30 March 2021; Accepted 14 July 2021 ; Published online 14 September 2021
Abstract
We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity. The primal method employs Navier’s equations in terms of the displacement unknowns, and the mixed method employs both displacement and pressure unknowns. As benchmarks for what might be considered acceptable accuracy, we employ constant-pressure Abaqus finite elements that are widely used in engineering applications. As a basis of comparisons, we present results for compressible elasticity. All the methods were completely satisfactory for the compressible case. However, results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case. The results for the mixed methods behaved very well for two of the problems we studied, achieving levels of accuracy very similar to those for the compressible case. The third problem, which we consider a “torture test” presented a more complex story for the mixed methods in the nearly-incompressible case.
Keywords
Isogeometric analysis; isogeometric collocation; nearly-incompressible elasticity