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ARTICLE

Isogeometric Collocation: A Mixed Displacement-Pressure Method for Nearly Incompressible Elasticity

S. Morganti¹, F. Fahrendorf², L. De Lorenzis³, J. A. Evans⁴, T. J. R. Hughes^5,* and A. Reali⁶

1 Department of Electrical, Computer and Biomedical Engineering, Universita degli Studi di Pavia, Pavia, 27100, Italy
2 Institute of Applied Mechanics, Technische Universitat Braunschweig, Braunschweig, 38106, Germany
3 Department of Mechanical and Process Engineering, Zurich, 8092, Switzerland
4 Department of Aerospace Engineering Sciences, University of Colorado Boulder, Colorado, 80309, USA
5 Institute for Computational Engineering and Sciences, The University of Texas at Austin, Texas, 78712, USA
6 Department of Civil Engineering and Architecture, Universita degli Studi di Pavia, Pavia, 27100, Italy

* Corresponding Author:T. J. R. Hughes. Email:

(This article belongs to the Special Issue: Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister)

Computer Modeling in Engineering & Sciences 2021, 129(3), 1125-1150. https://doi.org/10.32604/cmes.2021.016832

Received 30 March 2021; Accepted 14 July 2021; Issue published 25 November 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.

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