Mixed multiscale three-node triangular elements for incompressible elasticity
ISSN: 0264-4401
Article publication date: 10 May 2019
Issue publication date: 15 October 2019
Abstract
Purpose
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.
Design/methodology/approach
Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.
Findings
The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.
Originality/value
The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.
Keywords
Acknowledgements
This study is supported by the National Natural Science Foundation of China, under the Grant No. 11172313.
Citation
Wu, W. and Zheng, H. (2019), "Mixed multiscale three-node triangular elements for incompressible elasticity", Engineering Computations, Vol. 36 No. 8, pp. 2859-2886. https://doi.org/10.1108/EC-10-2018-0488
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited