A stabilized one-point integrated mixed formulation for finite element and meshfree methods in modeling nearly incompressible materials
Journal
Acta Mechanica
Journal Volume
233
Journal Issue
3
Start Page
1147
End Page
1172
ISSN
00015970
16196937
Date Issued
2022
Author(s)
Chao, Chialien
Abstract
This study develops a stabilized Galerkin mixed formulation within a one-point integrated framework to model nearly incompressible materials. The variational multiscale formulation addresses the hourglass modes and Ladyzhenskaya–Babusska–Brezzi (LBB) instability in conventional Galerkin mixed formulation. The multiscale decomposition of the variational equation results in a residual-based stabilized Galerkin framework. The derived fine-scaled terms act as a stabilization that alleviates hourglass instability and pressure oscillations. The strain smoothing method is employed in coarse-scale terms to satisfy the integration constraint. A smoothed divergence is applied to the fine-scale terms to relax using a higher-order basis function. The proposed method is applied to the reproducing kernel particle method and the smoothed finite element method to demonstrate its efficacy in general meshfree and mesh-based methods. The effectiveness of the formulation is verified by solving a series of elasticity problems under the incompressible limit. The proposed method outperforms the other two classical stabilization approaches, which are also derived in this study.
Subjects
Finite Element Method
Stabilization
Element Method
Hourglass Modes
Incompressible Material
Integrated Frameworks
Meshfree Methods
Mixed Formulations
Multi-scale Decomposition
Multiscale Formulations
Nearly Incompressible
Variational Multiscale
Galerkin Methods
Publisher
Springer
Type
journal article