A stabilized quasi and bending consistent meshfree Galerkin formulation for Reissner–Mindlin plates
Journal
Computational Mechanics
Journal Volume
70
Journal Issue
6
Start Page
1211
End Page
1239
ISSN
01787675
14320924
Date Issued
2022
Author(s)
Wei, Yen Ling
Abstract
The state-of-the-art locking-free meshfree Galerkin formulation for modeling the Reissner–Mindlin plate problems is plagued by the following issues: (1) the requirement of a large enough kernel support size in avoiding kernel instability because of the quadratic basis in meeting the Kirchhoff mode reproducing condition, as well as (2) the tedious construction of the conforming representative domains and the smoothed strain in the stabilized conforming integration scheme. This study introduces an efficient and stabilized approach that circumvents the above-mentioned issues. A quasi-consistent reproducing kernel approximation is first developed to enable a smaller kernel support size to be used without the moment matrix singularity issue under a controllable loss of completeness; thus, the approximation construction is accelerated. Then, a bending consistent nodal integration method is proposed where the bending consistency in Galerkin formulation is achieved via an assumed strain approach without using the conforming cell. A variational multiscale stabilization method from our earlier research is implemented to avoid low energy instability while maintaining the locking-free property. The performance of the present formulation is validated in several benchmark problems.
Subjects
Quasi-consistent Approximation
Reissner–mindlin Plate
Reproducing Kernel Particle Method
Stabilized Bending Consistent Nodal Integration
Benchmarking
Galerkin Methods
Integration
Locks (fasteners)
Galerkin Formulation
Locking-free
Meshfree
Nodal Integrations
Quasi-consistent Approximation
Reissner-mindlin Plate Problem
Reissner/mindlin Plate
Reproducing Kernel Particle Method
Stabilized Bending Consistent Nodal Integration
State Of The Art
Mindlin Plates
SDGs
Publisher
Springer Science and Business Media Deutschland GmbH
Type
journal article