A variational multiscale stabilized and locking-free meshfree formulation for Reissner–Mindlin plate problems

TH Huang - Computational Mechanics, 2022 - Springer
Computational Mechanics, 2022Springer
In this study, a variational multiscale stabilized locking-free meshfree formulation is
introduced for modeling Reissner–Mindlin plate problems under arbitrary plate thickness.
Under this framework, the plate quantities are decoupled into coarse-scale and fine-scale
components in the variational equations, where the fine-scale solution represents a
correction to the residual of the coarse-scale equations that can be solved by an effective
collocation-type approach with an approximation method meeting locking free conditions …
Abstract
In this study, a variational multiscale stabilized locking-free meshfree formulation is introduced for modeling Reissner–Mindlin plate problems under arbitrary plate thickness. Under this framework, the plate quantities are decoupled into coarse-scale and fine-scale components in the variational equations, where the fine-scale solution represents a correction to the residual of the coarse-scale equations that can be solved by an effective collocation-type approach with an approximation method meeting locking free conditions. The substitution of fine-scale solutions in the coarse-scale system leads to a residual-based Galerkin formulation. In the proposed framework, the reproducing kernel approximation, as well as the smoothed gradient and divergence, are adopted to ensure the bending exactness in the Galerkin formulation. The multiscale approach is also beneficial for problems exhibiting localized phenomena. The effectiveness of the proposed method is tested by solving a series of numerical examples and compared with classical methods.
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