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

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.

Automated summary

A variational multiscale stabilized locking-free meshfree formulation is introduced for modeling Reissner-Mindlin plate problems under arbitrary plate thickness, where the plate quantities are decoupled into coarse-scale and fine-scale components in the variational equations. The effectiveness of this method is demonstrated through solving numerical examples and comparing with classical methods, showing benefits for problems exhibiting localized phenomena. The approach uses reproducing kernel approximation, smoothed gradient, and divergence to ensure bending exactness in the Galerkin formulation.