High frequency modes meshfree analysis of Reissner–Mindlin plates

Abstract

Finite element method (FEM) is well used for modeling plate structures. Meshfree methods, on the other hand, applied to the analysis of plate structures lag a little behind, but their great advantages and potential benefits of no meshing prompt continued studies into practical developments and applications. In this work, we present new numerical results of high frequency modes for plates using a meshfree shear-locking-free method. The present formulation is based on Reissner–Mindlin plate theory and the recently developed moving Kriging interpolation (MK). High frequencies of plates are numerically explored through numerical examples for both thick and thin plates with different boundaries. We first present formulations and then provide verification of the approach. High frequency modes are compared with existing reference solutions and showing that the developed method can be used at very high frequencies, e.g. 500th mode, without any numerical instability.

Keywords

• High frequency
• Meshfree
• Moving Kriging interpolation
• Reissner–Mindlin plate
• Shear-locking