A unified approach to meshless analysis of thin to moderately thick plates based on a shear-locking-free Mindlin theory formulation

• Published in: Thin-walled structures Vol. 124; pp. 161 - 179
• Main Authors: Khezri, M., Gharib, M., Rasmussen, K.J.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2018
• Subjects: Meshless; Modified Mindlin theory; Plate bending; Reproducing kernel particle method; Shear-locking; Shear-locking; Modified Mindlin theory; Reproducing kernel particle method; Plate bending; Meshless
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2017.12.004

The conventional numerical approximation of Mindlin plate equations can lead to erroneous solutions for thin plates. The so-called shear-locking problem has been well studied in the context of the finite element method (FEM) whereas the development of numerical formulations for its successful elimination in meshfree methods is still a subject of intensive research. This paper studies the effectiveness of some of the most commonly adopted techniques for the reduction of shear-locking and presents the application of a shear-locking-free formulation based on first-order Mindlin plate theory. In this modified formulation, the shear strains are incorporated as degrees of freedom (DOFs) in lieu of the rotational DOFs in the conventional Mindlin theory formulation. A straightforward transformation technique is presented for the enforcement of boundary conditions and comparisons are made with available analytical and numerical solutions. The generalised reproducing kernel particle method (RKPM) is adopted as the numerical tool and a series of numerical examples are presented to demonstrate the accuracy and performance of the presented method. •A shear-locking-free Mindlin formulation is employed for meshfree analysis of plates.•A technique is proposed for precise enforcement of BCs in the modified formulation.•Plates with various BCs, aspect ratios, geometries and perforations are analysed.•The proposed method is shown to completely suppress the shear-locking problem.•The effectiveness of p-refinement approach in alleviating shear-locking is studied.