Analysis of thick plates by the natural radial element method

• A new numerical approach is developed and extended to the analysis of thick plates.
• The reduced size of the proposed meshless influence-domains increases the efficiency.
• The proposed interpolation functions are obtained using simple Euclidean norms.
• The proposed numerical approach strongly attenuates the shear-locking phenomenon.
• The proposed numerical approach shows low computational cost and high accuracy.

An innovative numerical approach, combining the simplicity of low-order finite elements connectivity with the geometric flexibility of Meshless methods, is extended to the elastostatic analysis of thick plates. The nodal connectivity is enforced using the natural neighbour mathematical concept and the background integration mesh is constructed uniquely depending on the nodal mesh. The nodal connectivity is imposed through nodal sets with reduced size, reducing significantly the test function construction cost. The interpolation functions are constructed using Euclidean norms and easily obtained. It is considered as the Reissner–Mindlin plate shear deformation theory. Several thick plate elastostatic benchmark examples are solved.