Locking-free stabilized conforming nodal integration for meshfree Mindlin–Reissner plate formulation Original Research Article

The cause of shear locking in Mindlin–Reissner plate formulation is due to the inability of the numerical formulation in representing pure bending mode without producing parasitic shear deformation (lack of Kirchhoff mode). To resolve shear locking in meshfree formulation of Mindlin–Reissner plates, the following two issues are addressed: (1) construction of approximation functions capable of reproducing Kirchhoff modes, and (2) formulation of domain integration of Galerkin weak form capable of producing exact solution under pure bending condition. In this study, we first identify the Kirchhoff mode reproducing conditions (KMRC), and show that the employment of a second order monomial basis in the reproducing kernel or moving least-square approximation of translational and rotational degrees of freedom is an effective means to meet KMRC. Next, the integration constraints that fulfill bending exactness (BE) in the Galerkin meshfree discretization of Mindlin–Reissner plate are derived. A nodal integration with curvature smoothing stabilization that fulfills BE is then formulated for Mindlin–Reissner plate. The curvature smoothing stabilization is introduced in the nodally integrated Galerkin weak form. The resulting meshfree formulation is stable and free of shear locking in the limit of thin plate. Both computational efficiency and accuracy are achieved in the proposed meshfree Mindlin–Reissner plate formulation.