A meshfree model without shear-locking for free vibration analysis of first-order shear deformable plates

Difficulty in imposing essential boundary conditions in the standard element-free Galerkin method (EFG) is due to the lack of Kronecker’s delta function property of shape functions generated by moving least square approximation (MLS). In this paper, we further apply a meshfree model based on the moving Kriging interpolation method (MK) to free vibration analysis of first-order shear deformable plates. The deflection and two rotation field variables of plate are approximated by the MK method, which is employed to construct the shape functions having the delta function property. With this approach, the drawback in enforcement of the boundary conditions caused by the MLS is now avoided. The present formulation is based on the first-order shear deformation plate theory (FSDT) associated with an effective elimination of the shear-locking phenomenon completely, and hence the approach is applicable to both moderately thick and thin plates. Numerical examples considering various aspect ratios and different boundaries are examined and solutions on natural frequencies obtained by the present method are then compared with existing reference solutions, and very good agreements are observed.

► A meshfree model proposes for the eigenvalue analysis of relatively thick plates. ► Moving Kriging interpolation satisfies the delta function property. ► Difficulty in imposing the boundary condition is avoided. ► Shear-locking phenomenon is eliminated completely in the present formulation. ► Effects of various parameters, different boundaries and aspect ratios are investigated.