An analysis of the dispersive features of Galerkin meshfree formulation for shear deformable beam

A dispersion analysis is presented for the Galerkin meshfree formulation of shear deformable beam problem. The meshfree formation employed herein is based on the method of stabilized conforming nodal integration. This formulation can exactly reproduce the bending exactness and more importantly is locking-free. The dispersion analysis is carried out by expressing the nodal variables in a harmonic form. Subsequently by substituting the nodal variables into the meshfree semi-discretized equation the characteristic equation can be rationally established. Thereafter the numerical frequency can be obtained from the characteristic equation. The dispersion performance of the present formulation is compared with those based on the methods of Gauss integration and direct nodal integration. Numerical results show that the present formulation has the most favorable dispersion performance.