Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures

A dispersion analysis is carried out to study the dynamic behavior of the Hermite reproducing kernel (HRK) Galerkin meshfree formulation for thin beam and plate problems. The HRK approximation utilizes both the nodal deflectional and rotational variables to construct the meshfree approximation of the deflection field within the reproducing kernel framework. The discrete Galerkin formulation is fulfilled with the method of sub-domain stabilized conforming integration. In the dispersion analysis following the HRK Galerkin meshfree semi-discretization, both the deflectional and rotational nodal variables are expressed by harmonic functions and then substituted into the semi-discretized equation to yield the characteristic equation. Subsequently the numerical frequency and phase speed can be obtained. The transient analysis with full-discretization is performed by using the central difference time integration scheme. The results of dispersion analysis of thin beams and plates show that compared to the conventional Gauss integration-based meshfree formulation, the proposed method has more favorable dispersion performance. Thereafter the superior performance of the present method is also further demonstrated by several transient analysis examples.