The Point Interpolation Method Using Quadratically Consistent Three-Point Integration Scheme for Free Vibration Analysis

Abstract

Abstract The formulation of quadratically consistent three-point integration scheme based on point interpolant method (PIM-QC3) is proposed for free vibration analysis of two-dimensional solids. Based on the condition with regard to nodal shape function and its derivatives for arbitrary-order approximations, PIM-QC3 is developed using point interpolant method and T6-Scheme for node selection. Thus, complex calculation of inverse matrix at every quadrature points is avoided. And the shape functions including corrected derivatives of nodal shape functions at quadrature points, adopt quadratic basis, meet the so-called differentiation of the approximation consistency as well as the discrete divergence consistency. In addition, the Kronecker delta property is possessed. Some problems for the free vibration of two-dimensional solids are employed to examine the accuracy and efficiency of the PIM-QC3. The numerical results indicate that PIM-QC3 is a very accurate, stable and highly efficient method for the structural analysis of free vibration.