An Error Indicator Based on a Wave Dispersion Analysis for the Vibration Modes of Isotropic Elastic Solids Discretized by Energy-Orthogonal Finite Elements

Abstract

This paper studies the dispersion of elastic waves in isotropic media discretized by the finite element method. The element stiffness matrix is split into basic and higher order components which are respectively related to the mean and deviatoric components of the element strain field. This decomposition is applied to the elastic energy of the finite element assemblage. By a dispersion analysis the higher order elastic energy is related to the elastic energy error for the propagating waves. An averaged correlation is proposed and successfully tested as an error indicator for finite element vibration eigenmodes.