AN ERROR INDICATOR BASED ON A WAVE DISPERSION ANALYSIS FOR THE IN-PLANE VIBRATION MODES OF ISOTROPIC ELASTIC SOLIDS DISCRETIZED BY ENERGY-ORTHOGONAL FINITE ELEMENTS

Abstract eng:
This paper studies the dispersion of elastic waves in homogeneous and isotropic elastic media discretized by the finite element method. Both the unbounded plain-strain solid and the unbounded generalized plane-stress plate are considered. 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 the dispersion analysis the percentage of higher order elastic energy is related to the elastic energy error for both the longitudinal waves and the shear waves. An averaged correlation is proposed to apply the percentage of higher order elastic energy as an error indicator for the vibration eigenmodes computed.

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