A Modal Error Indicator Based on a Work-Cancellation Property of Energy-Orthogonal Axisymmetric Finite Elements

Abstract

This paper approaches the convergence question of the dynamic modes computed in axisymmetric solids by the finite element method. It is concerned with hierarchical axisymmetric finite elements obtained from the standard eight-node quadrilateral and six-node triangle. These elements are formulated in energy-orthogonal form. It means that the stiffness matrix is split into basic and higher order components, which are produced from mean and deviatoric strain fields, respectively. The major subject of this paper is to decide which modes to keep for subsequent calculations, such as transient response analysis. Truncation is done according to an higher order energy cancellation criterion that may be tested mode by mode.