ASYMPTOTIC SOLUTIONS FOR PREDICTED NATURAL FREQUENCIES OF 2-DIMENSIONAL ELASTIC SOLID VIBRATION PROBLEMS IN FINITE-ELEMENT ANALYSIS

In order to assess the discretization error of a finite element soluti on, asymptotic solutions for predicted natural frequencies of two-dime nsional elastic solid vibration problems in the finite element analysi s are presented in this paper. Since the asymptotic solution is more a ccurate than the original finite element solution, it can be viewed as an alternative solution against which the original finite element sol ution can be compared. Consequently, the discretization error of the f inite element solution can be evaluated. Due to the existence of two k inds of two-dimensional problems in engineering practice, both the pla ne stress problem and the plane strain problem have been considered an d the corresponding asymptotic formulae for predicted natural frequenc ies of two-dimensional solids by the finite element method have been d erived from the fact that a discretized finite element system approach es a continuous one if the finite element size approaches zero. It has been demonstrated, from the related numerical results of three exampl es, that the present asymptotic solution, which can be obtained by sim ply using the corresponding formula without any further finite element calculation, is indeed more accurate than the original finite element solution so that it can be considered as a kind of corrected solution for the discretization error estimation of a finite element solution.