A PRACTICAL ERROR ESTIMATOR FOR FINITE-ELEMENT PREDICTED NATURAL FREQUENCIES OF MEMBRANE VIBRATION PROBLEMS

Based on the asymptotic solution for finite element predicted natural frequencies of a membrane vibration problem, the concept of asymptotic error and a practical error estimator are presented in this paper. Th e present practical error estimator contains two criteria: one is the error estimator criterion and the other is the finite element mesh des ign criterion. By using this practical error estimator, not only can t he accuracy of a finite element solution for natural frequencies of a membrane vibration problem be directly evaluated without any further f inite element calculation, but also a new target finite element mesh f or the solution of desired accuracy can be immediately designed from t he relevant information of an original finite element solution. Genera lly, for the purpose of designing a new target finite element mesh, th is original finite element solution is obtainable from a very coarse m esh of a few elements and usually does not satisfy the accuracy requir ement. Since the new target finite element mesh could result in a fini te element solution of desired accuracy, the finite element solution s o obtained can be used for structural design in engineering practice. The related numerical results from vibration problems of five represen tative membranes of different shapes have demonstrated the correctness and applicability of the present practical error estimator. (C) 1996 Academic Press Limited