A basic study of the accuracy estimation of structural analysis by the zooming method. Finite element analysis of the transverse bending of thin flat plates.

Abstract

As a basic study for the establishment of an accuracy estimation method in structural analysis using the zooming method, this report deals with the finite element analysis of the problems of transverse bending of thin, flat plates. From numerical experiments for uniform mesh divisions, the following expression was deduced, ε∝(h/a)k, k≥1, where ε is the error of the value by the finite element method relative to the exact value, and h/a is the dimensionless mesh diameter. Using this relations, the errors of gradients on a zooming boundary, and that of the bending moment at selected points in the zooming region can be estimated by the recursive analyses of the whole region or of the zooming region. The error of the bending moment at the selected points is expected to be smaller than the sum of these two errors. A computer program using this errors estimation method was developed and applied to sixteen problems of various shapes. The usefulness of this accuracy estimation method was illustrated by these application results.