ELIMINATION OF GIBBS PHENOMENA FROM ERROR ANALYSIS OF FINITE-ELEMENT RESULTS

A change of variables is presented that improves the accuracy of Fourier half-range sine series used in numerical harmonic analysis. The change in variables, a simple but effective extension of the period of the series, results in an interpolation formula that passes through the endpoints of tabulated data. In two dimensions, the change in variables produces an "extended grid" for use in computing coefficients in double sine series. The improved double sine series was developed for modifying a postprocessor code for error analysis of results from a general-purpose finite element code. Without going into the details of the error analysis, the paper illustrates the improved numerical harmonic analysis by applying it to the problem of a simply supported plate under uniform load. The elimination of Gibbs' phenomenon from the truncated series for the uniform load and from a discrete set of boundary conditions suggests that the extended grid transformation can be applied readily in a postprocessor for error analysis of discrete results for postbuckled stiffened panels.