SHAPE OPTIMIZATION WITH P-ADAPTIVITY

The p method of analysis, when used with shape optimization, has certa in advantages over the h method. The method of h adaptivity results in fine meshes with small elements in areas of stress concentration. The presence of these small elements prevents the shape from changing sig nificantly during optimization due to mesh distortion. The p-adaptive method uses relatively large sized elements, and adaptivity is achieve d by increasing the polynomial order of the shape functions rather tha n by introducing small elements as in the h method. Thus, the p-adapti ve method allows for greater shape changes without sacrificing the acc uracy of the analysis. A methodology is developed in this paper to int egrate p-adaptive analysis with shape optimization for general velocit y fields. The key contributions lie in an easily implementable shape u pdate strategy and an adaptive scheme to locally increase the polynomi al order based on error indicators. Numerical results show that signif icant shape change is achievable prior to serious mesh distortion, In addition, need for an h-p adaptive strategy rather than a pure p-adapt ive strategy is also highlighted.