Shape optimization with p-adaptivity

The p-method of analysis, when used with shape optimization, has certain advantages over the h-method. 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 significantly during optimization owing to mesh distortion. p-Adaptive method uses relatively large sized elements and adaptivity is achieved by increasing the polynomial order of the shape functions rather than by introducing small elements as in the h-method. Thus, p-adaptive method allows for greater shape changes without sacrificing the accuracy of the analysis. A methodology is developed in this paper to integrate p-adaptive analysis with shape optimization for general velocity fields. The key contributions lie in an easily implementable shape update strategy and p-analysis based on error indicators. In addition, the presented approach allows for specification of more general basis shapes. Examples are shown to illustrate the method.