Abstract: Based on the material derivative concept and direct differentiation approach, a numerical method for shape design sensitivity analysis using meshless natural neighbor Petrov-Galerkin method (NNPG) is proposed. The local weak form of governing equation of NNPG is directly differentiated with respect to design variables and subsequently discretized with NNPG to obtain the sensitivities. Based on the mathematical programming method, a shape optimization method is proposed, and the natural neighbour Petrov-Galerkin method is used to calculate the structure responses and their sensitivities. The numerical example shows the proposed optimization method is totally automatic, efficient. Absolutely, no remeshing is needed.

Key words: Meshless method　Natural neighbor interpolation, Sensitivity analysis, Shape optimization