Natural neighbour Petrov-Galerkin Method for Shape Design\\ Sensitivity Analysis
Kai Wang; Shenjie Zhou; Zhifeng Nie; and Shengli Kong

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 26, No. 2, pp. 107-122, 2008
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Keywords shape design sensitivity analysis; meshless method; Petrov-Galerkin method; natural neighbour interpolation
Abstract The natural neighbour Petrov-Galerkin method (NNPG) is one of the special cases of the generalized meshless local Petrov-Galerkin method (MLPG). This paper demonstrates the NNPG can be successfully used in design sensitivity analysis in 2D elasticity. The design sensitivity analysis method based on the local weak form (DSA-LWF) in the NNPG context is proposed. In the DSA-LWF, the local weak form of governing equation is directly differentiated with respect to design variables and discretized with NNPG to obtain the sensitivities of structural responds. The calculation of derivatives of shape functions with respect to design variables is avoided. No background meshes are needed to integrate the weak form, no assembly process is needed to generate the global stiffness matrix and no user-defined parameters are used as well. Three numerical examples are solved using DSA-LWF and the results show the proposed method gives very accurate solutions for these problems.
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