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| Improved reproducing kernel particle method for shape design sensitivity analysis |
| Revised:August 06, 2003 |
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| DOI：10.7511/jslx20054083 |
| KeyWord:meshless methods,reproducing kernel particle method,shape design sensitivity analysis,shape optimization |
| WANG Xue-ming~ |
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| Abstract: |
| Based on the material derivative approach and the Direct Differentiation Method (DDM), the Reproducing Kernel Particle Method (RKPM) is developed further for shape design sensitivity analysis (DSA). DSA formulations based on meshless approximation are derived, and in particular, the differences between meshless method and FEM are stressed when taking material derivatives of shape functions with respect to design variables. A unique approach is presented to improve the efficiency of meshless methods, in which RKPM shape functions and their material derivatives are expressed explicitly in terms of kernel function moments. Two 2-D elasticity DSA examples are given. There is good agreement between the numerical results and the analytical results with regard to displacement sensitivities as well as stress sensitivities. In addition, comparison of time-consuming between the classic RKPM and the improved RKPM demonstrates that the present method can improve the efficiency of DSA markedly. |
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