基于RKPM的灵敏度分析及核函数的影响研究

Sensitivity Analysis and Effects of Kernel Functions in Structural Optimization with Reproducing Kernel Particle Method(RKPM)

基于重构核粒子法的结构优化设计的关键是灵敏度分析。笔者采用罚函数法施加位移边界条件,在结构分析的基础上,利用直接微分法,建立了基于重构核粒子法的结构灵敏度方程,而且其表达形式与结构控制方程非常相似,计算过程容易实现。编写相应的MATLAB程序对两个具有解析解的经典算例进行了灵敏度分析,并详细讨论了节点数、不同核函数及其参数对灵敏度计算精度的影响。计算结果与解析解吻合较好,表明该灵敏度分析方法是正确有效的,同时给出了灵敏度分析过程中合理选择核函数的建议。

Sensitivity analysis is the key to structure optimization design based on Reproducing Kernel Particle Method（RKPM）.In this paper,the penalty method is employed for imposing essential boundary conditions,and the structure sensitivity equation is proposed by using Direct Differentiation Method（DDM） on the basis of structural analysis.The expression form of sensitivity equation is so similar to the governing equation that the solving process is easy to implement.The corresponding MATLAB programs are developed,and then the sensitivity analysis of two classical numerical examples with analytical solution are performed successfully.The effects of node number,various kernel functions and their parameters on the displacement sensitivity accuracy are discussed in detail.Computational results are in good agreement with analytical solution and it shows that the present sensitivity analysis method is effective.Finally,advices for choosing of the kernel functions in sensitivity analysis based on RKPM is given.