B样条小波权函数无网格法及其在杆、板结构中的应用

Meshless method based on B-spline wavelet weight function and its application in pole and plate structure

以三次B样条小波函数作为权函数,设计了一种无网格实用算法。以一维杆和二维板结构为例,分别采用基于Gauss权函数、三次样条权函数与三次B样条小波权函数的无网格算法进行仿真分析。计算结果表明,本文算法得到的位移、应力近似解与精确解在多尺度、稳定性方面具有比其他权函数更好的拟合效果。本文研究拓宽了无网格法在工程结构分析中的应用范围。

A practical meshless algorithm was proposed using the cubic B-spline wavelet function as the weight function. The simulations of the 1-D pole and 2-D plate as examples were performed using the meshless algorithm based on the Gauss weight function, the cubic spline weight function and the cukic B-spline wavelet weight function. The simulated results show that the approximated solutions of the displacement and the stress achieved by the proposed algorithm is characterized by better fitting effect than the exact solutions with respect of multi-scaling and stability. The obtained results open up the broad prospects for the application of the meshless method in the engineering structure analysis.