基于Taylor展开的无单元插值形函数及应用

在无单元伽辽金法的基础上,构造了基于Taylor展开的具有过点插值的无单元形函数,它可以和有限元法一样处理边界条件,克服了传统的无单元伽辽金法遇到的瓶颈问题;对非凸边界的处理,提出了新的准则--弧弦准则(arc-string criterion).这样,可大大减少了无单元法的计算工作量,提高了边界处理的精度,并且继承了无单元法及有限元法的优点.

Interpolating Shape Function of Meshless Method Based on Taylor Expansion Theory and Its Application

Based on the theory of Element-free Galerkin methods, the EFM shape function based on Taylor expansion and having the pass-nodes interpolation character is constructed. The shape function can deal with the boundary condition as same as finite element and get rid of the bottleneck problems in the traditional EFGM. Also it advances a new criterion-arc-string criterion for non-convex boundary. These results can reduce EFM calculation workload greatly, improve the precision about boundary management and inherit the merit of EFM and FEM.