基于光滑有限元法的体积锁定研究

Study of volumetric locking based on the smoothed finite element method

针对数值模拟中求解几乎不可压缩材料时产生的体积锁定问题,提出了2种基于光滑有限元法的解决方案。方案1基于光滑子单元域有限元法,通过将材料特性矩阵划分为剪切部分和挤压部分,利用选择积分分别形成相应的刚度矩阵,对产生体积锁定的挤压部分运用一个光滑子单元进行计算,而对剪切部分运用多个光滑子单元进行计算;方案2综合应用光滑节点域有限元法和光滑边域有限元法,用免于体积锁定的光滑节点域有限元法计算挤压部分,用结果精确的光滑边域有限元法计算剪切部分。算例研究结果证明了2种方案的正确性和有效性,且方案2的计算精度高于光滑节点域有限元法。

Aimed at the volumetric locking problems that were produced by the calculation of the nearly incompressible material in numerical simulation,two schemes based on the smoothed finite element method（SFEM） were proposed.The first scheme was to decompose the material properties matrix into two parts,the volumetric part and non-volumetric part,and the stiffness matrix was also correspondingly decomposed into two parts.Then,the cell-based smoothed finite element method（CS-FEM） using one subcell（SC=1） was used only on the volume-part and the CS-FEM using more than one subcell（SC〉1） was used on the remaining part.The second scheme was to use the node-based smoothed finite element method（NS-FEM） that was free from volumetric locking to calculate the volumetric part and to use the edge-based finite element method（ES-FEM） that had accurate results to calculate the remaining part.Results of the numerical study showed that both schemes were correct and effective,and the second scheme was more accurate than NS-FEM.