弹性近不可压缩问题的精化元法

Refined-element methods to solve elastic incompressible problems

对于弹性问题,材料近不可压缩可引起有限元法的体积闭锁.为解决此问题,以精化元法为基础,将单元应变正交分解为常应变和高阶应变,其中常应变可以保证收敛,对于近不可压缩问题只需忽略高阶应变中的体应变,从而避免单元体积不可压缩闭锁.按照上述方法修改了平面八节点等参元(IQ 8),并用于平面应变厚壁筒计算,通过与ABAQUS系统软件的八节点等参元计算结果对比,表明IQ 8单元用于可压和近不可压缩问题都有效.

For elastic problem, volumetric locking may occur when the material response is incompressible. To solve this problem, a new method based on the refined-element technique is proposed. The strain in the present method can be decomposed into two parts： one is the constant strain that ensures the convergence, and the other is the higher-order strain that the volumetric strain can be ignored to avoid volumetric locking for incompressible problem. At the same time, the improved 8-node isoparametric element （IQS） is also proposed and applied to analyzing the problem of thick-walled cylinder. Compared with the element Q8 in ABAQUS, numerical results show that the present IQ8 possesses the ability to solve compressible and incompressible problems.