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.