弹性近不可压缩问题的精化元法

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(IQ8),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IQ8单元用于可压和近不可压缩问题都有效.

Refined-element methods to solve elastic incompressible problems

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(IQ8) 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.