A technique to avoid aspect-ratio locking in QUAD8 element for extremely large aspect-ratios

作者：Rajendran S^*

来源：Structural Engineering and Mechanics, 2011, 37(6): 633-648.

• finite element method
• quadrilateral element
• aspect-ratio
• locking
• exact arithmetic
• ill-conditioning

This paper investigates the aspect-ratio locking of the isoparametric 8-node quadrilateral (QUAD8) element. An important finding is that, if finite element solution is carried out with in exact arithmetic (i.e., with no truncation and round off errors), the locking tendency of the element is completely avoided even for aspect-ratios as high as 100000. The current finite element codes mostly use floating point arithmetic. Thus, they can only avoid this locking for aspect-ratios up to 100 or 1000. A novel method is proposed in the paper to avoid aspect-ratio locking in floating point computations. In this method, the offending terms of the strain-displacement matrix (i.e., B-matrix) are multiplied by suitable scaling factors to avoid ill-conditioning of stiffness matrix. Numerical examples are presented to demonstrate the efficacy of the method. The examples reveal that aspect-ratio locking is avoided even for aspect-ratios as high as 100000.

• 出版日期2011-3-25
• 单位南阳理工学院