scholarly journals The Partial Selective Reduced Integration Method and Applications to Shell Problems

2009 ◽  
Author(s):  
F. Brezzi
Keyword(s):  
Integration Method ◽  
Reduced Integration ◽  
Selective Reduced Integration

Resolution of Defects in Degenerated Shell Elements Through Modification of Gauss Integration

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1877-1883 ◽  
Author(s):  
Y. D. Kwon ◽  
N. S. Goo ◽  
B. S. Lim
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Shell Element ◽  
Zero Energy ◽  
Integration Rule ◽  
Shell Elements ◽  
Reduced Integration ◽  
Stiffness Matrices ◽  
Assumed Strain ◽  
Degenerated Shell Element

In this paper, the modified Gauss integration method is developed to eliminate the shear and membrane locking phenomena of the degenerated shell element. The behavior of the element based on the Mindlin/Reissner theory in plates and shells sometimes causes a problem. In displacement-based shell elements, the full integration of stiffness matrices leads to a 'locking' or over-stiff behavior. The selective or reduced integration procedures may often overcome these difficulties, while overstiff solutions may still occur in the analysis with a highly constrained boundary. Except for the six zero-energy modes associated with shell rigid body movements, during the reduced integration of the stiffness matrices, many extra zero spurious energy modes are introduced due to reduced integration. This is a serious defect of degenerated shell element. In previous studies, several methods such as the addition of nonconforming displacement modes, an assumed strain method, and hybrid and mixed elements have been introduced in an attempt to overcome these difficulties. In this study a newly modified Gauss integration method combining both a selective and a weight-modified integration is suggested. Numerical experiments show that the new selective integration and weight-modified integration rule is very effective in eliminating the shear and membrane locking in static and modal analyses, and removes spurious zero-energy modes as well. Also, the effectiveness of proposed shell element is tested by applying it to some example problems. We solved post-buckling problem by the Riks arc-length method and dynamic problem by the Newmark's time integration method, as well as static problems.

A Selective Reduced Integration 8-Node Hexahedral Element by Assumed Strain for Coining Simulation

2012 ◽  
Vol 472-475 ◽  
pp. 533-537
Author(s):  
Wen Zhong ◽  
Yu Qi Liu ◽  
Yun Ming Hu ◽  
Sheng Qiang Li ◽  
Heng Jian Xu
Keyword(s):  
Velocity Gradient ◽  
Shear Locking ◽  
User Input ◽  
Reduced Integration ◽  
Numerical Tests ◽  
Assumed Strain ◽  
Hexahedral Element ◽  
Selective Reduced Integration ◽  
Assumed Strain Method ◽  
Simulation Package

A selective reduced integration 8-node hexahedral element for coining simulation is developed in this paper. The element is free of volume locking by assumed strain method. The standard velocity gradient matrix is derived in which the shear items are ignored to avoid shear locking. Hourglass modes are successfully suppressed without user-input parameters. The element is successfully employed in the coining simulation package - COINFORM. Numerical tests and experiments of a typical coin are carried out to show the good performances of the element.

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