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School of Mechanical Engineering, Sharif University of Technology
Abstract
one of the simplest numerical integration method which provides a large saving in computational efforts, is the well known one-point Gauss quadrature which is widely used for 4 nodes quadrilateral elements. On the other hand, the biggest disadvantage to one-point integration is the need to control the zero energy modes, called hourglassing modes, which arise. The efficiency of four different anti-hourglassing approaches, Flanagan (elastic approach), Dyna3d, Hansbo and Liu have been investigated. The first two approaches have been used in 2 and 3-D explicit codes and the latters have been employed in 2-D implicit codes. For 2-D explicit codes, the computational time was reduced by 55% and 60% for elastic and Dyna3d, respectively. However, for 3-D codes the reduction was dependent on the number of elements and was obtained between 50% and 70%. Also, the error due to the application of elastic methods was less than that for Dyna3d when the results were compared with those obtained from 2-points Gauss quadrature. Nevertheless, the convergence occurred more rapidly and the oscillations were damped out more quickly for Dyna3d approach. For implicit codes, the anti-hourglassing methods had no effect on the computations and therefore a 2-points Gauss quadrature is recommended for implicit codes as it provide the results more accurately.
Majzoobi, G. H., Farrahi, G. H., & Ferdows Farahani, F. (2003). Efficiency of Anti-Hourglassing Approaches in Finite Element Method (TECHNICAL NOTE). International Journal of Engineering, 16(1), 79-88.
MLA
G. H. Majzoobi; G. H. Farrahi; F. Ferdows Farahani. "Efficiency of Anti-Hourglassing Approaches in Finite Element Method (TECHNICAL NOTE)". International Journal of Engineering, 16, 1, 2003, 79-88.
HARVARD
Majzoobi, G. H., Farrahi, G. H., Ferdows Farahani, F. (2003). 'Efficiency of Anti-Hourglassing Approaches in Finite Element Method (TECHNICAL NOTE)', International Journal of Engineering, 16(1), pp. 79-88.
VANCOUVER
Majzoobi, G. H., Farrahi, G. H., Ferdows Farahani, F. Efficiency of Anti-Hourglassing Approaches in Finite Element Method (TECHNICAL NOTE). International Journal of Engineering, 2003; 16(1): 79-88.