Efficiency of Anti-Hourglassing Approaches in Finite Element Method (TECHNICAL NOTE)

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.