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

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 ۴ 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), Dyna۳d, Hansbo and Liu have been investigated. The first two approaches have been used in ۲ and ۳-D explicit codes and the latters have been employed in ۲-D implicit codes. For ۲-D explicit codes, the computational time was reduced by ۵۵% and ۶۰% for elastic and Dyna۳d, respectively. However, for ۳-D codes the reduction was dependent on the number of elements and was obtained between ۵۰% and ۷۰%. Also, the error due to the application of elastic methods was less than that for Dyna۳d when the results were compared with those obtained from ۲-points Gauss quadrature. Nevertheless, the convergence occurred more rapidly and the oscillations were damped out more quickly for Dyna۳d approach. For implicit codes, the anti-hourglassing methods had no effect on the computations and therefore a ۲-points Gauss quadrature is recommended for implicit codes as it provide the results more accurately.

کلیدواژه ها:

Hourglassing ، anti ، Hourglassing Control ، Flanagan Method (Elastic) ، Dyna۳d ، Hansbo ، Liu ، Explicit ، Implicit