Development of a strain-smoothed finite element - Ho, Qi Heng. (2011)
The finite element method (FEM) has proven to be a widely popular tool in various engineering fields, and has helped to improve the standard of engineering designs and design process methodology. However, the FEM suffers from a few drawbacks, one being the inability to model strain and stress gradients within linear elements, causing discontinuities in strain and stress values across elements. The development of the smoothed finite element method (SFEM) in recent years was intended to solve this problem. This report examines an alternative and more simplistic approach for strain smoothing by utilizing existing classical finite element formulations to derive smoothed elemental strain matrices. The derivation of a smoothed 2-node bar element and a smoothed TRIA3 element was presented in this report, along with test problems to perform comparative studies against the respective classical elements. It was found that the smoothed elements generally performed better compared to their classical counterparts especially for higher order problems involving non-linear loading conditions, but also suffered from the problem of locking present in the classical linear elements.