Flexible Integration Points Coupled with Smoothed Strain in Elasticity Problems

In this paper, alpha finite element method (αFEM) with modified integration rule (αFEM-MIR) using quadrilateral elements is developed. The key feature of αFEM-MIR is to combine the smoothed strain and compatible strain using flexible integration points. With simple adjustment of integration points in the stiffness, it is found that the softening or stiffening effect of αFEM-MIR model can be altered. In addition, the exact, upper and lower bound solutions of strain energy in the αFEM-MIR model with different integration points are examined for both overestimation and underestimation problems. Furthermore, the displacement solutions can be improved significantly compared with traditional integration points in the standard finite element method (FEM) and αFEM models. In this work, the strategy to overcome the volumetric locking and hourglass issues are also analyzed using different integration points. In addition, it is found that the stability of discretized model is proportional to parameter r (rcontrols the locations of integration points of stiffness) in the αFEM-MIR model. Extensive numerical studies have been conducted to confirm the properties of the proposed αFEM-MIR, and an excellent performance has been observed in comparing traditional αFEM and FEM.