Flexible Integration Points Coupled with Smoothed Strain in Elasticity Problems

Abstract

In this paper, alpha finite element method ([Formula: see text]FEM) with modified integration rule ([Formula: see text]FEM-MIR) using quadrilateral elements is developed. The key feature of [Formula: see text]FEM-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 [Formula: see text]FEM-MIR model can be altered. In addition, the exact, upper and lower bound solutions of strain energy in the [Formula: see text]FEM-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 [Formula: see text]FEM 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 [Formula: see text] ([Formula: see text]controls the locations of integration points of stiffness) in the [Formula: see text]FEM-MIR model. Extensive numerical studies have been conducted to confirm the properties of the proposed [Formula: see text]FEM-MIR, and an excellent performance has been observed in comparing traditional [Formula: see text]FEM and FEM.