This study presents a comparative assessment of three various plane stress finite element formulations—CPS4, CPS4R, and CPS4I—implemented in ABAQUS for the prediction of maximum stress in a rectangular plate with a central circular hole subjected to uniaxial tension. Numerical results were benchmarked against the theoretical solution based on the gross-section stress concentration factor over hole diameter-to-width ratios up to 0.8. The primary objective was to quantify the influence of element formulations on maximum stress estimation with increasing hole diameter-to-width ratio. Numerical results suggested that all element types successfully captured the progressive increase in maximum stress with increasing hole size. Nevertheless, systematic differences in accuracy were observed. The CPS4 element produced slight overestimations, whereas CPS4R consistently underestimated the reference solution, with discrepancies becoming more noticeable at higher geometric ratios where stress gradients are more pronounced. Among the examined formulations, CPS4I exhibited the most consistent and accurate agreement with the theoretical results, maintaining small and stable error levels across the entire investigated range. This was attributed to its incompatible mode enhancement that provides improved strain field representation, enabling more reliable resolution of localized stress peaks. The findings underscored the critical role of element formulation in ABAQUS for achieving accurate maximum stress predictions in perforated structural components subjected to uniaxial tensile loading.
Dundar et al. (Mon,) studied this question.