A new non-conforming finite element for free vibration analysis of thin plates with and without cutouts: ABAQUS implementation using the UEL subroutine

This paper presents a novel strain-based finite element (NSBPE4K) developed for the free vibration analysis of thin plates, both with and without cutouts. The element incorporates three primary degrees-of-freedom per node: a transverse displacement (w) and two normal rotations (θx, θy) about the x and y axes, respectively. The displacement field is formulated based on assumed functions for the strain components, ensuring the compatibility equations are satisfied. The non-conforming element was successfully implemented in the ABAQUS software using the UEL subroutine (user element). Free vibration analysis results demonstrate the exceptional efficiency and accuracy of the new element. The results obtained with the present element excel those obtained with standard ABAQUS elements and other non-conforming elements found in the literature. This superiority is noticeable in free vibration scenarios, demonstrating the effectiveness of the proposed finite element for accurate and reliable simulation of the vibrational behavior of thin plates.