Novel quadrilateral strain-based finite element for static, free vibration, and buckling analysis of plates

This paper focuses on the static analysis, free vibration, and buckling validation of Reissner–Mindlin plates using a newly developed quadrilateral finite element, termed FNSBP, which is based on the strain approach. The proposed element is equipped with three essential external degrees of freedom at each of its four corner nodes. The displacement field is formulated using assumed strain functions that inherently satisfy the compatibility equations. This new element was developed to improve upon the previously introduced SBRP strain-based rectangular plate element. The effectiveness and robustness of the FNSBP element are evaluated through various numerical examples involving both thick and thin plates of different geometries. Its performance is benchmarked against displacement-based elements from the literature and analytical solutions, demonstrating superior accuracy and convergence in many cases. The results indicate that the FNSBP element provides significant improvements in computational efficiency and accuracy, especially for complex plate configurations under different loading and boundary conditions, validating its applicability in structural analysis.