Formulation of an efficient strain-based finite element for large deflection analysis and free vibration of plates

This study presents the development and evaluation of a finite element based on the strain-based approach for the nonlinear analysis of plate structures. Unlike traditional displacement-based methods, the strain-based formulation allows enhanced control over the deformation field, offering improved accuracy and adaptability, particularly under complex loading and boundary conditions. The proposed element combines a membrane component for capturing large displacement effects and a bending component derived from Reissner–Mindlin theory, making it suitable for both static and free vibration analyses. A comprehensive set of numerical examples is conducted to assess the performance of the element, including square plates with various boundary conditions, trapezoidal plates, and plates with concentrated or uniformly distributed loads. Comparative studies demonstrate excellent agreement with experimental results, nonlinear analytical solutions, and benchmark finite element models such as ABAQUS S4R. The results confirm the element’s high accuracy, robust convergence behavior across regular and irregular meshes, and its effectiveness in modeling both standard and irregular geometries. This research highlights the potential of the strain-based approach for advanced nonlinear plate analysis and extends its applicability beyond linear regimes.