<p>The strain-based approach has been widely employed in linear analysis due to its demonstrated efficiency and rapid convergence. The significant advantage of this method lies in its flexibility to control the displacement field, thereby enabling improved accuracy when required. However, due to the complexities associated with nonlinear analysis, the application of this approach by many researchers has remained largely confined to linear problems. This paper introduces, for the first time, a novel strain-based finite element formulation for the nonlinear static and free vibration analysis of isotropic and functionally graded material plate structures. A quadrilateral strain-based Mindlin plate element is coupled with a strain-based membrane formulation and utilizes von Kármán geometric nonlinearity through the principle of virtual work. The Newton–Raphson iterative method is employed to address the geometrically nonlinear issue. Extensive convergence studies and numerical simulations are carried out under various loading conditions, boundary conditions, and material gradations to assess the robustness and accuracy of the proposed element. The numerical results exhibit excellent agreement with both analytical solutions and experimental results, and the proposed element demonstrates excellent convergence with regular and irregular mesh sizes than existing finite elements in both linear and nonlinear analyses. The study further investigates the influence of gradient index, thickness ratio, aspect ratio, and boundary conditions on the nonlinear response of plate structures, highlighting the critical role of nonlinear analysis in capturing realistic structural behavior.</p>