<p>The present work focuses on the nonlinear bending behavior of plates made of functionally graded material (FGM) subjected to various loading conditions, while previous studies have primarily focused on linear analyses or considered limited nonlinear cases. A novel contribution is provided by formulating the Reissner–Mindlin plate equilibrium equations in strong form using a hybrid numerical strategy that couples the ANM with a spectral Chebyshev collocation meshfree approximation, enabling highly accurate solutions in both linear and nonlinear regimes. Unlike conventional mesh-based approaches, the present formulation solves the equilibrium equations in strong form without meshing constraints, offering clear advantages for problems involving large deflections. The number of degrees of freedom is reduced by using spectral approximation compared to other meshfree methods, while ensuring rapid convergence and high accuracy. Based on the Reissner–Mindlin plate theory, the method effectively incorporates shear deformation effects in moderately thick plates. A key originality lies in the strong matrix formulation expressed in terms of generalized forces, yielding a simple and physically intuitive implementation. Validation against analytical and numerical benchmarks affirms the efficiency and robustness of the introduced framework for tracing complex nonlinear equilibrium paths. The results highlight its potential for advancing the modeling of functionally graded structures undergoing large deflections, while recognizing that the density of spectral stiffness matrices may increase computational cost.</p>