<p>This study presents axisymmetric accurate nonlinear analytical solutions for circular thin plates subjected to a central concentrated load, marking a significant advancement in the understanding of plate nonlinear mechanics. The novel approach employs innovative orthogonal deflection series, including natural logarithm terms multiplied by power series, meticulously tailored to handle the central singularity and satisfy displacement boundary conditions. The convergence and accuracy of this method, particularly in the selection of similar series terms, are significantly better than those of Zheng’s well-known accurate series solutions, exemplifying a remarkable advance in analytical techniques. Notably, the central deflection error of the circular thin plates presented in this study is less than 0.0001%, setting unprecedented benchmarks for the verification of various nonlinear numerical and approximate analytical solutions. The significance of these discoveries underscores the substantial contributions of the present method, making it not only commendable but also highly deserving of further exploration and promotion.</p>