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In this paper, the large deflection problem of an uniformly loaded circular plate with edge simply hinged is considered. First, a new algorithm for the deflection problem is proposed based on Adomian decomposition method. Then, a new approximate analytic solution of the large deflection problem is obtained by the algorithm. Final, its bending moments are analyzed corresponding to different center deflections. And the relationship between the center deflection and the external load is discussed. Through comparing the errors of the obtained approximate solution with the previous perturbation solution and homotopy perturbation solution, one can see that the obtained solution in this paper is a better one and the result in this paper has a certain practical value. [ABSTRACT FROM AUTHOR]