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In this paper, the homotopy analysis method (HAM) is successfully applied tosolve the Von Karman's plate equations in the integral form for a circularplate with the clamped boundary under an arbitrary uniform external pressure.Two HAM-based approaches are proposed. One is for a given external load Q, theother for a given central deflection. Both of them are valid for an arbitraryuniform external pressure by means of choosing a proper value of the so-calledconvergence-control parameters c_1 and c_2 in the frame of the HAM. Besides, itis found that iteration can greatly accelerate the convergence of solutionseries. In addition, we prove that the interpolation iterative method is aspecial case of the HAM-based 1st-order iteration approach for a given externalload Q when c_1=-theta and c_2=-1, where theta denotes the interpolationparameter of the interpolation iterative method. Therefore, like Zheng andZhou}, one can similarly prove that the HAM-based approaches are valid for anarbitrary uniform external pressure, at least in some special cases such asc_1=-theta and c_2=-1. Furthermore, it is found that the HAM-based iterationapproaches converge much faster than the interpolation iterative method. All ofthese illustrate the validity and potential of the HAM for the famous VonKarman's plate equations, and show the superiority of the HAM over perturbationmethods.

Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure (II): Equations in Integral Form