Existence and Uniqueness of the solution of large deflection of circular plate by the Burger’s method

In the analysis of classical mechanics problems, there are cases where linear mathematical model can not fully describe the phenomena. If the deflection of the plate is of order of magnitude of its thickness, the differential equations for the deflection and displacements can be written in terms of nonlinear equations. These nonlinear equations are usually difficult to obtain the solution. Thus, several attempts have been tried to obviate the difficulties.
Among these attempts, it was Berger’s method which drew much attention. Berger[1] derived as implified nonlinear equations for a plate with large deflections by assuming that the strain energy due to the second invariants of the middle surface strains can be neglected when deriving the differential equations by energy method. Berger restricted his analysis to static and isotropic cases.
Later, his procedure was generalized to dynamics of isotropic plates by Nash and Modeer [2] and to dynamic phenomena in anisotropic plates and shallow shells by Nowinski [3]. Berger’methods is dealt in recent books [4] and [5]. In the research paper[6], Banerjee and Mazumdar review various 

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