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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