An Asymptotic Nonlinear Theory of Thin Elastic Plates

Abstract

The present paper is concerned with the derivation of an asymptotlc theory describing the behaviour of thin elastic plates undergoing large transverse deflections. The domain occupied by a thin plate is first transformed into a domain of comparable dimensions in which the equations of three dimensional nonlinear elasticity in material coordinates are tried to be solved by representing the field variables as asymptotic series in a thickness parameter and by assuming a linearly elastic response. The theory corresponding to the lowest order members in the hierarchy of equations so obtained is studied in detail and it is shown that this corresponds to the well-known von Kârmân’s theory under certain boundary conditions. Ali stress components are computed and the spatial Cauchy stresses are also evaluated.