Abstract：The distribution of in-plane stresses and buckling of thin rectangular elastic plates with all edges simply supported (SSSS), under nonlinearly distributed in-plane loadings along two opposite edges are studied by using the Hamilton system of elasticity and Galerkin method. Based on the Hamilton system of plane elasticity in a rectangular domain, the general solutions of the in-plane stress distribution in terms of undetermined constants corresponding to the zero and nonzero eigen-values are obtained by using the symplectic eigen-solution expansion method. After applying all stress boundary conditions, the formulae determining the in-plane stress distribution in a thin rectangular plate under parabolic distributed compressive edge loads along two opposite sides are derived. Due to the complexity of the in-plane stress distribution, it is impossible to obtain analytical buckling load for a simply supported plates under parabolic edge compressions. Therefore, the Galerkin method is employed for obtaining the buckling loads of rectangular plates with various aspect ratios. The present results agree very well with existing DQ (differential quadrature) data confirms the validity of the proposed method. Based on the results reported herein, one may conclude that the symplectic eigen-solution expansion method could provide a new way for obtaining in-plane stress expressions of thin rectangular plates subjected nonlinearly distributed in-plane edge loadings.
2010, Vol. 31 
