SYMPLECTIC ELASTICITY SOLUTIONS FOR THIN RECTANGULAR PLATES SUBJECTED TO NON-LINEAR DISTRIBUTED IN-PLANE LOADINGS

The eigenvector solutions corresponding to the zero and nonzero eigenvalues are carried out according to the symplectic eingen-solution expansion method in rectangular domains. Including the nonzero eigenvalues in the eigenvector solution yields the general solution of the in-plane stress with undetermined constants. After applying the boundary conditions, one gets a set of coupled equations to determine the unknown constants. These equations are solved by the software Maple. The formula determining the stress distribution of a thin rectangular elastic plate subjected to in-plane compressive loads varying half-cosine along two opposite edges are derived. The examples of the square plates under half-cosine and parabolic load distributions are analyzed to verify the efficiency and accuracy of the proposed method. The results are agreed well with the numerical results of differential quadrature (DQ) method and FEM. The results reported herein could provide reasonable preparations for the buckling analysis in engineering applications.