Hamiltonian Solving System For Buckling Analyses Of Rectangular Thin Plates Subjected To Nonlinearly Distributed Loadings

The problem of buckling of the thin plate structures subjected to in-plane compressive is important in the shipbuilding, aircraft, and automotive industries. So it is widespread concerned. Up to now, many academician have introduced many approaches to solve this problem, making certain research results. According to the theory of thin plate deflection, buckling analysis needs to determine the stress distribution in-plane first. However, there have been very few previous satisfactory analytical solutions for the in-plane stress distribution of the thin plates under nonlinearly distributed edge loadings. Despite the numerical methods for solving the in-plane stress distribution under complex and diverse forms of the edge loadings, is of good supplement, but still effective analytical method is indispensable. Therefore, this dissertation introduce Hamilton solution system, using the theory of Hamiltonian solving system about rectangular domains for solving the problem of the in-plane stress distributed of thin rectangular plates with nonlinearly distributed loadings along two opposite plate edges. On the basis of the accurate stress distribution, solve the buckling problem of the simply supported and/or clamped plates by using the Galerkin methods. The main content of the research is as follows:1. Using the theory of Hamiltonian solving system, the stress distributions in-plane of isotropic rectangular plates under symmetric deformation. 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.2. Based on the general solution given by the Hamiltonian solving system, the expressions of the stress applying the edge boundary are given buy using series method with the help of symbolic computational software Maple. The figures of the stress distributions for various aspect ratios are presented. Compared with the computing results of DQ method, it shows the correctness and effectiveness of approach in this dissertation3. Considering the complexity of the expressions of the in-plane stresses, the thin plate deflection function is expressed as in the form of triangular series which meet the bending plate boundary conditions by using the Galerkin method. Build the Galerkin formula, and then the buckling problem is transformed to eigenvalue problem. A group of buckling loads for the simply supported and clamped plates subjected to half-cosine and/or parabolic distributed in-plane loads for various aspect ratios is obtained. Comparing with the results in exist literatures, the results in this dissertation are agree well with numerical result of FEM and DQ method. Based on the results of herein, one may conclude that the proposed method for buckling analysis of the rectangular plates under in-plane nonlinear edge compressions is useful in engineering application.