On The Theoretical Solutions For The Stability Of Plates And Shells Based On The Symplectic Method And State Space Method

Plates and shells are widely used in aerospace engineering,ship engineering,ocean engineering,civil engineering,etc.as important engineering structures.In recent years,with the increasing demand for structural lightweight design and the increasing tendency of buckling failure of plates and shells,so,the stability of plates and shells has attracted more and more attention.Because the theoretical solutions not only serve as benchmarks for validation of other methods but also provide a tool for rapid parameter analysis and optimization,and help people understand various mechanical behaviors more deeply,the study of theoretical solutions has always been at the forefront of mechanical research.In this dissertation,the symplectic method and the state-space method have been applied to study the linear and nonlinear pre-buckling problems,bifurcation buckling problems,initial post-buckling and imperfection sensitivity problems of plates and shells in order to provide theoretical guidance for relevant structural analyses and designs.On the linear buckling analysis of rectangular plates,this dissertation used the symplectic superposition method obtain the new buckling solutions of completely free plates,used the symplectic superposition method combined with the continuity of boundary conditions to study the buckling problems of side-cracked plates and the effect of crack length on critical buckling loads.The analytic solutions above have been verified by the finite element method and the numerical results in relevant literature.(Chapter 2)On the linear buckling analysis of cylindrical shells,this dissertation introduced the governing equations for buckled and bent cylindrical shells into the Hamiltonian system using the variational principle and fundamental equations,and obtained new buckling and bending analytic solutions of non-Lévy-type cylindrical shells by the symplectic superposition method,which have been validated by the finite element method.The influence of curvature on the bearing capacity of cylindrical shells has been studied by the new analytic solutions,and the new analytic solutions of bending problems has paved a way for solving the buckling problems of shells under complex stress state.(Chapters 3 and 4)On the nonlinear eigenvalue bucking analysis of shells,this dissertation used the perturbation method to expand the nonlinear governing equations of cylindrical shells into the zeroth-order equations(pre-buckling equations)and the first-order equations(bifurcation buckling equations),which are solved by the symplectic method and state space method,respectively.The nonlinear governing equations of the two kinds of spherical shell theories were obtained by the variational principle based on the Donnell theory and small strainmoderate rotation theory,and the zeroth-order equations and the first-order equations of spherical shells were solved by the iterative method and state space method,respectively,and obtained the nonlinear deformation and critical loads of the spherical shells.Based on the precise integration method,this dissertation improved the solution schemes of the state space method.By adding the intermediate state vectors as the start and end vectors of state transfer,this dissertation settled the numerical stability problems due to the long transmission distance in the state space method for solving the shell problems with large diameter-to-thickness ratio,expanded the applicable range of diameter-to-thickness ratio and length-to-diameter ratio for the shell problems of state space method,and studied the influence of geometric nonlinearity on the critical loads of spherical shells.(Chapter 5)On the post-buckling analysis and imperfection sensitive analysis of plates and shells,this dissertation proposed a “pointwise perturbation method”,which introduced the imperfection into the governing equations and post-buckling expansion coefficients instead of assuming the post-buckling equilibrium path in advance in the traditional Koiter method,and obtained the load corresponding to any deformation state using the perturbation theory,thus predicting the bearing capability of the imperfect shells more accurately.In the post-buckling study of imperfect plates,this dissertation obtained the explicit analytic solutions by the perturbation method and symplectic method,and studied the influence of boundary conditions on the bearing capacity of plates,and designed the experimental equipment and scheme independently for experimental verification in addition to the numerical verification.In the imperfection sensitivity analysis of axially compressed cylindrical shells,the pointwise perturbation method predicted the bearing capacity of cylindrical shells with larger imperfection amplitude more accurately than the traditional Koiter method,which have been verified by the Riks algorithm.(Chapter 6)...