The Theory Of Stability And Geometrical Nonlinear Analysis Of Thin-walled Structure Based On Finite Rotaton

Based on the critical review to the elastic stability theory of thin-walled member, this paper anlysises the default of the classic theory. The problem existing in the present theory of flexural-torsional buckling of structures are discussed that the buckling procedure is found to be restricted to certain development order to of displacements and rotations by the present theory. A simplified small rotation matrix is often used in the formulation of finite element models for the flexural-torsional stability analysis of thin-walled beams of open cross-section. However, the approximations in the small rotation matrix may lead to the loss of some significant terms in the stability stiffness matrix. Without these terms, a finite element line model may predict the incorrect flexural-torsional buckling load of a beam. In geometrically nonlinear analysing of three-dimensional members, enforing the behavior of nodal moment through an external matrix to the geometrical stiffenss matrix can predict the result of space frames.In the analysis of three-dimensional member, finite rotation which is not true vector, can not simple additive like two dimensional rotation. Theoretical considerations based on Euler's theorem and the second-order transformation matrix are presented. The improved displacement field is introduced using the second-order terms, the strain-displacement relations for the thin-walled structures are presented. Based on Bernoulli assumption and Vlasov's theory, the relation between rotation and transverse displacement derivative are derived. Introduced the Rodiguez' rotation and semitangential rotation as the spatially rotational parameters, the formulation of the flexural-torsional buckling is used to the theory for stability of thin-walled structures, which verifies the traditional formula and makes the traditional theory more perfect.Using the Proposed theory, the stabilities of simply supported bemas and cantileves under different lodaings are studied. For simply supported bemas, this new theory is the same as the traditional theory. Using the traditional theory, Tong G S's theory of stability of Thin-Walled Members considering the effects of transverse stresses and the proposed theory, this thesis investigates the buckling of cantilevered thin-walled bemas. When cantilevers under uniform bending, Tong G S's theory and the proposed theory is the same, but the traditional theory is not correct because it not allow the moment rotating at the free end of the cantilever. In this case the work done during buckling must be increased by the work done by the end moment. While for cantilevers under tranverse loads, this new theory is the same as the traditional theory. Comparisons between the test result from the literature, the results of the proposed theory suggestes that the proposed theory has an excellent agreement with the test results. These anayalses showed that the proposed theory eliminated all the problems existed in current available theories and is suitable for buckling analysis of bemas under any boundary conditions and loadings.The rotation variables contained in the nodal displacement vector are represented by transverse displacement derivatives, which may lead to inconsistency for the moment imbalance at the corner nodes of frame structures. This paper selectes the Rodiguez' rotation and semitangential rotation as the element rotation displacements, uses the virtual-work expressions to derive load stiffness matrix, which eliminates the unbalance moment problem. An updated Lagrangian formulation is used to develop the new geometrical nonlinear stiffness matrix. The numerical examples are given to testify the correction and precision of this method.