Lateral Buckling Analysis Of Thin-Walled Structures With Irregular Cross Section

The main content of this thesis is lateral buckling analysis of thin-walled structures with irregular cross section by transformed 63 spline finite member element method. The results of this method are compared with those of finite member element method adopting linear functions as interpolation functions and those of Classical theory. By this method, lateral buckling analysis of thin-walled structures with stepped cross sections is studied as well.This method is based on energy equations and variational principles. The energy equations of lateral buckling of thin-walled structures are deducted at first, then discretize the longitudinal warping displacements on the cross section by transformed 83 spline functions, and the transverse displacements are expressed by the displacements of the centroid of cross section with some reasonable presumptions adopted. The general solution of displacements of static analysis is adopted to simulate the buckling displacements or possible displacements in vibration and relevant variational principles (displacement variational principle for buckling analysis) are adopted to form the stiffness matrix. The eigenvalues and the corresponding eigenvectors of the stiffness matrix are the buckling load and corresponding buckling mode, or the frequencies and the corresponding vibration modes.The proposed method can reflect shear lag effect by considering the shear deformation of the median surface of thin-walled members. By taking the real displacements of the nodes as the unknown parameters, the transformed 63 spline function naturally satisfies the continuity of the displacements of cross section with bifurcate branches of walls. The number of the basic variables may be different on different cross section, thus greatly increase the flexibility of the method. This method avoids calculating shear center and sectorial coordinate, so it can be easily understood and applied. This kind of simulation system is applicable to any cross section, and developed a new way for the applications of the spline function.