Abstract
Slender thin-walled members are main components of modern engineering structures, whose buckling behavior has been studied widely. In this article, thin-walled members with simply supported loaded edges can be discretized in the cross-section by semi-analytical finite strip technology. Then, the control equations of the strip elements will be rewritten as the transfer equations by transfer matrix method. This new method, named as semi-analytical finite strip transfer matrix method, expands the advantages of semi-analytical finite strip method and transfer matrix method. This method requires no global stiffness matrix, reduces the size of matrix, and improves the computational efficiency. Compared with finite element method’s results of three different cross-sections under axial force, the method is proved to be reliable and effective.
Highlights
Buckling analysis is the most important step during the design of slender elements which can be applied in different branches of engineering, including mechanical construction, marine applications, and civil architecture.[1]
It is based on energy rule that the elastic buckling modes of I-section beams has been studied.[5]
If the orthogonal conditions about kpeq and kpgq given by Yao et al.[41] can be used, the control equations of the buckling strip can be obtained by virtual work principle, which are kpep À kpgp dp = Rp ð13Þ
Summary
Buckling analysis is the most important step during the design of slender elements which can be applied in different branches of engineering, including mechanical construction, marine applications, and civil architecture.[1]. Each nodal line i has two membrane degrees of freedom (DOFs) ui and vi and two bending DOFs wi and ui This numbering system will be used to depict the state vector of the nodal line and the transfer matrix of the strip in section ‘‘Semi-analytical FSTMM for buckling analysis.’’. If the orthogonal conditions about kpeq and kpgq given by Yao et al.[41] can be used, the control equations of the buckling strip can be obtained by virtual work principle, which are kpep À kpgp dp = Rp ð13Þ where kpep is the elastic stiffness matrix of equation (8), kpgp is the geometric stiffness matrix as shown in equation (11), dp is the nodal line displacement vector, and Rp is the generalized internal forces acting on the strip, which can be expressed as. Coefficient matrix of equation (18) can be denoted as
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