In this paper, a one - dimensional high order model based on a set of basic deformation modes of cross section is proposed to analyse one-dimensional dynamic model of cold-formed channel beam Considering the Deformable Cross-section. The model considers the displacement field through the linearly superimposing of 36 basis deformation modes, which stem from the discretization of the cross-section into 9 points and 8 segments. The corresponding deformation function is approximated with Hermite Interpolation. The governing equation is deduced from the principle of Hamilton, then use quadratic Lagrange interpolation for finite element realization. Numerical examples have also been presented and the comparison with ANSYS shell model showed its accuracy, efficiency, and applicability in reproducing three-dimensional behaviors of cold-formed channel beam.

In order to accurately analyse the dynamic performance of the arm segment, a dynamic model of u-shaped thin-walled beam based on one-dimensional high-order beam theory is proposed to predict the three-dimensional displacement of the beam at any point. First, a one-dimensional high-order model is established using Hamilton’s principle. The high-order model considers the displacement field by linear superposition of a set of basis functions that vary axially along the beam. A basis function represents a deformation mode, and interpolation polynomials are used to approximate the three-dimensional displacements of nodes on the center line of the section. At the same time, different section discretization methods are analysed, which have different influences on the precision of the model by discretization of the curved surface part of u-shaped section by straight transposition. Finally, the generalized characteristic of the model is worth to obtain the natural frequency, which is compared with the ANASYS plate and shell theory. The error range of the first 16 orders is within 1.5%. The results show that the discrete mode of the model has a certain influence on the frequency error, and the more discrete nodes of the circular arc part, the higher the accuracy.