Stiffness Matrix for Nonlinear Analysis of Thin‐Walled Frames

This paper describes a new stiffness matrix for large deflection and buckling analysis of three‐dimensional thin‐walled frames, which is decomposed as the sum of three matrices. The element formulation allows the use of beam‐columns with generic cross sections. Longitudinal displacement is described by the principle of sectorial areas using Vlasov's theory of thin‐walled beams, taking into account the cross‐sectional warping and nonuniform torsion. The displacement field is modeled by Hermitian function, and requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each beam node. The updated Lagrangian procedure has been employed for developing a geometrically nonlinear matrix. Nonlinear terms usually found in doubly symmetric sections, and terms only found in nonsymmetric sections, are explicitly identified as the elements of the doubly symmetric section matrix or of the generic section matrix, respectively. Moreover, the correction matrix for accurate consideration of finite rotation at frame joints is also presented. Numerical examples using the proposed matrices are compared with previous results.