Stability Of Thin-walled Members Research Articles

Geometrically nonlinear Hessian eigenmode decomposition for local stability analysis of thin-walled structures

A nonlinear geometric formulation based on position and unconstrained vector is originally proposed to evaluate the local stability of thin-walled members. The Hessian is decomposed into linear and geometric equivalent installments. As the Hessian matrix exhibits a definite positive quadratic form, stability condition for large displacements requires that the Hessian matrix positivity be verified at each load small steps. This condition must be established by evaluating the smallest eigenvalue signal at the critical point imminence. The positional finite element method is formulated from a total Lagrangian reference. The mechanical system equilibrium is guaranteed by the total potential energy stationary principle. The constitutive law of Saint–Venant–Kirchhoff is obtained from the linear relationship between the second Piola–Kirchhoff stress tensor and Green–Lagrange deformation tensor. Some examples demonstrate the applicability of the methods.

Stability of thin-walled members having arbitrary flange shape and flexible web

A finite element method is presented for analysing thin-walled structural members comprising a flexible web connected to one or two rigid flanges of arbitrary shape. A general thin-walled beam-column element is used to model the flanges while a thin plate element is used to model the web. Based on the derived total potential energy functional, explicit linear and geometric stiffness matrices for the two types of element are obtained. Using static condensation and appropriate transformations, the beam-column element and the plate element are combined to yield a super element with 22 degrees of freedom capable of modelling the flexural, torsional, web distortional and coupled web and flange local buckling modes of a general thin-walled member. The technique may be used to predict the elastic buckling load of members under any loading and boundary conditions. Several numerical examples are presented to demonstrate the accuracy, efficiency and versatility of the method.