Gemetric non-Linear Analisys of thin Walled Spatial Frames

Abstract

An incremental and piecewise nonlinear finite element approach is developed for the large displacement large strain regime with particular reference to elastic-plastic behavior in metal structures.
A large displacement, small strain formulation (as applicable to problems of structural stability) is obtained from this theory by assuming that changes in lenght of line elements and relative rotations are negligible when compared to unity. A consistent Updated Lagrangian formulation is derived from the energy balance equation in
reference to propper configuration. Differences between the existing formulations and similar ones in the literarure are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. A complete formulation for the equilibrium of a thin walled member of arbitrary open cross-section is used and a complete displacement fied (axial and transversal) is developed including higher order terms. A more restricted approach under the hypothesis hypotesis of linearized field of displacements is adopted in order to show an application and a new stiffness matrix for geometrically non-linear incremental analysis of
three dimensional beam-column with bisymmetrical, thin walled, I-type cross section is presented. Corrections in the element matrix are made to propperly consider: the behavior under finite rotations. The formulation implemented in a computer program uses the Newton-Raphson scheme for nonlinear incremental analysis.