Nonlinear Analysis of Space Frames

Abstract

This work presents a method developed and implemented to consider material and geometrical nonlinearities in the behaviour of space frames.

A geometrically nonlinear formulation is developed in which the compatibility and equilibrium relations are established in the structure’s deformed configuration using a co-rotational description of the movement. The use of total lagrangian, updated lagrangian and co-rotational descriptions of the movement is discussed. An exact method is presented to consider three-dimensional finite rotations, which cannot be added like vectors as assumed in geometrically linear analysis. The finite rotations are considered by using Euler’s finite rotation formula. That formulation allows obtaining the correct relationships between the rotational degrees of freedom considering large displacements and rotations.

The material nonlinear behaviour considered in this work is due to the use of general nonlinear axial stress-axial strain relationships. Based on these assumptions for the material behaviour, and by using an approximation for the internal forces field throughout the frame element, a material nonlinear formulation for three-dimensional structures is presented. The use of an approximation for the internal forces field instead of the usual approximation for the internal displacements field is discussed. An unusual method of integration over the cross-section is presented, where the integrations are carried out over its perimeter, thus allowing any geometrical polygonal shape for it.

In this work, despite large displacements and rotations being allowed, only small deformations are considered. This allows the material and geometrical nonlinearities to be treated in a completely independent way.

The incremental and iterative strategies used are discussed. The capabilities of the formulations presented here are exemplified by the analysis of a few benchmark problems.