Geometric non-linear analysis of space frame with rotation greater than 90°, with Euler angles and quasi-fixed local axes system

Abstract

The geometric non-linear analysis of space frames with definition of the local axes through rotations similar to Euler angles, presents difficulties when the rotations reach 90° in the fixed local axes. To surmount these difficulties this work presents a new technique using a system coined quasi-fixed local axes. In this technique, the direction cosines of these axes of the actual increment of loading are defined through the direction cosines of the moving local axes of the last iteration of the previous increment and of the quasi-fixed local axes of the previous increment (or fixed, in case of the first increment). The technique of definition of the quasi-fixed local axes is used with updated Lagrangian reference. The numerical examples presented herein show the great numerical stability of the technique.