A conjugate modal force strategy for instability analysis of thin-walled structures: an unconstrained vector positional finite element approach

Abstract

The importance of knowing critical loads and post-critical behavior of thin-walled structures motivates the development of several scientific and practical studies. Most references are concerned with stability analysis for small displacements (first order approach), or with second order stability analyzes, a less precise geometric nonlinear strategy. However, very flexible structures or ones that present small loss of stiffness after the first critical load need more careful analysis. Here we present a shell numerical formulation capable of carrying out stability analysis of thin-walled structures developing large displacements. This formulation uses generalized unconstrained vectors as nodal parameters instead of rotations. To make possible a complete stability analysis using unconstrained vectors, we present an original strategy that imposes a Conjugate Modal Force at the vicinity of critical points, allowing an accurate choice of post-critical paths. Non-conservative forces are also considered and results are compared with literature benchmarks, demonstrating the accuracy and capacity of the proposed formulation.

Keywords:
Conjugate Modal Force; Instability Analysis; Geometrically Exact FEM; Positional FEM

Graphical Abstract