Large Displacements and Instability: Buckling Versus Nonlinear Instability: Fid-Bau Portal

Large Displacements and Instability: Buckling Versus Nonlinear Instability

Ibrahimbegovic, Adnan / Mejia-Nava, Rosa-Adela

We here present the geometrically nonlinear approach to structural analysis and corresponding instability problems that can arise within the framework of large displacements and rotations. The main interest is to quantify the risk of pre-mature failure with a disproportional increase of displacement, strain and stress due to a small increase of external load, which is the intrinsic definition of instability. Two models used for detailed illustration are geometrically nonlinear truss and geometrically nonlinear beam. We also point out the difference between the linearized instability or buckling, characterized by small pre-buckling displacements, versus the nonlinear instability, associated with large displacements and rotations at critical equilibrium point. We present three different criteria for identifying the critical equilibrium point. We finally present a very powerful computational approach to computing the solution to linearized instability of any complex structures within the finite element framework. We point out the key role played by so-called von Karman strain measure, based upon the hypothesis that the displacements and strains (but not rotations) remain small before reaching the critical bifurcation point. Finally, we briefly illustrate another original concept in constructing the solution to linearized instability problem under coupled thermomechanics conditions.