Truss optimization with buckling considerations using geometrically nonlinear beam modeling

A unified approach that accounts for various buckling phenomena in truss design optimization is presented. Euler buckling of slender members, global buckling and stability of sequences of bars are all considered by optimizing the geometric nonlinear response instead of by imposing a large number of constraints. In the proposed approach, each truss member is modeled as a sequence of co-rotational beam elements with appropriate end-releases. By applying various imperfections, buckling of single truss members, unstable configurations and global buckling can be taken into account implicitly. A detailed discussion on key aspects of the proposed approach is presented, showing how the choice of imperfections highlights certain buckling types and leads to respectively stable designs. A comparison to other approaches and to results from the literature shows that the proposed approach can ensure local and global stability without actually imposing any buckling constraints. Finally, truss optimization for various levels of global deflections is presented, exposing the potential of the formulation for optimizing highly nonlinear responses.