Topology optimization of geometrically nonlinear trusses with spurious eigenmodes control

In this paper, topology optimization of geometrically nonlinear trusses with and without stability constraints is investigated. It is shown that if classical minimum compliance formulation is considered without any stability constraints, the optimized designs are unstable and convergence issues may be encountered in the nonlinear structural analyses. To address these issues, a minimum compliance formulation with critical load factor constraint is proposed together with a strategy based on spurious modal energy ratio to determine the true critical eigenmodes and the corresponding critical load factor. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach, which show that the optimized truss topologies obtained using the proposed approach are stable. More importantly, the critical load constraint is able to guarantee that the first critical load of the optimized design is always above the applied load so that the proposed approach is free from convergence issues during the Newton Raphson solution process.