Stiffness design of geometrically nonlinear structures using topology optimization

The paper deals with topology optimization of structures undergoing large d eformations. The geometrically nonlinear behaviour of the structures are mo delled using a total Lagrangian finite element formulation and the equilibr ium is found using a Newton-Raphson iterative scheme. The sensitivities of the objective functions are found with the adjoint method and the optimizat ion problem is solved using the Method of Moving Asymptotes. A filtering sc heme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs. Different objective functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smal ler or larger loads. The problem of obtaining degenerated "optimal" topolog ies which only can support the design load is even more pronounced than for structures with linear response. The problem is circumvented by optimizing the structures for multiple loading conditions or by minimizing the comple mentary elastic work. Examples show that differences in stiffnesses of stru ctures optimized using linear and nonlinear modelling are generally small b ut they can be large in certain cases involving buckling or snap-through ef fects.