Local stability of trusses in the context of topology optimization Part I: Exact modelling

The paper considers the problem of optimal truss topology design with respect to stress and local stability (i.e. buckling) constraints. In a context of topology optimization, the exact. management of buckling constraints is highly complex: member forces must satisfy functions which discontinuously depend on the design variables.New terminologies and an exact problem formulation are provided. It turns out that the classical constraints (equilibrium, stress) together with topological local buckling constraints do not necessarily guarantee the existence of a solution structure. We discuss a simple but typical example demonstrating this effect inherently contained in the problem. It is proved that the inclusion of slenderness constraints guarantees a solution. These additional constraints are motivated by practice and preserve the topology nature of the problem. Finally, an alternative formulation is developed serving as a basis for computational approaches. The numerical treatment is the topic of Part II.