Evolution of structures with homogeneous equivalent stress

Abstract

AbstractA phase field model is used to evolve structures with almost homogeneous equivalent stress σv. The model combines the sensitivity of a stress‐based and a couple‐stress‐based objective function. Since couple‐stress typically increases at stress‐singularities, it is an efficient parameter to influence the topology of load‐bearing structures facing that problem. Further, it will be shown that this combination yields an increased solution space concerning the topology of the evolving structures. The effect is demonstrated for the topology of a bridge. Whereas traffic load q onto the driving surface prefers to evolve an arch as topology, the self‐weight g of the bridge prefers to evolve a topology similar to a suspension bridge. The couple‐stress‐based objective function evolves the combination of both topologies such that a smooth transition appears between the topology for q/g = 0 and the topology for q/g → ∞.