Topology optimization of the multi-fasteners jointed structure considering joint load constraint and fatigue constraints

The purpose of this paper is to present an important strength issue in the design of multi-fasteners jointed structures. Multi-fastener joints such as bolts and rivets are widely used in assembled structures and always act as critical elements in damage tolerance design. Therefore, fasteners static strength and fatigue performance are simultaneously considered in this paper. On one hand, constraints on joint loads are issued to avoid the fasteners failure. On the other hand, two multiaxial fatigue criterion, i.e., Sines criterion and Crossland criterion are introduced to avoid the failure in the connection areas around fasteners. In addition, the total material usage is limited for the light-weight design. The standard topology optimization is thus extended to minimize the structural compliance with joint load constraints and fatigue failure constraints. Beam elements are used to model the fasteners. The joint loads can therefore be derived easily based on the finite element formulation. In order to eliminate the high stresses caused by the nodal connections of the beam elements, compositional modeling method is used to evaluate the stress level around the fasteners, in which beam elements are used to simulate the stiffness of fasteners and spring/shell elements are used to simulate the interaction of multi-fastener joints. Fatigue constraints are handled in the context of stress-based topology optimization while the corresponding analysis is based on static finite element due to the decomposition of harmonic loads. To address the singularity problems related to stress constraints, q - p relaxation is used and p ≥ q ≥1. Fatigue constraints should be evaluated in every element which inevitably brings in a large number of constraints. P-norm is therefore used as the constraints aggregation scheme. The aggregation factor of P-norm, i.e., Pn is assigned as 6 in this paper. With respect to the constraints aggregation process, the design sensitivities of fatigue constraints and joint load constraints are derived and calculated. Two numerical examples, namely an assembled I-shape beam and a cabin of the high-speed flight vehicle are tested. Optimized results with the proposed method are compared with standard topology optimization design. All the constraints are completely controlled by the prescribed upper level and the loss of stiffness in the optimized configuration can be seen as a trade-off for the strength. It is shown that the fatigue performance is strongly affected by the structural layout and the load carrying path. The effects of different fatigue constraints on the optimized configuration are studied.