Topology Optimization Of Multi-fastener Jointed Structure Considering Joint Load Constraints

This study focuses on the topology optimization of multi-fastener jointed structure considering joint load constraints.Based on this topic,joint load constraints,fatigue constraints,the design of thin-walled reinforced rib structure,and geometrical nonlinearity are involved from the perspective of engineering.In this work,the following aspects are mainly discussed.(1)A topology optimization method for multi-fastener jointed structure considering joint load constraints is established.The finite element modeling of multi-fastener joints involves contact behavior,friction,pre-tightening force and other factors.Therefore,the optimization problem would be quite challenging to address.Here,typical modeling methods and their influence on joint load calculation are discussed respectively.Based on the classic beam theory,the sensitivity of joint load considering the shear effect is deduced.In the process of design,constraints agglomeration method is introduced.The influence of the joint load constraints on the structural topology configuration and load path is studied.Using 3D printing technology,the force transmission performance of the optimized results was investigated by static loading test,and the effectiveness of the proposed method was verified.(2)The issue of fatigue failure in the design of multi-fastener jointed structure is developed.In order to prevent failure in the connection area,Sines criterion and Crossland criterion are introduced.Fatigue constraints are handled in the context of stress-based topology optimization.To eliminate the high levels of stress caused by the finite element modeling,the combination modelling method is used to evaluate the stress states around the fasteners.The standard topology optimization is extended to minimize the structural compliance with fatigue failure constraints and joint load constraints.To address singularity problems related to stress constraints,q-p relaxation is used.P-norm is applied as the constraints aggregation scheme.Based on the above,the design sensitivity of fatigue constraints is derived and calculated.The proposed method is verified by numerical example.(3)A topology optimization approach for assembled aircraft structures design with joint load constraints accounting for as well geometrical nonlinearity is proposed.Topology optimization is carried out to minimize the structural end-compliance meanwhile controlling joint load intensities over fasteners so as to avoid the failure of fastener joints.A superelementbased scheme is proposed to circumvent the numerical instability appearing in density-based methods when dealing with geometrical nonlinearity.The degrees of freedom of weak regions are condensed such that their influences are ruled out from iterative Newton-Raphson(NR)solution.In addition,to allow for the implementation of commercial software packages,a particular semi-analytical formulation has been particularly derived upon adjoint sensitivity analysis for both end-compliance and joint load.The efficiency and robustness of the proposed method has been validated by s a series of numerical examples.(4)Considering the features of the aerospace thin-walled reinforced rib structure,the problem of thin-wall reinforced topology optimization design in the jointed structure is proposed.Joint load and manufacturing constraints are considered simultaneously.On one hand,the joint load is calculated and constrained within a limited value to avoid the failure of fasteners.On the other hand,the manufacturing constraints of the material distribution in the machining directions of stiffeners are implemented by an improved piecewise interpolation based on a beveled cut-surface.The objective function is proven to be strictly continuous and differentiable with respect to the piecewise interpolation.The effects of the extended method with two different constraints are highlighted by typical numerical examples.Compared with the standard topology optimization,the final designs have clearly demonstrated the layout of stiffeners and the joint load have been perfectly restricted to a satisfying level.