Topology Optimization Of Multi-material Fatigue-constrained Structures Based On Polygon Mesh Modeling Strategy

Fatigue and stress are the most important criteria in engineering problems.Most failures in structural and mechanical applications are caused by fatigue and stress failure.Therefore,it is not enough to optimize the stiffness and other global responses(such as frequency)of the structure without considering the stress and fatigue failure in the optimization process.In this research,fatigue-based topology optimization is studied under the framework of multi-material structure.Its goal is to find the best distribution of materials by considering fatigue failure.In order to predict fatigue,the calculation method of fatigue is crucial.Therefore,in this article,a multi-material structure statics method and a multi-material dynamics method are proposed,and based on this,the topology optimization based on the multi-material fatigue constraint is studied.The main research contents are as follows:First,a topology optimization method based on static and dynamic stiffness of multi-resolution and multi-material structures is proposed.The mathematical model of multi-material structure topology optimization,material interpolation model,ZPR update criterion,and HHT-? method to solve structural dynamic response problems are studied.Second,through the polygonal mesh modeling strategy,many complex numerical examples are provided,including structural static stiffness design,structural dynamic stiffness design and fatigue-constrained structural design.And verify the topology optimization of the multi-material structure.Third,in order to accurately meet the local fatigue constraints and reduce the number of constraints,this thesis uses the augmented Lagrangian method to treat the original problem as an unconstrained problem,and compared with the optimization results of the P-norm method,the results show that the local fatigue constraint conditions The optimized structure below has better fatigue resistance and less material consumption.Therefore,a structural topology optimization method under the condition of local finite life fatigue constraints is proposed.Fourth,considering the proportional load effect of variable amplitude,the Palmgren-Miner linear damage hypothesis and the Sines fatigue criterion are used to evaluate the fatigue strength of the material points,and the local fatigue performance is taken as the constraint condition,and the lightweight design model of the multimaterial structure is established.