Topology Optimization Method For Structural Dynamics Of Vibration And Impact Problems

With the development of the economy and technological progress,the capability of forward developing products in China for industries,such as automotive,aerospace,rail transportation and many others,has gradually reached a world-class level.As a powerful design tool,topology optimization has received a lot of attention as it can creatively generate a design from scratch in a given design domain,and satisfy specific design constraints while ensuring optimal performance.It has achieved significant outputs in reducing development cycle and improving the quality of product.However,most of the existing topology optimization methods are oriented to the static performance of the structure,so that when it comes to dynamic problems,engineers and researchers often need to ”equivalent” the problem to a static problem for the optimization,but such ”equivalent” can only be guaranteed when the load is slow enough to ignore inertial forces,and in other cases,the dynamic performance of the structure needs to be considered directly;on the other hand,the existing topology optimization methods are mostly based on deterministic assumptions,while the real world is full of aleatory and epistemic uncertainty.To improve the robustness or reliability of the design,it is necessary to consider various possible sources of uncertainty in topology optimization to improve product quality;the design of structures that fail due to impact,such as automobiles subjected to high-speed collisions or special equipment under attack,or bridges,dams,buildings,etc.,need to incorporate complex dynamic fracture behavior into topology optimization to achieve fracture-resistant designs.We denote that the current research on this topic is still vacant.The objective of this thesis is to develop density based-topology optimization methods for several challenging dynamic structural problems.In this thesis,we proposed a normalization strategy for elastodynamics to obtain optimized material distributions of the structures that reduces frequency response and improves the numerical stabilities of the bi-directional evolutionary structural optimization(BESO).Then,to take into account uncertainties in practical engineering problems,a hybrid interval uncertainty model was employed to efficiently model uncertainties in dynamic topology optimization.A perturbation method was developed to implement an uncertainty-insensitive robust dynamic topology optimization in a form that greatly reduces the computational costs.In addition,we introduced a model of interval field uncertainty into dynamic topology optimization.The approach was applied to single material,composites and multi-scale structures topology optimization.Finally,we developed a topology optimization for dynamic brittle fracture structural resistance,by combining topology optimization with dynamic phase field fracture simulations.This framework was extended to design impact-resistant structures.In contrast to stress-based approaches,the whole crack propagation was taken into account into the optimization process,which constitutes a breakthrough in this field.The main contributions of this work can be concluded as follows:(1)A normalized BESO method was proposed for topology optimization of the frequency response problem.We extended the BESO method and revealed problems of the conventional BESO method in dealing with problems with strong local characteristics.Then,we proposed a normalization strategy for dealing with sensitivity numbers for improving the stability and convergence of the BESO method for this kind of problem.We demonstrated the advantages of the proposed method over the conventional BESO method for the topology optimization of frequency response problems with several numerical examples.(2)A robust topology optimization method was proposed for the dynamic performances of the structures,specifically the single-material structures,composite laminates and multi-scale composite structures,with random uncertainties featured by imprecise probabilities.We employed a hybrid interval random model to quantify the random uncertainties with imprecise probabilities.And then,an improved hybrid purterbation method is proposed efficiently predict the dynamic performance of structures under uncertainties.The efficiency and accuracy of the method are verified by comparing with the classical Monte Carlo Simulation.We applied this method to the topology optimization of single-material structures,composite laminates and multi-scale composite structures by means of the robust topology optimization.Compared with the topology optimization based on deterministic assumptions,the above robust design exhibits better structural dynamic performance under uncertainty.(3)An interval-field model was introduced into robust topology optimization for modeling the spatially varied non-probabiilistic uncertainties,in which the non-probabilistic uncertainties in topology optimization were no longer limited to scalar uncertain variables while avoiding expensive computational costs due to dimensional explosion.We employed an interval field model with convex model characterized spatial correlation function.And then an interval-field purterbation method was proposed for evaluating the worst case of the single material structures under uncertainty associated with material properties and loading,and its efficiency and accuracy were validated.Based on the robust topology optimization framework,the sensitivity analysis was derived.The effectiveness of the proposed method in designing structures with uncertainties was verified.(4)A novel topology optimization framework that encompassed dynamic fractures was developed,by which the topological design with minimal fracture energy under dynamic impact was achieved.We improved the dynamic phase field method for topology optimization problems,in which a continous differentiable history function was proposed,and an alternative staggered scheme was established.We formulated path-independent semi-analytical sensitivity analysis expressions,the accuracy of which was verified.We performed topology optimization for minimal fracture energy in the numerical examples,which is different from the stress-based method and takes into account the whole crack propagation of the dynamic fracture damage inside the structure.(5)An extension of the proposed dynamic fractures topology optimization framework was investigated,by which the quasi-brittle structures for optimal impact resistance was designed by maximal external work.We defined the external work of the quasi-brittle structures subjected to impact loading as the objective function.Similarly,the semi-analytical sensitivity expressions for this objective function were derived and verified.We compared those topological design obtained by this method and conventional external work maximization method for static and fracture-free structures,and the results showed that the designs obtained by our method exhibited better impact resistance.