Multi-material Structural Topology Optimization Considering Mechanical Interface Behaviors

Multi-material structures are widely used in fields like aeronautical,aerospace and automotive engineering.This kind of structures can make full use of each material phase's advantage,to meet the requirements of lightweight and multi-functionality.Multi-component structure can be seen as a special multi-material structure,and it typically includes a supporting structure and functional components with fixed shapes.Multi-component structures can make full use of space and implement special functionality.This dissertation focuses on multi?material and multi-component structures with complete bonding interfaces.This kind of structures can be obtained with adhesively bonding,welding,3D printing and some other methods.Researchers have proposed a series of methods on multi-material topology optimization and integrated topology optimization of multi-component structures.Most of these methods are based on the perfect bonding interface assumption.However,real material interfaces do not have infinite stiffness and strength,and thus the performance of designs obtained with the above-mentioned methods may be affected by the interface's mechanical behaviors.Therefore,it is necessary to consider the interface's mechanical behaviors in multi-material topology optimization and integrated topology optimization of multi-component structures.Similar to the opening process of a material interface,in the flracture process of a structure the crack surfaces develop(in material or on the interface between materials).Fracture breaks the integrity of structures and usually causes catastrophic consequences.In engineering practice,if fracture often occurs in a certain component or functional region of a complex structure,this phenomenon may be caused by the unreasonable design of the structural load transmission path.The method to design structures with consideration of the stiffness and fracture performance in the design stage remains a hot issue for researchers.At present,some research work has been conducted on basis of the shape optimization and size optimization techniques to optimize the fracture resistance of structures.However,research on enhancing structural fracture resistance based on the topology optimization method is very limited.Based on the above-mentioned background and development of relevant research,this dissertation carries out the following research:1.Multi-material topology optimization problem with consideration of interface's mechanical behaviors is studied.A cohesive zone model is used to accurately describe the mechanical behaviors of material interfaces,i.e.the non-linear relationship between the traction on the interface and the separation of the interface.The level set method is adopted to give clear description of the material distribution and the material interface location.The extended finite element method and the level set description are combined to describe the strong discontinuity of the displacement field on the interface that varies in shape during the optimization process.The non-linear structural response is solved in incremental form and with the Newton-Raphson method.Based on the velocity field level set method,the optimization formulation is proposed.For this optimization problem,the work of external force is adopted as the objective function.And the scalers which are defined on fixed level set grid and used to construct the velocity field,are defined as the design variables.With the adjoint method,the sensitivity of the objective function that includes non-linear structural responses is derived,and the optimization problem is solved with the MMA algorithm.The numerical examples shows that the material interface's mechanical behaviors have significant influence on the optimized designs.The optimized designs with considering of interface behaviors may exhibit tension/compression non-symmetric topology.2.Integrated topology optimization of multi-component structures with consideration of interface's mechanical behaviors is studied.The cohesive zone model is used to reflect the non?linear mechanical behaviors of the interfaces between the supporting structure and the embedded components.The]eve]set method is adopted to provide clear description of the material distribution of the components and the host structure,and the location of the material interfaces.For multi-component structures,in order to improve the accuracy of the finite element analysis(the shape of the interface here relies on the shape of the components),an adaptive meshing technique is adopted to generate body-fitted mesh and interface elements to discretize the structure and the interfaces(i.e.to generate finer mesh at locations with large curvature feature).The optimization formulation is proposed on basis of the velocity field level set method,and the work of external force is adopted as the objective function to maximize the stiffness of the structure.During the optimization process,the non-overlap of the embedded components is ensured with an integral form non-overlap constraint.The optimization problem is solve with the MMA method.Through the numerical examples the effects of the components'initial positions,the parameters in the interface's constitutive model and the load on the optimized designs are studied.3.Topology optimization considering fracture behavior at specified functional region is studied.Considering the brittle fracture of material an optimization model is proposed on basis of the SIMP method,which optimizes the fracture resistance of a specified functional region by designing the load transmission path.This optimization model assumes that the functional region is not designable,and uses the J integral value of prescribed crack(s)in the functional region to measure the fracture resistance of this region.The crack is modelled with finite element method.To improve the accuracy of cracking modelling,singularity elements are adopted at the crack tip to describe the singularity there.The compliance and the J integral are linearly weighted to be used as the objective function to simultaneously optimize the stiffness of the structure and the fracture behavior of the functional region.For different design cases,two kinds of objectives to minimize or maximize the J integral value are proposed to enhance the fracture resistance at specified functional region or to design easily detachable structures for particular applications.