Topology Optimization Of Structures With Specific Geometric Features For Additive Manufacturing

Topology optimization can creat innovative and even subversive configurations by freely optimizing the material layout in the design domain,which has become an important structure design tool.Additive manufacturing,as an advanced manufacturing technology,can realize the manufacturing of complex structures in a layer-by-layer way.Combining topology optimization with additive manufacturing to develop design methods has become a hot research topic.High quality design and manufacturability are the focus of developing these methods.First,topology optimization designs need to have specific geometric features to ensure that they can be successfully manufactured in additive manufacturing.In addition,some additive manufacturing structures with specific geometric features have excellent mechanical properties,so it is an effective way to directly design structures to be configurations with these specific geometric features to obtain high-quality structures with specific properties.Therefore,it is of great significance to find and characterize the typical geometric features and establish the topology optimization methods of additive manufacturing structures with these typical geometric features.Enclosed void,structural interface and fiber orientation are three important geometric features.In additive manufacturing,it is challenging to remove the supports in the enclosed voids,and this requires the enclosed void to be self-supported and infill-supported.Description of the enclosed void is crucial to realize the above requirements.The shell-infill structure and continuously-varying-fiber reinforced composite structure are excellent structures with high specific stiffness,high buckling resistance and specific strength,and the description of structural interface and fiber orientation is the key to the design of these structures.Therefore,under the above background,this thesis aims to establish the description methods of these three typical geometric characteristics,i.e.enclosed void,structural interface and fiber orientation,and corresponding manufacturability constraint model,and finally to develop topology optimization methods for structures with specific geometric features,i.e.structure with selfsupported enclosed voids,structure with infill-supported enclosed voids,shell-infill structure and continuous-fiber reinforced composite structure.The research works are listed as follwed:(1)Typical geometric feature description method.Three typical geometric features,i.e.enclosed void,structural interface and fiber orientation,are proposed.Firstly,in order to identify and describe the enclosed voids,a nonlinear virtual temperature field(N-VTM)method is proposed,which assumes that the solid area of the structure is an insulating material,and the void part is a high conductivity heating material with nonlinear heat source.By solving the virtual thermal problem,the temperature in different enclosed voids with varying sizes,positions and wall thicknesses will converge to a same prescribed value,while it is close to zero in open regions.Hence,the enclosed voids can be identified by the temperature difference.Secondly,an erosion based interface identification method is established,that is,the original structure is eroded,and the eroded part is described as the interface.The analytical relationship between the erosion parameters and the interface thickness is derived through a onedimensional case.Third,in order to solve the high non-convexity issue between structural properties and fiber orientations,this paper proposes a new orientation description method based on a coarse and fine matching way,which divides the direction search interval into several subintervals.Then,the angle is determined by the combination of subinterval selection and angle disturbance in subintervals.Based on this,a new discrete-continuous parameterization(DCP)method is proposed to describe orthotropic material with continuously varying orientation,making the large angle change easier and improves the ability of jumping out of local optimum.(2)Topology optimization of structures with self-supported enclosed voids.It is challenging to remove the supports in an enclosed void of an additively manufactured structure.while it is much easier in open regions.This thesis presents a novel approach to control the minimal overhang angle only in enclosed voids in order to improve the manufacturability of AM structures with as little performance loss as possible.Based on the nonlinear virtual temperature method(N-VTM),a multiple filtering/projection process is developed to identify the overhang interface of enclosed voids,and then a logarithmic function-based constraint is developed to control overhang angle in enclosed voids by restricting the length of overhang interface of enclosed voids,and this constraint is integrated into the topology optimization for the design of structures with self-supported enclosed voids.(3)Topology optimization of structures with infill-supported enclosed voids.To fill the enclosed voids with porous material is another method to handle the issue where the supports in enclosed voids are chanllenging to remove.The porous infill material can work as supports in the AM process,but at the same time are part of the final structures and will never be removed.In this way,the difficulty of removing the supports in enclosed voids can be naturally avoided.In the proposed method,the nonlinear virtual temperature method(N-VTM)is normized and then works as a filter to separate the enclosed voids and open regions,and the corresponding sensitivity modification factor is also analytically derived.By using the N-VTM filter,a multiple-filtering based interpolation is proposed to model the structure with infillsupported enclosed voids.The robust formulation is applied to enhance the performance of the proposed topology optimization method,and a sensitivity computation strategy is also suggested to save time.Several compliance optimization problems illustrate the effectiveness of the procedure.(4)Topology optimization of shell-infill structures.The crucial issue for the design of shell-infill structures is how to accurately describe the material interfaces,which is often regarded as a relatively difficult problem in density-based topology optimization.This paper applies the proposed erosion-based interface identification method to handle this difficulty by defining the different parts of the original and eroded structures as interfaces.A multiple filtering/projection process is provided to separate the shell and infill,and a corresponding interpolation function is developed to model the whole composite objects.Enhanced by the worst-case based robust formulation,the minimum length scale of optimized structures can be controlled.Several 2D and 3D compliance optimization examples are provided to illustrate the effectiveness of the proposed method.(5)Concurrent optimization of continuous material orientations and structural topologies for fiber-reinforced composite structure.Combining topology optimization and continuous orientation design of fiber-reinforced composites is a promising way to pursue lighter and stronger structures.However,the concurrent design problem of structural topologies and continuous orientations is a tough topic due to the issue of local optimum solutions,which is mainly caused by the high nonlinearity of the rotation matrix with periodic trigonometric functions.In this work,a new and general concurrent topology optimization method is built based on the proposed discrete-continuous parameterization(DCP).The results show that the proposed method greatly reduces the risk of fiber orientation falling into local optimum.Compared with the traditional method,the mechanical properties of the optimized structure are greatly improved.