Topology Optimization Of Self-supporting Structures Considering Inclination Angle And Minimum Size Constraints

Structural topology optimization is a design technique to obtain optimal distribution of materials under the constraints and loads within the given design domain,which has a very high design freedom.Additive manufacturing is a manufacturing technology to form complicated solid parts in a layer-by-layer way,which has a very high forming freedom.Therefore,combining topology optimization and additive manufacturing has become an important research direction.However,structures designed by traditional topology optimization can hardly be fully adapted to the current additive manufacturing because of its distinct forming principle and the limitation of the additive manufacturing equipment,so there are some design limitations such as inclination angle constraint,minimum size constraint and et al,which must be taken into account for structural topology optimization,otherwise optimal structure need to be introduced support material during the additive manufacturing process or cannot be fabricated.For these defects,a method of considering inclination angle as well as minimum size constraints simultaneously based on density projection is proposed in this paper,and be applied to the topology optimization of selfsupporting macrostructure,the self-supporting microstructure and the self-supporting multiscale structural.The main works are as follows:Firstly,a method of considering inclination angle as well as minimum size constraints simultaneously based on density projection is proposed.In order to restrict the inclination angle of the structural model,the printed densities and the base densities of elements are introduced,and restrict the printed density of elements which cannot be higher than the maximum base density.In order to limit the minimum size of the structure model,a method of variable radius density filtering based on Heaviside function is proposed.Then we establish the macrostructure topology optimization model of considering inclination angle constraint as well as minimum size constraint simultaneously based on SIMP method,calculate sensitivities of objective and constraints,the optimization criterion is used to solve the proposed model.Several 2D examples and its additive manufacturing experiment are implemented to demonstrate the feasibility and effectiveness of the proposed method applied to the self-supporting macrostructure topology optimization.Secondly,The proposed method of density projection is introduced into the microstructure topology optimization.Then we establish the microstructure topology optimization model of considering inclination angle as well as minimum size constraints simultaneously based on Energy-based homogenization method,calculate sensitivities of objective and constraints,the optimization criterion is used to solve the proposed model.Several examples of extreme performance microstructure topology optimization and its additive manufacturing experiment are implemented to demonstrate the feasibility and effectiveness of the proposed method applied to the self-supporting microstructure topology optimization.Thirdly,A two-scale topological optimization model associated with free distribution of material regions is adopted,and considering inclination angle as well as minimum feature size constraints simultaneously in the process of microstructure design.Then we establish the multi-scale structural topology optimization model of considering inclination angle as well as minimum size constraints simultaneously,calculate sensitivities of two stage topology optimization,the optimization criterion is used to solve the proposed model.Several 2D examples and its additive manufacturing experiment are implemented to demonstrate the feasibility and effectiveness of the proposed method applied to the cellular material and structures integrated topology optimization.Finally,the prototype system for additive manufacturing oriented self-supporting structure topology optimization under the environment of ANSYS secondary development is produced.MBB beam as well as cantilever beam of the self-supporting structure topology optimization are realized through exploited prototype system.