Design And Optimization Of Complex Topology Structures For 3D Printing

There are various of complex topology structures like truss structures and honeycomb structures exist in nature.Complex topology structures not only show the best cost-effective mechanical properties,but also have the affinity for cell growth and reproduction in biology.Therefore,complex topology structures have been widely used in lightweight modeling,implantation of artificial organisms and other fields.With the booming development and promotion of 3D printing technology,the manufacturing and production of complex topology structures is no longer a big problem.Researchers in the fields of engineering mechanics,biology and materialogy have designed more and more complex topology structures with diversified shapes and multiple functions.Among them,the porous structures based on triply periodic minimal surface have received great attention in recent years.Triply periodic minimal surface is a kind of minimal surface,which extends infinitely and periodically in three dependent directions.It possesses excellent properties such as good smoothness,easy to control,full connectivity and so on.As a result,triply periodic minimal surface has aroused great interest among chemists,materials scientists and biologists.The main content of this thesis is to utilize triply periodic minimal surface to design and optimize complex topology structures according to requirements(This thesis is all about the application needs of engineering mechanics).First,multi-scale porous structures are designed with explicit and implicit representation by using triply periodic minimal surface(TPMS).The multi-scale porous structure based on explicit representation is designed by introducing periodic parameter into TPMS.After the surface is represented explicitly with triangular mesh,a uniform thickness is obtained by offsetting.One can adjust the shape of porous structure through periodic parameter and thickness parameter.However,this method of generating thickness may cause self-intersection.Therefore,taking advantage of the implicit function expression of TPMS,this paper proposes a multi-scale porous structure based on implicit representation.This structure can be completely expressed by functions,and its pore size distribution and thickness distribution can be controlled by topological parameter and geometric parameter,respectively.The porous structures we proposed above inherit the advantages of triply periodic minimal surface,such as good smoothness,full connectivity(no closed hollows),high controllability(the geometric structure and topological structure can be adjusted by two parameters),quasi-self-supporting(almost without support structures when printing small and medium size),and other excellent characteristics.And then,the designed multi-scale porous structures are applied to structural optimization in the field of mechanics,and two algorithm frameworks are proposed:lightweight optimization modeling framework and structural compliance optimization modeling framework.The solid model is filled with multi-scale based on explicit representation.With stress constraint and volume minimization as the goal,the periodic parameter and the thickness parameter are optimized to achieve the purpose of lightweight modeling.But the traditional finite element method is still used in the optimization process of the lightweight framework.The porous structure needs to be remeshed in each step of the iteration,which is very time-consuming.To solve this,the implicitly expressed multi-scale porous structure is used to establish structural compliance optimization modeling framework.With the goal of minimizing structural compliance and the constraints of volume and gradient,the topological and geometric parameters of the structure are optimized to obtain the optimal structure with the largest global stiffness.This framework can be completely expressed,analyzed,optimized and stored with functions,which is very efficient.Finally,the performance of the proposed two optimization frameworks are tested through a large number of experiments.Experiments have proved that the designed multi-scale porous structure shows a better lightweight effect than other works in lightweight modeling.The structural compliance optimization framework which avoids the remeshing of the grid in the tradition methods has high efficiency.Various experiments show that the designed multi-scale porous structure and the corresponding optimization framework have obvious advantages in terms of effectiveness,accuracy and efficiency.