Multi-scale Topological Optimization Of Stress Properties Of Thermoelastic Lattice Structures

The ultra-lightweight lattice structures can reduce products' mamufacturing cost and energy cosumption and improve the quality of products.Especially with the rapid development of the field of aerospace,more and more ultra-lightweight structures,especially the multifunctional ultra-lightweight structures are requred.As a kind of ultra-lightweight structure for its high specific strength,high specific strength,good heat dissipation performance,high toughness impact resistance,energy absorption noise reduction and multi-functional application,lattice structure is widely used in aircraft,aerospace equipment structure,automobile manufacturing and so on.Extended Multi-scale Finite Element Method(EMsFEM)is introduced to analysis lattice structures with lots of micro bars,which improved computational efficiency significantly.Aiming at the problem that the physical meaning of the lattice structure is not clear under the action of thermal load and mechanical load,the structural minimum strain energy is used as the optimization objective,and the concurrent optimization of micro-scale and macro-scale of the thermo-elastic lattice structures is studied,comparing with minimum compliance optimization design.The concurrent optimization of macro-structure and micro-structure of the thermo-elastic lattice structures is done,considering the structural strength and stiffness constraints.With the continuous improvement and development of the manufacturing process,the preparation of lattice structure with periodic microstructure has become easier.especially in recent years,the rapid development of 3D printing technology,the production of lattice structures with a variety of microstructure forms is more and more easier.So the lattice structure is not necessary to be rigidly adhered to the lattice structure under the unified microcell.Based on the different states of the single cell,the microstructures of the lattice structures,the lattice structure with kinds of microstructures was designed.The concurrent topology optimization of micro-structure and macro-structure of thermo-elastic lattice structures based on EMsFEM is studied.Through the analysis and comparison of the strain energy and the compliance of the different lattice structure models under the thermal load,the physical meanings of the strain energy of the lattice structures are revealed,that is,the strain energy of the lattice structure is the measure of the average stress level of the structure.Set strain energy of thermal-elastic lattice structure as the objective,the concurrent topology optimization of macro-structure and micro-structure of thermo-elastic lattice structures is studied,considering the influences on optimization of size of truss unit cells,the size of thermal load and the amount of base material.Through numerical examples,we can find that the optimal configuration of micro-structures is closely related to the macro-structural topological shape.The number of design variables of the structure increases with the increase of size factor of micro-structure,which reduces the structural strain energy.Due to the different meaning of strain energy and flexibility,the minimum strain energy design and the minimum compliance design show different optimization trends with the increase of the ratio of thermal load.When the amount of material increased to a certain value,continue to increase the amount of material,the structure of the strain can almost no change.For the lattice structure under the action of thermal load,considering the strength constraint and stability constraint of all the micro-bar members,the micro-structure design and the macroscopic multi-scale design of the lattice structures are studied.A new coagulation function that can effective condense to a global constraint for lots of constraints and solve the “more peak” difficulty.The multi-scale design of lattice structures considering all the micro-bar strength constraints and stability constraints is studied.The influence of the relative size of temperature load and mechanical load on the optimization of lattice structure is also discussed.Based on the characteristics of the microcell stress state at different positions of the lattice structure under the specific load and constraint,the optimization of lattice structure with kinds of micro-structures is studied.Based on the different characteristics of the unit states of the lattice structure,the lattice structure is partitioned,and the microcell structures in different partitions are optimized,so as to realize the more reasonable distribution of the material.The relative density of the equivalent macroscopic unit and the cross-sectional areas of some kinds of micro-strucures are introduced.By comparing the lattice structure cluster optimization design with the classical optimization design of lattice structures with the same microstructure.It is proved that the cluster optimization design is superior to classical optimization design.The optimal design of the structural cluster is analyzed and the influence of the number of partitions on the optimization results is studied.Considering that the lattice strain of the lattice structure under the specified load is too prominent to cause the grouping is not ideal,And the partition is more reasonable.