Multi-scale Concurrent Optimization Of Lightweight Lattice Structures Based On Parallel Topology Optimization Framework

With the rapid development of additive manufacturing technology,the lattice structures,as a novel lightweight material,are increasingly used in aerospace vehicles,medical equipment and other advanced industrial equipment manufacturing due to their excellent specific strength,specific stiffness,impact resistance and thermal insulation capabilities.However,the complex lattice structures are constructed with a large number of micro trusses,it is computational intensive to analysis them with traditional finite element method.Because of that,the optimization design for lattice structure turns to be difficult for reason of low efficiency of finite element analysis.This paper is based on a multi-scale analysis algorithm-Extended Multiscale Finite Element Method and the concurrent two-scale optimization framework of lattice structure.In the MPI cluster environment,the high the high-performance parallel scientific computing library PETSc(The Portable,Extensible Toolkit for Scientific Computation)was introduced,and a two-scale analysis and optimization program framework for lattice structure based on parallel computing was developed.Based on this,multi-scale analysis and optimization of 3D lattice structure was studied.The main work and research results are as follows:1.Analyze the parallelism of EMsFEM algorithm,and study the formation of macroscopic and microscopic finite element equations,the introduction of macroscopic boundary conditions and microscopic linear boundary conditions and the parallel solution of finite element equations in the EMsFEM algorithm from the perspective of PETSc-based parallel program implementation.Explore the scale of the problem that the program framework can handle on a normal computer,and then use a high-performance server to calculate the parallel acceleration ratio and parallel efficiency of the program.It is pointed out that for the EMsFEM algorithm,the analysis on the macro scale has large parallel granularity,and the parallel acceleration effect is obvious.The micro-scale analysis has smaller parallel granularity,serial calculation or limited the number of processors called can be used to improve the performance of multi-scale analysis program.2.Based on the parallel multi-scale analysis program of lattice structure,the idea of multiscale concurrent optimization is introduced,and the parallel two-scale concurrent optimization framework of lattice structure is developed.The numerical examples are used to verify the ability of the framework in dealing with large-scale 3D lattice structure optimization problems.Investigating the influence of the macro element density and the upper bound of the material used in micro unit cell on the optimization results,it is found that increasing the macro element density can make the material distribution on the macro-micro scale more reasonable,reduce the structural compliance.And for lattice structures which only consider mechanical load,the value of micro design variables sensitivity is larger than the value of macro variables sensitivity in the average sense,which means that the material will be preferentially assigned to the micro scale.It is proved by numerical examples that the more the material is distributed to the microscale,the better the structural stiffness performance is when the amount of the matrix material is given.This is consistent with the point that the structural stiffness is better when the solid material is used in microscale in the generally accepted porous material study.