Research On Application Of Variable Density Method In Topology Optimization Of Continuum Structure And Lattice Material

Structural topology optimization is a mathematical method that optimizes material distribution in a given area based on given load conditions,constraints,and performance metrics,thereby achieving optimal structural performance.It has a wide range of applications in aerospace,automotive body design,architectural design and other fields.The variable density method is one of the most widely used methods in structural topology optimization because of its simple form.In this thesis,the application of variable density method in topology optimization for continuum and lattice materials is studied.The main works are as follows:First,the improvement and application of variable density method in topology optimization for continuum structures is studied.Compared with other topology optimization methods,the variable density method is prone to numerical instability such as grid dependence and checkerboard phenomenon.Although the problem can be solved by sensitivity filtering methods,there are still some difficulties in applying these methods to unstructured grids models with complex structures.In view of the shortcoming of the above methods,this thesis proposes an improved sensitivity filtering algorithm,which can effectively solve the numerical instability of variable density method in complex grid model.Based on this improved method,a prototype system for continuum structural topology optimization was designed and developed,and some complex structures were optimized by this system,and good topology results were obtained.Secondly,the application of variable density method in multi-scale concurrent topology optimization for lattice materials is studied.At present,most topology optimization methods for lattice materials have the problem of small design space,which makes it difficult to improve the structural performance of lattice materials compared with the optimal topology of continuum with the same volume constraints.Even in the case of fewer types of micro-structures,its structural stiffness is lower than that of continuum.A new multi-scale topology optimization method for lattice material proposed in this thesis can further enhance the structural performance of the lattice material.It uses the variable density method on both scales and the microstructures in each unit are optimized independently,which fully expands the design space.The validity and effec-tiveness of the method are verified by some numerical examples.Finally,the distributed parallel optimization algorithm for lattice material based on variable density method is studied and realized.One of the main problems in multi-scale concurrent topology optimization for lattice materials is the high computational cost.This thesis proposes and implements a distributed parallel optimization algorithm for lattice material materials based on SPARK parallel framework by using the current parallel computing and cloud computing technology.The algorithm greatly improved the topology optimization efficiency of lattice material through distributed parallel optimization of micro-structures.Some test results show that the algorithm can make optimization speed almost increase linearly with the growth of cluster size,which provides a strong support for the multi-scale topology optimization for lattice materials to be applied to practical engineering problems.At the end of this thesis,the research work is briefly summarized and the future research work is prospected.