Multi-scale Topology Optimization Design Of Heterogeneous Porous Materials And Structures

With the rapid development of the shipbuilding industry,industrial pollution is serious and environmental problems are becoming more and more serious.In the naval architecture field,building green ships with low fuel consumption,low pollution,environmental protection and energy saving is an important means to achieve energy conservation and emission reduction,strengthen environmental protection,and improve structural performance.Ship lightweight design is one of the key technologies for building green ships and developing high-tech ships,and is one of the important topics for the future development of the shipbuilding industry.Therefore,it is very important to carry out research work on lightweight design for both water and underwater structures.The topology optimization method is an important means to achieve lightweight design and design lightweight structures.Compared with the traditional structural topology optimization design under a single scale,the multi-scale topology optimization design of materials and structures can achieve the matching of materials and structures,and further improve the structural performance and reduce the weight of structures.Therefore,this paper proposes a multi-scale topology optimization design method for heterogeneous porous materials and structures based on the Moving Iso-surface Threshold Method(MIST).The main research contents are as follows:(1)Topology optimization design method of heterogeneous connectable gradient microstructure based on MIST framework.Considering the load and boundary conditions of the macrostructure,the optimization goal is to maximize the stiffness of the macrostructure.The relationship between the macrostructure performance and the micro design variables is established under the MIST framework to obtain the microstructure topology that satisfies the optimal macrostructure performance,that is,the initial microstructure.Based on the initial microstructure,a series of heterogeneous connectable porous microstructures are obtained using a progressive iteration algorithm,and the effectiveness of the method is verified by numerical examples.(2)A multi-scale topology optimization design method for materials and structures based on the combination of MIST and SIMP is built.A series of non-homogeneous porous connectable graded microstructures are obtained by using the progressive iteration algorithm.The homogenization method is used to predict the equivalent elastic properties of the microstructures.For any intermediate density unit,the linear interpolation method is used to obtain its equivalent elastic modulus.Then,the SIMP method is used to optimize the layout of the microstructure on the macro scale.Numerical examples are given to verify the effectiveness of the proposed multi-scale topology optimization design.(3)The topology optimization design method of adjustable Poisson’s ratio structure with simple driving and complex deformation is proposed.For a reentrant honeycomb unit cell with adjustable Poisson’s ratio,the nonlinear large-deformation finite element analysis was performed to obtain the relationship between Poisson’s ratio and the internal angle of the honeycomb structure under different strains.Then write the analytical expressions of the elastic modulus of the structure on the internal angle of the honeycomb structure,and write the optimization formula,optimize the distribution of the Poisson’s ratio inside the structure.Finally,two numerical examples are calculated.It can be found that the optimized structure can realize the designed deformation form under simple driving,which verifies the effectiveness of the method and provides method basis for the design of variant structures.