Research On Multi-Scale Topology Optimization Of Periodic Structures Based On Isogeometry Analysis

Composite periodic structures have been widely used in the fields of power machinery,thermal equipment and automobile industry because of their unique configuration and multifunctional physical characteristics such as sound absorption and heat insulation,vibration reduction and collision avoidance,light weight and high strength.For example,the carrier of automotive engine catalytic converter is a typical periodic porous structure.However,most of the periodic structures that rely on empirical design are generally not optimal structures,and the application and promotion of various high-performance anisotropic composites also make the design of composite periodic structures more and more difficult.In addition,with the continuous expansion of the application field of industrial products,the requirements of various complex working environments on the structural performance and reliability of products continue to improve,which makes the composite periodic structure under a single scale more and more unable to meet the requirements of high-precision industries for "structural lightweight","functional specialization" and "performance integration" of industrial products.A multi-scale topology optimization model of anisotropic periodic structure based on isogeometric analysis is proposed in this work.The macro periodic structure design,microstructure design and periodic structure multi-scale design considering single microstructure and multiple microstructure of anisotropic materials are studied in detail.The research contents include:(1)The periodic structure topology optimization model for steady-state heat transfer and static of anisotropic materials are established based on IGA.The effects of the number of design subdomains,multilevel periodic constraint,thermal conductivity factor,Poisson’s ratio factor and off-angle on the optimal periodic structure and its performance are studies based on the established model,and the recommended ranges of the above parameters are provided.(2)The topology optimization model of anisotropic material microstructure with the relative density of isogeometric control points as the design variable and the maximum bulk modulus,maximum shear modulus and negative Poisson’s ratio as the objective function is established,and the corresponding sensitivity formula of the objective function is deduced.The effects of the initial design domain shape of microstructure,Poisson’s ratio factor and off-angle on the optimal microstructure and its properties are discussed in detail based on the established model,and the recommended ranges of the above parameters are provided.(3)A multi-scale topology optimization model of anisotropic periodic structure considering single and multiple microstructure are established,which takes the minimization of multi-scale periodic structure compliance as the objective function and the relative density of isogeometric control points of macro structure and microstructure as the design variables respectively.A distribution positions of various microstructures in macro periodic structures are determined by introducing a material distribution model.The effects of the number of design subdomains,regularization scheme,Poisson’s ratio factor and off-angle on the optimal periodic multi-scale structure and its performance are studied in detail,and the recommended ranges of the above parameters are provided.In this paper,the IGA method is introduced into anisotropic periodic structure multi-scale design,and the macro periodic structure,microstructure and periodic structure multi-scale topology optimization model considering single and multiple microstructures are established,which is of positive significance to reduce the modeling difficulty of periodic structure multiscale design and improve its calculation accuracy.In addition,considering anisotropic materials and macro periodic structure design in multi-scale design has certain theoretical and practical significance for improving the mechanical and thermal properties of structures.At the same time,it also provides a reference for the follow-up research on geometric analysis,anisotropic materials,multi-scale and periodic structure topology optimization.