Research On Multiscale Topology Optimization Method For Ultralight Cellular Structures

Cellular structures is a new type of advanced structures with high porosity and light weight,which are characterized with superior mechanical properties,such as high specific strength/stiffness,impact energy absorption,thermal insulation,acoustic and vibrational damping,and designability.It has been widely used in the field of aerospace,automotive,ships,biomedical.As an advanced structural optimization method,topology optimization with the excellent capacity to optimize macroscopic structural topology and microscopic material configuration simultaneously,lays the technical foundation for the optimal design of cellular structures.However,the traditional multiscale design method based on homogeneous materials cannot maintain the increasingly demanding performance requirements.Therefore,the multiscale design method of eliminating the frontier between material and structure and fully exploiting the potential of material has become the development trend of the next generation of new cellular structure design.In this thesis,aiming at the bottleneck problems of traditional multiscale topology optimization methods,such as limited design space,intensive computational cost and poor connectivity between two adjacent microstructures,an efficient multiscale topology optimization method based on nonuniform microstructures is firstly proposed for designing ultra-lightweight cellular structures.Then the proposed method is extended and applied to the fundamental frequency optimization problem,structural frequency response optimization problem and the design of sandwich structures with graded cellular cores.Firstly,inspired by the graded distribution of porous micro-material of natural or biological structures,an efficient multiscale topology optimization method based on nonuniform microstructures is proposed.At microscale,multiple prototype microstructures are topologically optimized by using a parametric level set method(PLSM).A shape interpolation technology is developed to map these optimized prototype microstructures to generate a series of nonuniform microstructures.The Kriging metamodel is constructed by using the mapped nonuniform microstructures to predict the effective properties of all the nonuniform microstructures within macrostructure.At macroscale,the variable thickness sheet(VTS)method is employed to generate an overall free material distribution patterns.In the proposed method,all the nonuniform microstructures within macrostructure are well connected with each other due to the shape interpolation technology.The effective properties of all the nonuniform microstructures are predicted by the Kriging metamodel,which can bring the considerable reduction of the computational cost.The spatially-varying nonuniform microstructures fully broaden the design space to substantially improve the macrostructural performance.Secondly,multiscale topology optimization for maximizing natural frequencies of inhomogeneous cellular structures is proposed.Firstly,a multiscale topology optimization model with the goal of maximizing the fundamental frequency of the inhomogeneous cellular structure is constructed.Aiming at the mode exchange of fundamental frequency during optimization process,an efficient mode-tracking strategy based on modal assurance criterion(MAC)is employed to track the target mode accurately.Then the sensitivity analysis at both scales is carried out,and the design variables are updated by a gradientbased algorithm.In the proposed method,both spatially-varying microstructural configurations and their macroscopic distribution are simultaneously optimized.Due to the PLSM employed to optimize the prototype microstructures at microscale,the local vibration can be naturally avoided,and the optimized cellular structures are featured with the precise and smooth boundary in geometry.Thirdly,multiscale topology optimization for minimizing frequency responses of inhomogeneous cellular structures is proposed.The multiscale optimization model of frequency responses under a wide excitation frequency range is firstly constructed.Aiming at the connectivity issue between two adjacent microstructures,a progressive optimization scheme based on the PLSM is proposed to ensure the similar shapes of multiple prototype microstructures.A shape interpolation method is employed to interpolate the shapes of the prototype microstructures for generating a series of nonuniform microstructures with perfect interconnections.The quasi-static Ritz vector method(QSRV)is incorporated to reduce the finite element model for efficient frequency response analysis.The continuously-varying microstructural configurations and their macroscopic distribution are simultaneously optimized,which provides a sufficiently large design space to minimize the frequency response of inhomogeneous cellular structures.Fourthly,multiscale topology optimization of sandwich structures with graded cellular cores(SSGCC)is proposed.At macroscale,the VTS method is applied to optimize the thicknesses of two solid face-sheets and achieve the graded distribution of cellular sandwich cores at a single layer,where the single layer is arrayed periodically at its height direction to obtain sandwich layers.At microscale,a progressive optimization scheme is employed to topologically optimize multiple representative cellular cores(RCCs),so as to achieve their similar topological configurations.Then,the shape interpolation method is employed to interpolate the shapes of RCCs for generating the configurations of all graded cellular cores(GCCs)with perfect interconnections.In the proposed method,the thicknesses of two solid face-sheets,the graded distribution of cellular sandwich cores at a single layer and their configurations are simultaneously optimized to well suit for loading conditions.Compared with the traditional honeycomb and lattice sandwich structures,the SSGCCs by the proposed method has significant performance advantages.Fifthly,the frequency response analysis of the optimized inhomogeneous cellular structures is simulated in ANSYS software and compared with the macrostructure design,so as to verify the effectiveness of the proposed method.Then,the proposed method is applied to optimize the sandwich structure of a satellite,and the comparisons of the optimized SSGCC with the lattice sandwich structure applied in the engineering are implemented in ANSYS software.The results show that the proposed method has significant advantage in designing ultra-lightweight cellular strucutures.Finally,the conclusions of the current works and key innovations are given and the prospects for further research are outlined.