Parameter-driven Topology Optimization Method For Multi-material And Multiscale Structures

Structural topology optimization method is an innovative configuration design method for achieving high performance and lightweight design of aerospace vehicles and equipment.In the twenty-first century,complex problems like multi-material,multiscale and multi-field coupling start to be considered and solved in the scope of topology optimization.However,when solving these problems,traditional topological optimization methods such as density-based method and Level Set Method(LSM)often confront numerical problems,such as intermediate materials,large number of design variables,and poor convergence.Computer-Aided Design(CAD),Computer-Aided Engineering(CAE)and other technologies in engineering applications often use various parameters to directly model and control the structure.However,due to different consideration,they have considerable gaps with traditional topology optimization methods for a long time,and the optimization results are usually difficult to be directly applied.In order to overcome the above-mentioned problems,this work conducts a series of studies on parameter-driven topological optimization methods for multi-material and multiscale structures,based on emerging feature-parameter-driven topology optimization methods and B-spline multi-parameter-driven topology optimization methods.The main research contents and achievements of this work are listed as follows:(1)A feature-parameter-driven topology optimization method for multi-material structures is proposed.This method is based on fixed grids and multiple super-ellipse features with different material properties,and topology is optimized through the movement,deformation and fusion of features.Multiple level set functions are used to describe different material boundaries.The extended finite element method(XFEM)is used to accurately calculate the displacement and stress of different materials.Through a comparative study,the optimal form of the XFEM under different material interfaces or material-void interface is obtained,and the optimization problem considering the stress constraints is solved.The stress constraints are aggregated and combined to the objective function with a penalty factor to acquire a fast and smooth convergence.Besides,a feature-parameter-driven “Structure &Material” integrated design method is proposed using feature material properties as design variables.This method consists of two parts: discrete material optimization and fiber direction optimization.In the discrete material optimization,all feature materials converge to one of the given candidate materials by constructing a material interpolation formula with penalty.In the fiber direction optimization,the fiber angles of the feature material is defined as continuous design variables,and the homogeneous method is used to calculate the equivalent properties of the material of any fiber direction.The optimization results show that the fiber direction of the structure is consistent with the local principal stress direction,and the reasonable matching of the material and topology greatly improves the structural response.(2)A feature-parameter-driven topology optimization method for multiscale structures is proposed.This method employs multiple macro and micro features for multiscale modeling and optimization,and optimizes the topology of each scale through the movement and deformation of corresponding features.The macro and micro scales of this method are separated but still numerically related by the homogenization method.When dealing with the overlapping regions of macro features,a sub-optimization problem is constructed and solved for the selection of microstructures.By doing this,the optimal microstructures can be selected.This method can produce a variety of different microstructure types with fewer variables,and has higher optimization efficiency.In addition,the effects of design-dependent loads on multiscale optimization methods are also studied.The equivalent calculation model of gravity,centrifugal force and thermal stress load at different scales are explored respectively.Then,the numerical problem of parasitic effects caused by design-dependent loads is explored in multiscale optimization.It can lead to slow and even unreasonable results to the optimization process.A modified load model is proposed for this problem and numerical examples verifies this model with good results and improved convergence.(3)A B-spline multi-parameter-driven topology optimization method is proposed for multi-material structures,and then applied to static conditions(including thermo-elastic conditions).This method uses multiple density-based B-spline parameters to construct multiple independent B-spline spaces covering the entire area to describe the distribution of multiple materials.The evolution of the structure is achieved by adjusting the density values of the B-spline parameters.The material properties such as Young’s modulus,specific mass,and thermal stress coefficient of the structure can be calculated from the corresponding values of the B-spline spaces.Two common multi-material interpolation models,i.e.uniform multiphase material interpolation(UMMI)and recursive multiphase material interpolation(RMMI)are explored in the proposed method.Numerical examples show that the UMMI has better convergence than the RMMI,and the structure has aggregated and separated material layout leading to easy manufacturing.Compared with the traditional element-based or node-based optimization method,the B-spline multi-parameter-driven optimization method has satisfactory performance under static load and thermal load conditions,especially when dealing with thermal load conditions.It can naturally avoid numerical instabilities such as intermediate materials and checkerboard,and has the advantages of good convergence and smooth boundaries.(4)A multiscale lattice structure modeling and optimization method driven by features parameters and B-spline parameters is proposed.Microscale geometric features are used to construct freely transformed lattice cells,of which the parameters are described by several globally distributed B-spline spaces.Therefore,the microstructure at any point can be determined by the corresponding feature parameters of the B-spline space.Since the features’ parameters has high-order continuity in the B-spline spaces,the connectivity between the microstructures can be naturally guaranteed.In order to improve the efficiency of the homogenization method,the least squares method and polynomial interpolation are used to calculate the equivalent properties of unit cells of arbitrary parameters.In multiscale structural optimization,the configuration of the microscale unit cells can be continuously transformed between many different types of unit cells.The evolution of the macro structure is achieved through the presence or absence of geometric features in each unit cell.There is no need for macro design variables thus leading to a reduction of the design variables and an increase of computation efficiency.