| Due to the rapid development of the design theory and the manufacturing technology,structures composed of multi-material have been widely used in different fields,such as the aerospace,aviation,marine,and general machinery.Compared with a structure composed of single-material,multi-material structures provide the significant advantages in high specific stiffness,high specific strength,light weight,and multi-functional applications.Based on this conception,research on multi-material topology optimization is performed in the present study,and two typical design problems(the discrete lattice structure and the continuum)with important requirements in the practical engineering will be considered.Firstly,to overcome the large computational cost caused by the significant difference between the size of the micro-1 and macrostructure,a multiscale frequency analysis method about the multi-material lattice plate/shell structure based on asymptotic homogenization is established.Based on that,the multiscale concurrent topology optimizations considering the distribution of multi-phase materials is carried out to improve the structural frequency performance and its safety in service.Secondly,based on the inverse motion analysis method,the topology optimization formulation considering the geometry and material nonlinearities is proposed.Through an optimization,the structural functions coupled with the deformed configuration are ensured while improving the structural bearing capacity and realizing the precise control of the deformed geometry.Aiming at the two design problems above,the contents of the present study are as follows:(1)Concurrent multi-scale frequency optimization of multi-material lattice plate/shell structure based on asymptotic homogenization method.Making use of the multiscale nature and deformation characteristics of the lattice plate/shell structure,the micro unit cell is built up by Euler-Bernoulli beam element,and Mindlin-Reissner shell element is used to obtain the macrostructural response.Based on the assumption of the unit-cell deformation mode at the microscale,a multi-scale frequency analysis method of the lattice plate/shell structure based on the asymptotic homogenization analysis theory is established.Through a comparison with the direct numerical solution,it shows that the established multiscale analysis method can accurately and efficiently predict the frequency performance of the lattice plate/shell structure.Based on this,a multiscale concurrent topology optimization is performed to determine the cross-sectional and material selection parameters at the microscale,and the distribution of the lattice material at the macroscale.Two types of design problems,i.e.,maximizing the fundamental frequency with the constraint of the available amount of material,and maximizing the structural stiffness with the frequency constraint are considered.The numerical examples show that improving the complexity of initial ground structural configuration can improve structural frequency performance;The size and position of the point mass will affect the ratio of the macrostructural stiffness to the mass in local,and thereby have significant influences on the optimized results;Increasing the lower limit of the frequency constraint can improve structural frequency performance,but the structural stiffness is decreased.(2)Parallel computation framework based on the nonlinear inverse motion analysis.A precise geometry control for the deformed configuration can be realized through the inverse motion analysis method.However,the material and geometry nonlinearity will lead to an iterative solving process,and large number of load steps are often required,which will significantly reduce the efficiency of structural analysis and optimization.Therefore,a parallel framework for nonlinear analysis and optimization based on inverse motion analysis are established.Some critical issues in parallel computation are solved,which includes the modules division,data construction,data parallel storage,communication lockout,load balance and so on.In the numerical examples,the accuracy in solving the undeformed configuration via inverse motion analysis is verified.Simultaneously,the efficiency of the parallel framework is tested by using different number of processors.The test results show that the established parallel framework can significantly improve the efficiency of structural analysis,and is also of good scalability.(3)Nonlinear topology optimization considering a geometry-load concurrent control based on inverse motion analysis.The load distribution has a significant effect on the failure mode and the safety of a structure.However,for the case in a large deformation,the load distribution is often strongly coupled with its applied geometry.Challenges in realizing a precise control for both the deformed geometry and the load distribution do exist when the optimization based on the conventional forward motion analysis is employed.Therefore,based on the inverse motion analysis,a topology optimization formulation considering the geometryload concurrent control is established.In the numerical examples,optimizations for the 2D gapped ring structure and the 3D contact-like problem are performed to show the advantages of the optimization method based on inverse motion analysis in realizing a concurrent control for deformed geometry and load distribution.By using the proposed formulation based on inverse motion analysis,challenges caused by the coupling in material distribution,deformed geometry and load distribution is well overcome,and the structural load-bearing capacity is improved,simultaneously.(4)Multi-material topology optimization based on inverse motion analysis under the prescribed displacement boundary conditions.Under the prescribed displacement boundary conditions,a topology optimization formulation based on inverse motion analysis is established to maximize the structural secant stiffness considering the geometric and material nonlinearity,and a precise control of the deformed geometry.In the numerical examples,the rationality of the objective defined by the reaction force to maximize the structural secant stiffness is verified.After that,multi-material topology optimizations considering the deformation control of the specified point are carried out,which shows that the proposed optimization formulation can find optimized structural topology and multi-material layout under the prescribed displacement boundary conditions.Moreover,influences of the amplitudes of the prescribed displacement on the optimized results is studied,and it is found that the asymmetry of the optimized results is increased as the increased amplitude of the prescribed displacement. |
