Robust Topology Optimization Design Of Microstructures Considering Material Uncertainty

The macro mechanical properties of composite material are affected by its microstructure and composition,so it is feasible for us to design the composite which has expected performance by using topology optimization on microstructure.So this article does some work on robust topology optimization about composite with periodic microstructure.Firstly,this article sets up the model of topology optimization based on the Homogenization theory by using modified SIMP approach where taking unit cell density as design variable and material volume fraction as constraint condition,the components of material maximum bulk modulus are taken as objective functions.On this basis,the robust topology optimization of the material microstructures considering the uncertainty of elastic modulus and Poisson's ratio is obtained,and the optimized objective function and sensitivity are obtained by the polynomial chaos expansion method.The mean and standard deviation of random response between the deterministic and the robust results is calculated by Monte Carlo simulation,and the results are compared with the results of the chaotic polynomial expansion method to verify the accuracy.Then,the topology optimization design of material microstructures with minimized negative Poisson ratio is obtained through a relaxed objective function,with the volume fraction of materials and isotropic as constraints.And considering the uncertainty of the elastic modulus of the material,the robust topology optimization design of the negative Poisson ratio obtained by comparing the sensitivity filtering and the density filtration two filtering methods.At last the robust design results of negative Poisson's ratio under different initial configurations are analyzed.