Integrated Design Of Cellular Structures On The Macroscopic And Microscopic Scales

The cellular structure contains a large number of holes,so that it has the advantages of low relative density,high specific strength,good air permeability and so on.It is widely used in aerospace,biomedicine,automobile industry and other fields.The fabrication technology of cellular structure is becoming more and more mature,especially the rapid development of additive manufacturing technology,which overcomes the difficulties in traditional fabrication technology and expands the development space of cellular structure.The design methods of cellular structures emerge one after another,and the design method based on structural topology optimization is the most widely used.In the process of optimal design,by adjusting the material distribution,the distribution of holes in the gradient cellular structure is not uniform,which makes it have unique mechanical properties.Negative Poisson's ratio cellular structure is a hot topic in the study of gradient cellular structure.Generally,uniform negative Poisson's ratio cellular structure can only obtain a single structural deformation.In order to achieve complex structural target deformation,non-uniform negative Poisson's ratio structure needs to be considered.It is well known that cellular structures have complex microstructure,and the optimization results based on Cauchy continuum theory cannot take the microstructure effect into account.Relatively speaking,Cosserat continuum theory has a more perfect system,because it considers rotational degrees of freedom and the corresponding couple stresses,and these are the microsize effects of Cosserat continuum.Therefore,it is necessary to develop structural optimization methods based on Cosserat continuum theory.Firstly,a parameterized level set topology optimization method based on Cosserat elasticity is proposed to solve the problem of minimum compliance of Cosserat continuum.In this method,the effects of material characteristic length l_c and Cosserat shear modulus G_c on the optimized results are studied in detail.The results show that the micro-elastic parameters have a significant effect on the optimized topology structure,and the minimum feature size and geometric complexity of the optimized topology can be implicitly controlled by adjusting the feature length l_c and Cosserat shear modulus G_c.In addition,when the Cosserat shear modulus G_c approaches zero,the optimization results obtained by the parameterized level set method based on Cosserat elastomer will degenerate to those obtained by the parameterized level set method based on Cauchy elasticity.Secondly,a gradient cellular structure design method is proposed by introducing local volume constraints into the subdomain parameterized level set method.In this method,the level set functions can be defined,parameterized and updated independently on each subdomain,and the augmented Lagrange multiplier method is used to solve the equations with local volume constraints.Each subdomain in the method can match well and run parallel,which makes the method faster and more efficient.Finally,a method for the design of cellular structures with adjustable non-uniform negative Poisson's ratio is presented.The method uses penalty function method to establish the optimization problem of the minimum fitness value to solve the optimal Angle distribution.The optimized cellular structure with adjustable non-uniform negative Poisson's ratio can realize high order complex deformation.