Research On Topology Optimization Of Continuum Structure Based On Element Differentiatial Method

Topology optimization for continuum structure is one of the important optimization methods in industrial design,which mechanical topological relationship of the optimized object is constructed by the finite element method with the advantages of mature and simple algorithm.However,the accuracy of mechanical response calculation of finite element method is limited by the mesh scale,the stiffness of optimized structure of topology optimization for continuum structure under the low-scale mesh is poor,while increase the scale of the mesh can be better stiffness of the optimized structure,but because of mesh dependency,the tiny branches of optimized structure grow in quantity,its manufacturability is poor,and does not meet the actual production needs.In order to improve the stiffness of topology optimization for continuum structure and solve the mesh dependency existing in large-scale mesh,element differential method was studied to improve the traditional topology optimization for continuum structure in this paper.The main contents of this paper are as follows:(1)The construction process of mathematical model of topology optimization for continuum structure based on the material interpolation model of SIMP has been research in this paper,optimality criteria based on SIMP method is derived in detail,and the common numerical instability problems and solution of topology optimization is introduced.In order to solve the problem that the optimized structure would appear gray elements due to the average effect when using sensitivity filtering method to eliminate the checkerboard format,a method of scalling the sensitivity of elements gradely is proposed.The numerical example in this paper shows that this method can effectively eliminate the gray elements.(2)Aiming at the low accuracy of mechanical response analysis of topology optimization for continuum structure,the modeling process of element differential method is studied deeply in this paper.The node’s equations of the differential elements are configured,and they are combined according to the contribution of the elements to the whole structural system to form the final analytical equations.The numerical examples of the mechanical response analysis in this paper show that the accuracy of the element differential method is higher than that of finite element method in the same mesh scale,and the advantage is more significant under the smallscale mesh.(3)Element differential method is used to replace finite element method as the theoretical basis of mechanics response analysis for topology optimization for continuum structure,and construct a topological model of the optimized object in the field of mechanics and thhermodynamic coupling.A method of topology optimization for continuum structure based on the element differentiation method is proposed,and the model construction and algorithm design process of the continuum structure of topology optimization based on the element differentiation method is introduced in detail.Numerical examples in this paper show that the topology optimization for continuum structure using this method results in an optimized structure with less compliance,which stiffness is improved and have a more significant improvement under the small-scale mesh.(4)Aiming at the mesh dependency of topology optimization for continuum structure based on element differentiation method,the material interpolation model of this method is improved.Based on the characteristics of the element differentiation method,the sum of products of stress and strain at the internal point of all elements was used to as the objective function,and the numerical solution of the improved material interpolation model is carried out by using the proportional topology optimization method.Numerical examples in this paper show that the improved method can effectively suppress the mesh dependency of topology optimization for continuum structure with the increase of mesh scale.