Asymptotic Centralized Topology Optimization Design Based On Isogeometric Analysis

Structural topology optimization method is an advanced auxiliary design method involving multidisciplinary knowledge,which is applied in the initial stage of product design to find the optimal release of materials within the design domain under the conditions of objective functions and various constraints.Currently in the process of all kinds of industrial product design,initial design on products is conducted by using the computer has become more and more popular,and the design method of a kind of auxiliary application can reduce the designer’s labor,shorten the design period of products,make the design of the product become more efficient.At the same time,topology optimization can satisfy various design requirements at a lower cost through various simulation experiments.Although topology optimization methods have been widely studied,there are still many problems to be solved.Firstly,the research background and significance of topology optimization method was introduced in this paper,the development situation of topology optimization has carried on the brief narration,the basic principles and development status of several typical topological optimization methods,such as the variable-density method and the level set method,are introduced,and the principle and development of the recently popular isometric analysis methods are also described.On this basis,an asymptotic concentration method based on isogeometric analysis and solid isotropic material and penalty is proposed to solve the structural topological optimization problem.The existing solid isotropic materials and penalty methods are usually combined with the finite element analysis to interpolate the structural model.However,there are some errors in describing the structural model using the interpolation polynomials in the finite element method.In order to eliminate the error of geometric description,this paper uses isogeometric analysis instead of finite element analysis,According to the isoparametic element idea of finite element method,the geometric model is described by spline basis function.Because the spline basis function can accurately describe the geometric structure,the isogeometric analysis can precisely solve the structural geometry,so isogeometric analysis is used instead of commonly used finite element analysis in this article.Secondly,due to solid isotropic material and penalization(SIMP method)is a kind of method based on continuous density,when the method is used for structural topology optimization,there are units with a density value between 0 and 1 in the optimization results,which result in a gray interval at the boundary of the final optimization structure.The existence of gray interval affects the manufacturability of the structure.To solve this problem,an asymptotically concentrated method is proposed in this paper.Using the asymptotic concentration method to set all the cells density values from the middle of the density value to gradually focused on both ends,with the increase of the number of iterations,the cell density values gradually polarize to the solid material density and the empty material density,thereby eliminating the intermediate density.The objective function value oscillation may occur in the optimization process,in this paper,the equilibrium coefficient method is used to prevent the phenomenon of numerical oscillation.Combined with the excellent properties of nonuniform rational B spline(NURBS),the topology optimization model based on NURBS-SIMP is established,and the influence of parameters on optimization results was studied by selecting different parameters.Numerical examples are used to verify the applicability of the proposed method.Examples show that a clear optimization structure can be obtained by using the asymptotic concentration method based on NURBS-SIMP for topology optimization,and there is no gray element represented by intermediate density.As can be seen from the optimization results,there is no numerical oscillation in the optimization process.Finally,the asymptotic centralization method based on NURBS-SIMP is applied to topology optimization of heat dissipation structures.The topology optimization model of heat dissipation structure based on NURBS-SIMP is established,the appropriate objective function is selected,and the sensitivity expression equation is derived.Examples show that the method proposed in this paper is feasible and effective in dealing with topology optimization of heat dissipation structure,and the optimization result of the method proposed in this paper is better than that of NURBS-based SIMP method under the same optimization condition.